Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader.

Introduction:

This is the second article in a series on small calendar effects that I’ve been researching and trading. In the first, we looked at the holiday effect and ended up with a tradeable system. Now we’re doing the same thing with what’s called the Turn of the Month effect.

If you missed it, you can check out the holiday effect article here:

Systematic Trading with TradeQuantiX

Market Effect Research: Holiday Seasonality

Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader…

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3 months ago · 13 likes · 4 comments · TradeQuantiX

So, what is the Turn of the Month effect?

It’s the observation that stock returns are disproportionately concentrated around the end and/or beginning of each calendar month, rather than evenly distributed throughout the month. It doesn’t happen on one specific day, but across a window of roughly 10 trading days surrounding month end.

A lot of times these small market effects are too modest to trade individually. But if you incorporate them into a portfolio, they become much more interesting.

These effects can be stacked together into a portfolio of intentionally different return streams, where each one adds a small amount of edge.

Together, they compound into something much more meaningful. If you read the holiday effect article, you already get the idea.

In this article we will start by first going through the research phase, where we prove the effect exists thoroughly. During the research phase we try to understand what, when, and where the effect exists. Once we understand the what, when, and where of the effect, the how to trade it comes naturally, and we will build a few systems to capture it.

The goal of this market effect series is the following:

• Teach how to perform and interpret proper market research

• Share how to think about these small edges

• Use creativity to trade these market effects in novel ways

• Show how to combine many small edges into a broader portfolio

Let’s get into it.

Note For Paid Members:

As always, paid members get access to the full code at the end of this article.

You also have access to the Discord community where we can discuss this research and ask questions, and the GitHub repo with all published code.

Reason For The Effect:

Before we look at any data, let’s talk about why the Turn of the Month effect should exist in the first place. If there’s no solid mechanism, it’s more likely the edge is random noise.

There are two plausible reasons that I can think of.

1. Institutional cash flows. Pension and retirement contributions tend to be paid at the end of the month. That cash gets deployed into equities in the first trading days of the new month. These are price insensitive flows that buy equities with no regard to price, systematically, every month. This is likely the dominant explanation and it makes intuitive sense. Billions of dollars in scheduled cash flows hit the market at roughly the same time every month.

2. Portfolio rebalancing and window dressing. Large funds rebalance at month end reporting boundaries. Month end is a natural checkpoint for institutional portfolios, and you get predictable flow patterns as managers buy winners and sell losers to clean up their books and to produce attractive month end holdings snapshots for their investors.

Why does understanding causation matter? Because if this effect ever goes away, we need to assess whether the underlying causes have changed. If we don’t understand why it exists, we can’t distinguish temporary underperformance from a dead effect.

And the causes here are interesting. They’re structural and mechanical. Pension contributions happen regardless of market sentiment. Payroll deposits happen on a schedule. Rebalancing happens at reporting dates. These are flows that happen regardless of price. Pure systematic buying during the same timeframe every month.

It’s important to point out that the excess return may not be predictable to one or two specific days, but rather a range of days near month end. As more traders become aware of the effect it gets front run and the days where the effect shows through can shift around. But the underlying flows that create the window don’t disappear just because people know about them.

Our research in the next section will help us determine the optimal and stable window where this effect is most prevalent. Now let’s look at the data and see what we can understand about the effect.

Research Phase:

Establish The Baseline:

Let’s start by refreshing our memory on the scatter of returns of SPY data across 33 years of history.

This plot shows the return of every single SPY trading day from February 1993 through April 2026. Each gray dot is one trading day. The orange line at +0.04% is the average daily return across 33 years of trading days. So 0.04% is our benchmark to beat for a given day. If we can capture consistent performance above 0.04%, that shows this effect has “alpha”.

You’ll notice the cloud of dots looks pretty uniform. In calm markets, the range is tight, maybe plus or minus 1% to 2%. During crises (2000, 2008, 2020), the band explodes with individual days swinging 5% or more in a single session.

So there is definitely some variability to the 0.04% benchmark, but as long as we find something that consistently produces positive returns meaningfully above 0.04% per day, then that may be something worth trading.

Let’s break down this cloud of data points to see if we can spot any anomalies around month end. The next few sections will do that in numerous different ways.

Measure The Overall Effect (Day By Day):

This first plot will show the distribution of returns on average across 33 years of SPY data near month end. On the x axis, every trading day gets an offset relative to month end.

Day -1 is the last trading day of the month.

Day +1 is the first trading day of the next month.

Note: The offset jumps directly from -1 to +1; there is no Day 0. Each data point averages roughly 399 observations (one per month across 33 years).

You’ll notice one bar absolutely towers over the rest. Day +1, the first trading day of the new month, averages +0.22%. That’s 5.5 times the overall SPY daily average of 0.04%. That’s an interesting start.

But look at the broader shape of the distribution too. The roughly 10 trading days surrounding month end consistently outperform the rest of the month (days -5 to +5).

Days -4 through -2 are solidly above the 0.04% average line. Day -4 is surprisingly strong at +0.15%, which is 3.6 times the average.

Days +2 and +3 are modestly positive too.

And overall, the -5 to +5 days are generally consistently positive. It’s a cluster of elevated returns spanning both sides of the month end boundary.

One exception is the Day -1 returns. Day -1, the very last trading day of the month, is very red. It averages -0.05%. The last day of the month, on average across 33 years, loses money. That’s an interesting observation, and keep it in the back of your mind because we’ll come back to it later when we build systems from this research. We can do some interesting stuff with this knowledge.

So the Turn of the Month window clearly shows up in the full 33 year average result. But is this effect still working in more recent times, or has it been arbitraged away over time?

Has It Decayed Over Time? (Era Analysis):

This next chart breaks the same bar chart data into three eras: 1993 to 2003 (blue), 2004 to 2013 (green), and 2014 to 2026 (orange). For each day offset, you can see how the average return has shifted around across decades.

Day +1 showed to be the strongest when we looked at the whole timeseries together before, but when you break up the data by era the Day +1 returns have degraded over time.

It’s tempting to look at that result and conclude the Turn of the Month effect is dying. But that would be missing the forest for the trees. Day +1 is only one day. There is still an interesting phenomenon going on around the -5 to +5 day window.

In every era, there is a cluster of days surrounding month end that consistently show very above average returns. The specific days that perform the best or worst may shift over time (maybe Day +1 is the strongest in one era and Day -4 in another), but the overall window of elevated returns around the end of the month has remained consistent.

Also, Day -1 is constantly negative across all three eras. That negative last trading day of the month is stubbornly consistent.

Breaking down the returns bar plot by era tells us the effect has persisted constantly over time in a window around month end.

Thus far these plots have looked at daily returns in isolation, but when we trade we experience the cumulative sum of returns across all days we are in the trade. So in the next plot we will visualize how the edge sums up if you bought at -10 days and sold at +10 days.

Where Exactly Does It Happen? (Cumulative Walk):

This is a two panel chart. For each day offset from -10 to +10, it shows a running total of how much the average return at that day’s offset exceeds the overall daily average (+0.04%).

Think of it like an average equity curve of a trade from -10 to +10 days in a month, but the 0.04% average SPY return is subtracted out of the result. So these plots are showing excess return above the SPY average return.

A rising string of days means those days are producing above average returns. A flat string of days means the string of days are producing average returns. A falling string of days means they are experiencing below average returns.

You’ll notice the full sample line (bottom panel) tells a clear story. Starting from the left at Day -10, the cumulative line drifts slightly downward through the days -10 to -5, which are mid-month days.

Around Day -5, it starts climbing. Then Day -1 pulls the curve back down. Then at Day +1, there’s a sharp upward step.

Days +2 and +3 add a bit more rise to the curve, and then the line flattens again as we move into mid-month territory again.

The top panel shows the era by era comparison. The shape of the cumulative step up around month end is present in all three eras (Days -5 to +5).

The effect appears to be more or less consistent across all three time periods. The exact days and pattern that the effect takes changes a little bit, but the upward drift around month end appears to be consistent.

This has direct implications for system design. We can trade this end of month window. Entering a few days before month end and holding through a few days into the next month would capture the cumulative price increase.

So far we’ve been looking at averages, which tell us the typical day. But averages can be misleading if a few extreme outliers are doing all the work. Let’s look at the full distribution of returns to make sure this effect is consistent and not driven by a handful of lucky days.

Distributional Evidence (Is It Real Or Just Outliers?):

The next few sections are where we prove the Turn of the Month effect is a genuine shift in how returns behave and is not caused by a few lucky extreme outlier days.

One important note before we get to the charts. Earlier, we established that the overall daily average SPY return across all 33 years of data is +0.04%. But that number includes the EOM window days themselves, which pulls the average return up.

If we want a true apples to apples comparison, we need to know what non-EOM days return on their own (defined in this section as -5 to +5 Days). When we strip out the EOM window days from the average SPY return, the remaining non-EOM days average just +0.011% per day.

That’s the baseline we’ll use in this section. The -5 to +5 window around month end compared to all other days in the month.

The gap between +0.04% (all days average return) and +0.011% (non-EOM average returns only) already tells you how much the EOM window was pulling the overall average up.

Another thing to point out, I started using the abbreviation EOM to represent the end of month window of +-5 trading days. EOM stands for end of month. And when I discuss it I am talking about the +-5 day window around month end. When I say non-EOM, I am referring to days not in the +-5 day window, i.e. middle of the month days.

The EOM vs Non-EOM Comparison:

The plot below shows two histograms. The top panel shows only non-EOM days return distribution (4,373 days deep in mid-month, i.e. not within +-5 days of month end). The bottom panel shows the EOM window days return distribution (3,986 days).

While it’s probably hard to eyeball the distributions themselves (the next plot will help with that), if you look at the cards in the top left and right of each plot, you’ll notice the difference between the two groups:

• Non-EOM Days produce an average return of +0.011%, a standard deviation of 1.19%, and a VaR 5th percentile of -1.85% (the loss level you’d expect to exceed only 5% of the time).

• The EOM Days produce an average return of +0.072%, a standard deviation of 1.15%, and a VaR 5th percentile of -1.78% (the loss level you’d expect to exceed only 5% of the time).

EOM window days produce 6.7 times the average return of non-EOM days. And they do it at slightly less volatility and slightly less downside risk.

The plot below shows the same two distributions shown in the plot above, just overlaid onto a single chart so you can see the distribution shift directly.

The EOM distribution is shifted to the right relative to the non-EOM baseline. You’ll notice the EOM window days (blue) have fewer losses and more larger gains. The normal distribution fit overtop of the distribution (the dashed lines) shows this shift the most clearly, a clear shift to the right side of returns.

Where Does The Probability Mass Move?

This next chart took me a minute to wrap my brain around. Its a distribution difference chart.

The blue bars show return bins where EOM days have more observations compared to non-EOM days. Red bars show bins where EOM days have fewer observations compared to non-EOM days.

What you want to see is more red on the left side and more blue on the right side.

This would mean there are fewer losses (within the given return bin) on EOM days than non-EOM days, and more positive returns (within the given return bin) on EOM days than non-EOM days.

Still kind of confusing, I get it. Just sit with it for a second, it’s basically just the delta between the two histograms shown in the previous section.

But the plot shows what we want to see. Blue bars dominate the right side of the histogram, while red bars dominate the left side of the histogram. Moderate positive returns are more common on EOM days. And moderate negative returns are less common on EOM days.

This shows the Turn of the Month Effect is a consistent, small rightward distribution shift. It’s a slight upper hand in a game of poker. It won’t always play out, but you know over time the odds are in your favor.

The effect works by providing you slightly more +0.5% to +3% days, and gives slightly fewer -0.5% to -3% days. On average, month after month, that starts to add up.

The Changes In The Right Tail:

This next chart I think is pretty neat, it’s called an exceedance plot. For each percent return threshold on the x axis (from -5% to +5%), each line shows the percentage of days the average return was at or above the threshold on the x axis.

Basically, what is the probability of having a return higher than x%. The higher the line is on the right side of the plot, the higher the probability of larger returns.

The exceedance lines I am showing are the following:

• Non-EOM days (gray)

• Full EOM window (blue)

• Days +1 to +5 only (orange)

• Days -5 to -1 only (green).

You’ll notice in the 0% to 2% x axis range, the gray line (non-EOM returns) is the lowest. This means there is a lesser probability of higher returns than the other lines (which are EOM window returns).

For example, at the +1% return threshold the orange line (Days +1 to +5) sits at 16.1%, while the gray line (non-EOM) sits at 12.9%. That means the orange line has a 16.1% chance of a higher return than 1% and the gray line only has a 12.9% chance of a higher return than 1%. This basically shows that the EOM window has a slightly rightward shifted distribution when compared to the non-EOM window.

See the zoomed in right side of the exceedance plot below:

You’ll notice the orange line (early new month days) sits clearly above the gray line (non-EOM days) across the entire positive range from 0% to about +3%. The gap is approximately 3 percentage points in the +0% to +1.5% zone. Beyond +3%, the lines converge. This shows the effect is about consistent moderately sized winners rather than extreme outliers.

The takeaway from all the evidence thus far is as follows:

• The Turn of the Month effect is real, it operates through a genuine rightward distributional shift rather than large outliers.

• It’s concentrated in the early new month days (+5) but also in the end of previous month days (-5).

• It doesn’t happen every month, but on average over time, it does happen.

• The best performing days move around over time, but within the +-5 day EOM window, there is meaningful outperformance when compared to the overall SPY average return and the non-EOM SPY average return.

• The +-5 day EOM window also has slightly lower volatility and slightly lower risk than the non-EOM window.

• The effect isn’t massive, it’s small but it does exist, so we need to get creative about how we capture it.

We used multiple independent methods in this research section to measure the Turn of the Month Effect.

All the evidence points to the same conclusion, which is the +-5 day EOM window produces higher returns with less volatility and downside risk, and it persists across eras.

The question now is:

”How do we trade it?”

The next few sections will focus on the practical implementation of trading this effect. We’re going to work with three different systems, each one showing a different way to use this research result in practice.

System 1: Pure TOM Baseline:

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Introduction:

In November 2025, I was fully loaded in my mean reversion mini-portfolio. My entire portfolio was heading into a drawdown as the general market was selling off, and I was picking up more exposure as the markets tanked via the mean reversion mini-portfolio.

I was using portfolio margin to support the additional mean reversion buying. Even though the markets were selling off, my long term trend and momentum systems hadn’t begun to reduce exposure yet.

The entire portfolio was down 10% in just a matter of days. I was a little nervous to be completely honest with you.

I knew I had to stick with my systems though. I did the work, I knew the possible outcomes, I knew the portfolio would rebound. It’s just different to see it in a backtest than to actually experience it live with real money.

Eventually, the markets popped back up. The positions held by the mean reversion mini-portfolio quickly caused the entire portfolio to recover in just a few days; as you can see by the v-shaped recovery in the equity curve above.

I’ll admit, with the mean reversion mini-portfolio we have introduced in the past two articles, I was a little aggressive with my sizing at first. I was excited about these systems and I sized them for the upside and not the downside. I make mistakes too.

After this experience, I pulled back the allocation to the mean reversion mini-portfolio by about 25% to mitigate this volatility in the future.

This story was the first scary experience I had with these mean reversion systems. It wasn’t that the systems were poorly developed or that the parameters / indicators needed tweaking; it was simply that I was oversized and I learned that lesson the hard way.

The only thing that kept me in the trades and prevented me from selling the positions early or skipping the next trade was my confidence in these mean reversion systems. I had done the work, I knew they were robust, and I knew they would very likely make money over the medium to long term.

In this article, I want to share with you the in-sample and out-of-sample results for the mean reversion mini-portfolio, as well as the results of a few robustness tests. This is extremely important because the stability of these robustness tests and the out-of-sample results are what give you the confidence to keep trading through the scary times.

I also want to discuss more about what it’s like to manage and trade the mean reversion mini-portfolio. As you can tell from this story, there are times when it sucks. I want to ensure that expectations are set and point out that nothing is ever as easy or glamorous as it seems.

Let’s start first with the in-sample and out-of-sample results.

In Sample / Out of Sample Methodology

When I developed each of these mean reversion systems, the in-sample period was set from 2010 to 2018 and I used the leveraged ETFs during system development. 2010 to 2018 is the period I used for all decision making:

• What indicator to use

• What parameters to use

• What entry/exit logic to use

• What universe to use

• etc.

Everything was designed using only the 2010 to 2018 time window.

I focused on robust system design. I did not spend time optimizing or fiddling with trying to get a very specific time period to produce better results. That’s a dangerous path to overfitting. If a system underperformed from 2014-2015 for example, I left it alone. Any optimizing to make it look better during the specific timeframe would be curve fitting.

Instead, I knew these systems would be combined into the mini-portfolio and that the differences between when each system outperformed or underperformed would complement each other well.

Hence, I was not too concerned with optimizing the performance of one system to be perfect. I instead focused on making each individual system robust, and I knew the performance would follow once they were combined into the mini-portfolio.

For the out-of-sample time period, that was selected to be 2018 to 2026 (which is a pretty long time). Also, pre-2010 was used as out-of-sample on non-leveraged ETFs.

While I tend to heavily prefer more recent out-of-sample time periods rather than out-of-sample time periods from many years ago, it was still data I could leverage to increase my confidence (or hesitation) in these mean reversion systems even more. If pre-2010 had completely fallen apart, that would have probably been a red-flag, even if the post 2018 data results showed promise.

So what this means is I used about 8 years of data for development, but had 8 years forward in time of pure out-of-sample and 7+ years (depending on the ETF) of even more out-of-sample data for the pre-2010 time period. That’s over 15 years of out-of-sample. It’s not too often that you come across a system that can say it has more out-of-sample time than in-sample time.

These days, you’re lucky to find a system online that has ANY out-of-sample validation. Most systems are blindly optimized over a whole time period and then the author sells them like they are the holy grail.

My favorite is when a system underperforms after the release date and when they get called out about it, rather than the author taking accountability, they just say something like:

“Oh, well you need to re-optimize it for the new market environment”

I’ve personally seen this happen 3 or 4 times. It’s nonsense. They know what they did. Systems do fail, it’s unavoidable. But it’s one thing to do your best to develop a system right and it dies vs. blindly optimizing a system on all data and then presenting it with this beautiful backtest just looking to make a few bucks selling a junk system to some poor sucker.

Sorry I am going on a rant here. I wasn’t really planning on taking this article this direction, but here we are. I could delete the last few paragraphs, but I’m not; I feel like you all deserve to hear my raw opinions.

I guess I just want to point out that the things I write about in this newsletter are the actual things I am currently trading or am building to add to my portfolio in the future. If the author doesn’t put their own money behind what they build, then you know their incentives are not aligned with you being successful.

Here are my live results for this mean reversion mini-portfolio since I began trading it in August of 2025:

I put my money where my mouth is.

Combined IS and OOS Performance (Leveraged ETFs):

2010 to 2018 Combined IS Results:

2018 to 2026 Combined OOS Results:

You’ll notice the in-sample and out-of-sample results closely align. You could argue the out-of-sample looks slightly better with a higher rate of return, Calmar ratio, and expectancy.

These are the types of out-of-sample results that are very rare, but I get very excited when I see something like this. 90% of out-of-sample results degrade in some way, and that degradation is usually on the order of 20%-30% degradation to the in-sample results.

That other 10% of out-of-sample results are either just as good as the in-sample or better. This is when you start to think you’re onto something. But, with that said, it’s still possible to be a fluke!

That’s why we will check out some robustness test results in the second half of this article as well.

Unleveraged ETF Extended History (Pre-2010 OOS):

2000-2010 Combined OOS Results:

2010-2026 Combined OOS Results:

The out-of-sample results pre-2010 still look tradable and in-line with the in-sample results. The drawdown during the 2000 tech burst is mildly concerning as that was the largest drawdown throughout the entire history of the backtest. Granted, this was a very aggressive sell-off so it makes sense that there would be poor performance during this time.

It might be tempting to go back and start optimizing to this period to reduce that 2000 tech crash drawdown, but this is pure curve fitting. Why try to make your backtest look better than it actually is? You want to know that the true results actually looked like this. You need to know this information about possible worst case scenarios and not try to hide the bad portions of the results.

When you mute the worst case scenarios with curve fitting, you understate risk and overstate returns. This can be dangerous when it comes to allocating capital to the system as you will be tempted to over allocate to a curve fit system.

Instead of “fixing” the bad drawdown with curve fitting, handle it with position sizing. You know that a 1 in 20 year event could cause a drawdown like this, so either:

1. Accept that you’re going to be in pain a few times during your trading lifetime when these events eventually happen (and they eventually will happen).

2. Allocate to the mean reversion mini-portfolio accordingly. You know an ~11% drawdown on unleveraged ETFs is possible, so a ~30% or more drawdown is also possible on leveraged ETFs. Allocate capital from your overall portfolio to the mean reversion mini-portfolio accordingly. If you only want to experience a 10% drawdown in the mean reversion mini-portfolio, then you can only allocate ~ 33% of your overall portfolio capital to it. Controlling drawdown with portfolio level allocation percentages is a great way to control risk without relying on curve fitting to make the backtest look like the drawdown never happened.

The in-sample and out-of-sample results confirm the mean reversion mini-portfolio likely has merit. But it is also possible this result was complete luck. Hence, we should run some robustness tests on the mean reversion mini-portfolio to ensure it holds up to some scrutiny.

A truly robust system should be able to navigate some noise and turbulence and still be tradable. The markets will only get more noisy with time, so let’s ensure our system can at least withstand a historical backtest with some noise thrown at it.

Transaction cost note: All backtests include commission costs. Commissions are assumed to be the Interactive Brokers commission structure. Slippage is set to zero in the backtests because most entries and exits participate in the closing price auction and thus would see no slippage. Only one system enters intraday with a limit order, which would generally not see slippage unless the opening price gapped below the limit order (in which case there could be slippage as the limit order essentially gets converted to a market order at the open). Based on my 9 months of live trading these systems, zero slippage appears to be a reasonable assumption, at least based on my account size and allocation.

Robustness Testing

This section will cover a few robustness tests on the mean reversion mini-portfolio. It’s worth noting, every test I will show was run at the portfolio level: all four mean reversion systems (Z_Reversion, Vol_Reversion, Vol_Reversion_2, RSI_Reversion) combined together.

You could test the individual systems in isolation, but since these systems were designed to complement each other, scaling in and out of positions, it makes more sense to test from the perspective of the overall mini-portfolio.

How To Interpret These Robustness Results:

Generally speaking, I like to see robustness test results come in within 70% to 80% of the nominal system results. That’s my soft threshold. I’ve tested 100s of systems and have run robustness tests on pretty much all of them. Generally, the 70% to 80% threshold is reasonable.

Obviously the closer the robustness test result to the baseline system result the better, but there are plenty of caveats and edge cases. To keep it simple, the easiest way to determine if the robustness test is a pass would be to ask yourself:

“If the worst case scenario happened, or if the 5th percentile worst result of these robustness tests turned out to be the true performance of the system, would you still trade it? Would you still allocate your hard earned capital to it?”

Meaning, if your live performance was worse than 95% of results from the robustness tests, would you still be willing to trade it in your portfolio? If yes, then it’s a pass. If no, then it’s likely a fail.

I was very careful when I designed these systems to design them with robustness in mind. I wasn’t optimizing each system to maximize returns or to minimize drawdowns. I will always accept less returns or more drawdown for more overall system robustness. Rather, I was ensuring the parameters and rules I chose were widely stable and it didn’t really matter what I chose, it all more or less worked.

Remember, a curve fit backtest overstates returns and understates drawdowns, which leads to over-allocation. You end up putting more capital into something that returns less than you think and loses more than you think. Robustness testing helps point this out and make us aware of this possibility.

What I want is for the backtest to reflect the actual stability of the system so I can allocate properly. Robustness tests help answer the question:

“Is the backtest hyperinflating results, or is it actually a good representation of the median/likely outcome?”

If the robustness tests show the baseline system result is close to the median, you can probably use it as a good basis for capital allocation. If the robustness tests show the baseline system is in the upper end of the results, then it’s likely the performance is overstated. In this case, we either need to throw away the system, or allocate to it accordingly now that we know live performance would be expected to be lower than the backtest.

Robustness Template Refresher:

If you read the robustness testing article (see link below), you’ll remember the robustness testing Excel template.

Systematic Trading with TradeQuantiX

Robustness Testing Methods: A Complete Guide for Systematic Traders

Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader…

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2 months ago · 16 likes · 2 comments · TradeQuantiX

This template contains inputs for five robustness tests for a system or portfolio (excel robustness template is stored in the GitHub). If you haven’t read that article yet, consider reading it first. It’ll make the rest of this section make a lot more sense.

As a quick refresher: the robustness testing excel template has tabs for each robustness test. You put the raw output from the robustness test in the input tabs, then the excel sheet plots histograms showing your baseline systems results in relation to other results in the robustness test. It also has a table showing the percentile rank of the baseline system in relation to all results (i.e. is the baseline system in the 50th percentile, 5th percentile, 95th percentile etc. of results).

I ran the combined mean reversion mini-portfolio through three of the five robustness tests in this template. I focused on the parameter sensitivity, trade skip, and noisy data robustness tests. These three I felt where the most pertinent to the mean reversion mini-portfolio.

You can download this template from the GitHub and run these tests on your own systems. I’ll also have the results from these robustness tests in the GitHub as well.

In the rest of this section, we will walk through the results of each of the three tests and my interpretation.

Let’s first start with the parameter sensitivity test, which is one of my favorites.

Parameter Sensitivity (All Systems Varied Simultaneously):

This test works by varying each of the four systems’ key entry and exit parameters at the same time by approximately +-25%. Then, comparing the baseline combined mini-portfolio performance to other results across the +-25% parameter space. Each of the four systems had its parameters varied at the same time, it was not a one at a time system by system variation.

If the combined mini-portfolio only works with one precise set of parameters across all four systems, it’s overfit. A robust mini-portfolio should deliver acceptable performance across a very wide range of parameter combinations.

It’s worth noting, I do not have enough computer power to do an exhaustive +-25% parameter variation for all parameters within each of the four mean reversion systems. That’s billions of combinations, if not more.

Instead what I did was focus on the entry and exit rules specifically and run a -25% parameter, a nominal parameter, and a +25% parameter for each system. But even that was millions of combinations.

So I set up the +-25% sensitivity as I just laid out but had it randomly choose what parameters were varied on each run.

So it was not exhaustive, but rather a probabilistic run that randomly varied parameters +-25% (or kept the nominal parameter) across all four systems. I ran this 1,000 times and input the results to the robustness testing excel template.

While maybe not a fully exhaustive test (I don’t think an exhaustive test is even possible at the mini-portfolio level), I figured if there were any issues, they would start to present themselves after about 1,000 runs.

You are more than welcome to do more runs (maybe 10,000) but I would presume the result would be very similar to the 1,000 run result. I think you’ll notice I’m a big practitioner of the 80/20 rule and I like to do things in a reasonable way. I am not the person to wait and manage a robustness test for a week to get 10,000+ results.

I want to get what I think is the minimum viable amount of data which would present concerns (if they exist) and only do more testing if I feel it’s warranted after the 1,000 tests. Analysis paralysis is the best way to always be developing but never actually trading or making any money.

At a certain point you have to consider it good enough and pull the trigger on it and see what happens live. That’s just how I do it. And I would say the last 9 months of my live results are more meaningful than what these robustness tests could show (but I’ll show them anyway!).

With all that said, just to appease the skeptics, I ran the 1,000 random parameter sensitivity tests again in a secondary robustness excel sheet. I then looked at the results and compared to the first set of 1,000 random parameter sensitivity tests.

If my claims are true (that 1,000 tests gets you to around a converged solution), I would expect to see similar results between the two 1,000 test datasets. And that’s exactly what I saw, both datasets showing very similar results. Which means the 1,000 parameter sensitivity tests was enough to actually show meaningful results and make decisions from.

Combined Mini-Portfolio Parameter Sensitivity Table (Dataset 1):

Combined Mini-Portfolio Parameter Sensitivity Table (Dataset 2):

You’ll notice the Baseline Percentile row (bottom row) are very similar between the two datasets. This shows that the baseline system performance sits in approximately the same percentile in relation to all other parameter combinations within a +-25% space.

Since both datasets of 1,000 random parameter combinations result in approximately the same percentile, I am arguing that 1,000 tests is more or less converged and suitable to learn something from.

Let’s pick apart the results for a few of the metrics. Starting first with ROR, the system is in the 62nd to 65th percentile and about 3.5% to 4.5% above the average and median ROR result across the parameter sensitivity studies.

I generally tend to expect the 50th percentile or median result during live trading. The baseline system result is 13% ROR while the median result is 12.5% ROR.

So, the system results may be slightly overstated on the higher end, but only by about 0.5% ROR. I am more than comfortable with this result as the median ROR result is nearly identical to the baseline system ROR result.

Next let’s look at max drawdown. Keep in mind max drawdown will inherently be a less stable metric as it is only one data point over the entire backtest history. The baseline system is in the 80th percentile, which is a little better than ideal. The median max drawdown is about -14% while the baseline system max drawdown sits at -12.2%.

So, there is a 1.8% difference in max drawdown between the baseline system and what is more reasonable to expect (the median value). I can live with that. While the percentile may be saying the system is in the “overfit” range of results, the scatter of max drawdown outcomes is actually relatively tight, between -8% and -20%.

That may seem wide, but for how noisy the max drawdown data point is, that’s a tight scatter. I could even live with the worst case of that range. I am comfortable with this result given I can live with the worst case result and that there is only a 1.8% delta between baseline and median max drawdown results.

Let’s look at one more, Sharpe. The baseline system Sharpe sits somewhere in the 73rd to 78th percentile of parameter sensitivity results. Again, while high (we like to see the baseline system near the 50th percentile of results), take it in context with the scatter. The median Sharpe result was 0.99 while the baseline system Sharpe is 1.02, a 0.03 Sharpe difference. A couple of different trades in a backtest could make a larger difference in Sharpe than that.

The scatter of Sharpe results ranges from 0.77 to 1.17, the baseline system sits right near the middle at 1.02. So while the baseline system’s 73rd to 78th percentile result seems scary, really it’s only slightly overstated compared to the expected median Sharpe of around 0.99.

I think what we are learning here is we need to look at this table holistically and not just focus on the percentile results. The percentile results are a good way to do a fast spot check, but you need to contextualize it with the rest of the data to make quality judgements about a system.

A result that would scare me would be a percentile result of 70% or more for most metrics and a large delta between baseline and median/average results, and a large scatter between min and average.

As an example, if baseline Sharpe was 1.02 but the percentile was 75%, the median Sharpe was 0.85, and the min Sharpe was 0.5; that would signify there is a lot of variability in the parameter space. This would tell me the backtest results I am seeing are severely overstated and I need to be careful and allocate accordingly (or throw the system away).

Luckily this is not what we are seeing. While we see higher percentiles for a few metrics, the scatter is tight and the delta between baseline and median results is small, so I am much less concerned about a higher percentile result. These robustness test results are signifying we should expect just a few percentage points of degradation between baseline and median results for most metrics, which is normal and I am more than comfortable with.

Now let’s visualize this data in a slightly different way. Tables are nice but plots sometimes tell the story in a way that’s easier to visually understand.

Combined Mini-Portfolio Parameter Sensitivity Histograms:

What you want to see is the baseline system histogram bin (in red) sitting in the bulk of the distribution. While most of these distributions are not normal, there tends to be a region of high density in results, and that’s where you want to see your baseline system residing.

You don’t want to see your system in the right tail of the distribution (or the tail with better results). In this case, the mean reversion mini-portfolio is within the bulk of these distributions.

Some metrics have the mean reversion mini-portfolio sitting on the better side of the bulk distribution, but as discussed earlier, the difference between the baseline performance and the median performance is very small for the most part.

Overall, this mean reversion mini-portfolio is nowhere near an upper edge of performance and is showing to have similar performance with the bulk of the other parameter sets within the +-25% universe.

Another interesting way to visualize results is to just flip through the equity curves of the results. Tables and histograms can explain the deltas and expected stability, but the equity curve is what gets lived from day to day. If you can look at the equity curves and live with the median or even the worst case result, that’s a pretty good sign.

Below I show the worst and best result from the parameter sensitivity tests (dataset 2 specifically) based on Sharpe.

Worst Result (Based on Sharpe):

Best Result (Based on Sharpe):

The best case looks great, but we shouldn’t expect it. The worst case result is a little more choppy, but is still more than tradable (at least for me). Especially in an overall portfolio context, I’d be more than happy to have the performance of the worst result in my portfolio. Anything better than this worst case is just extra goodness.

So, overall when looking at the parameter sensitivity tests holistically, I am feeling good about these results. If I didn’t, I wouldn’t be trading the systems. Now let’s move on to the next robustness test, a trade skip analysis.

Monte Carlo: Trade Skip Analysis (All Systems Simultaneously):

In this robustness test, we randomly skip a percentage of trades across all four systems within the mini-portfolio at the same time and re-run the backtest across 1000 simulations. Each simulation will result in a different outcome because different trades were skipped. This produces a distribution of different outcomes.

The purpose of this test is to ensure the results are not dependent on a handful of lucky trades. We want to randomly skip trades and ensure the results are still tradable. If we start skipping trades and the equity curve completely falls apart, that would be a fail of this test. That would show that there is a small percentage of trades that matter and the rest is noise. We don’t want that.

Instead, we want stability over time, meaning every trade (or at least most trades) is meaningful, and when all trades are meaningful, no single trade is meaningful at the same time; so if a handful of trades get skipped, the system still works just fine.

To a smaller degree, this test also ensures that if trades are missed due to vacation travel, broker outages, mistakes, automation bugs, internet outages, etc. the system still holds up fine. Ideally no trades will ever be missed, but on rare occasions it will happen. This test also helps expose the possible outcomes of such instances. The reason for the test though is still the same, if the portfolio’s returns are concentrated in a handful of critical trades, missing them is catastrophic.

How I did this test for the mean reversion mini-portfolio was I added a bunch of binary random switches to the entry rules. If the random switch says “1” then execute the trade like normal, if it says “0” skip that trade. In this test, about 33.3% of the trades were skipped.

Because of the dynamics of this system and how it trades a specific universe of ETFs, if we start skipping trades the exposure of the mini-portfolio will decrease. That’s okay, we just won’t put as much weight into the metrics that are impacted by exposure (ROR, max drawdown, volatility etc.).

Instead, we can focus on metrics like expectancy, percent win, average win, average loss, profit factor etc. These metrics are not impacted by differences in exposure and will highlight if the system is stable when trades are randomly rejected.

For a system like a trend following system that trades a large universe you would interpret and use this test slightly differently. Since the universe is large, when a trade is skipped you can replace it with another trade that also meets the entry criteria. This keeps exposure consistent between baseline results and trade skip results.

So metrics like ROR, max drawdown, volatility etc. are comparable. But since this mean reversion mini-portfolio trades a small fixed basket of ETFs, there isn’t any trade replacement going on, so we can only focus on results not impacted by exposure.

The table below shows the baseline (actual) result compared to the min result, median result, max result, and spread (max - min) for the trade skip robustness test runs. Again, focus on the metrics: expectancy, percent win, average win, average loss, and profit factor.

First, let’s discuss percent wins, average win, and average loss. These three metrics in the baseline (actual) system result were 72.3%, 5.2%, and 5.3% respectively.

When we compare these metrics to the median result of the trade skip runs, we see percent wins go from 72.3% to 72.8% (slight increase), average win go from 5.2% to 5.3% (slight increase), and average loss go from 5.3% to 5.1% (slight decrease). This means that across the board the median result of the trade skip Monte Carlo is better than the baseline system.

This same story holds for expectancy and profit factor. Expectancy in the baseline system goes from 2.28% to 2.48% when compared to the median result; and profit factor goes from 2.49 to 2.70 when compared to the median result. Again, the median result is better than the baseline result.

This tells me that more bad trades are being skipped than good trades; which kind of makes sense given the negative skew of mean reversion. Mean reversion tends to have very ugly left tails and short but dense right tails. The trade skip is causing small winners to be skipped, but there are a ton of small winners, so skipping some of these doesn’t affect the result too much (which is exactly what we want to see).

But when a losing trade is skipped, there are higher odds it was a large loser, so skipping it makes a bigger difference to the outcome of the strategy. This is what we want to see. This result tells us that skipping trades does not have a negative impact on the stability of the system. The underlying system metrics hold together and there are not a handful of outliers inflating the results of the system.

It’s also worth pointing out, the difference between the min and max result from this trade skip test look great as well. The scatter between min and max for expectancy, percent win, average win, average loss, and profit factor is super tight, which means the system is super stable and all of the Monte Carlo runs resulted in a very similar outcome. I’d even be okay realizing the min result across the board in live trading, which is always a strong sign of robustness.

Monte Carlo: Noisy Data Analysis (All Systems Simultaneously):

I really like this next test because it’s the only test that changes the data itself, rather than the systems response to it. To perform this study, we add random noise to the price data feeding the mean reversion mini-portfolio. I created three different datasets with different levels of noise: low, medium, and high.

It is worth pointing out that noise is defined and can be implemented in different ways. These three methods are how I added noise to the data (I used all three methods at the same time with varying severity):

1. Candle shift: Shifts entire OHLC candles up or down by a random delta. Preserves the candle range (High minus Low stays the same).

2. OHLC noise: Adds independent random noise to individual OHLC fields. Reshuffles High/Low if OHLC constraints are violated.

3. Random walk: Blends the original price series with a synthetic random walk to create gradual drift. Preserves candle structure by applying the same delta to all OHLC fields.

If the combined portfolio only works on the exact historical price series it was tested on, the signals may be fitting to specific price paths and random patterns that will never repeat, rather than capturing a real structural edge. The system should be able to hold up to some noisy data and not self destruct the second the data changes a little, because the future will be slightly different than the past.

One thing I learned while running this test is that depending on how you implement the noisy data, your results can actually get better, which is counter intuitive.

Mean reversion systems enter on pullbacks, so if noise is added that shifts the price downward and the system enters, the next candle may not necessarily have any noise added, so it makes the rebound even more aggressive, increasing the returns of the system.

So, the most stringent way to add noise to this system would be to have very small candle shifts up and down and very small changes to OHLC data. This is because artificially lower closes and lows allow the system to get better fills, and artificially higher closes and highs allow the system to get better exits. Instead, focusing on the random walk implementation is where most of the noise was added.

A very small amount of candle shift and OHLC noise was added to the data, but varying severities of random walk was added. How the random walk is applied is by randomly generating a random walk price series with the same volatility as the underlying symbol, then a weighted average between the two series is applied; where the weighted average blend percentage can be played with to preserve more or less of the original price series.

See below for TQQQ examples of varying levels of noise from low, to medium, to high noise.

Low Noisy Data - TQQQ Example:

Medium Noisy Data - TQQQ Example:

High Noisy Data - TQQQ Example:

Real Data - TQQQ Example:

Here is a comparison that is more zoomed out of how the price series can differ due to the random walk weighted mix into the price series:

Zoomed Out With Random Walk - TQQQ Example:

Zoomed Out Real Data - TQQQ Example:

I ran three levels of noise: low, medium, and high. For each noise level I created 5 different universes of noise. This means noise was randomly added to 5 sets of data.

So, each data set had noise added to different candles, and different random walk sequences were created and mixed into the underlying price series. This allows us to test 5 different versions of the price series per noise level.

The configurations I ran for each noise level are as follows:

• Low Noise:

  

• Medium Noise:

  

• High Noise:

  

Now let’s get into the random data results table. It’s worth pointing out, I did run this test on the leveraged ETFs all the way back to 2010, but I kept running into issues on low priced tickers. Some of the tickers had very low prices on the back adjusted data in the early years, so adding the noise was causing some goofy results where a systems equity curve would shoot up massively.

I’ll need to look into this more and fix the noisy data code to account for this issue. But for now, I am just showing the 2018-2026 noisy data results to avoid some of the weird price noise anomalies that were happening in some of the high noise datasets.

Random Data Results:

The baseline data results are the bottom row. Each noise level and sub-run within each noise level are shown on the rows above the baseline data results.

We want to see the system perform similarly on noisy data as real data. Some degradation may be expected, but we definitely don’t want to see the system completely fall apart.

A good sign that the system can capture an underlying phenomenon and is not overfit to a specific price path is if the system can still make money when the price history is slightly different.

Adding noise doesn’t remove the phenomenon from the data that the system harvests, it just disguises it in a different way. If the system can still pluck it out of the data and trade it with similar profitability as the baseline data, that’s a great sign of robustness.

These results show just that. The noisy data results are on par with the baseline data results. There is some degradation, the max drawdown, volatility, and Sharpe generally get a little worse with the noisier data; but that is as expected. Even the results of the highest noise data is still more than tradable.

Below I show some example equity curves. I show first the baseline system from 2018-2026. Then I show one example equity curve from one of the noisy datasets (low, medium, and high). This will give you a feel for what the noise does to the results.

Baseline Results - Equity Curve:

Low Noise Run 4 - Equity Curve:

Medium Noise Run 2 - Equity Curve:

High Noise Run 4 - Equity Curve:

I would trade every equity curve shown here (and every other noisy equity curve not shown here as well).

Again, a great sign of robustness is when the underlying data is noisy and the system can still pick up on the underlying effect and trade it profitably.

Live vs Backtest Comparison:

As you can see from the previous section, the results of these robustness tests, along with the in-sample and out-of-sample results, gave me the confidence to pull the trigger and go live with this mean reversion mini-portfolio.

Also, just knowing how these systems were designed and how they intentionally had robustness and diversification built into the mini-portfolio gave me the further boost of confidence to go live (remember the whole thing about diversification across entry/exit timing, entry/exit price, indicator readings, instruments traded etc. that we discussed in depth in part 2).

I’ll be honest. I’m not a natural mean reversion guy. I’m naturally a longer term trend and momentum trader. I like the positive skew of trend and momentum, and the slower pace. Mean reversion is the opposite in all ways.

But the testing showed these were the most promising mean reversion systems I’d ever developed. The methodology this mini-portfolio follows is also one of the most robust methods I’ve ever developed. I had no excuse, so I pulled the trigger.

Sometimes trading these mean reversion systems still makes me nervous. Again, it’s just the nature of how these systems go against my natural trader mindset. But other times trading these systems makes me excited, because they capture the bounce that my other systems miss out on. And as you can tell from the story at the beginning of the article, sometimes I get too excited, which then leads to nervousness when negative outcomes happen.

Hence, why I had to size down my positions. Reducing my position size / allocation helped a lot. I find I am much less nervous now when the mean reversion mini-portfolio loads up on positions. So take the lesson from me and be on the safe side and allocate a little less than you think you should, rather than a little bit more.

Anyway, I know I have already shown these results, but here they are again. The live out-of-sample real money results since August of 2025 with my mean reversion mini-portfolio.

Compare these results to the backtested results for the same time period:

It’s worth pointing out a couple things. During live trading, I started on unleveraged ETFs for the first few trades as a proof of concept. I wanted to ensure everything was working before going to the full risk allocation on leveraged ETFs. That’s why the first few trades return a little less than the backtest.

Also, remember I sized down my allocation last December after the late November drawdown I experienced where my overallocation to the mean reversion mini-portfolio made me too nervous for comfort.

I also added one other mean reversion system partway through the time period on top of the four shared here. It’s nothing special, just different indicators and more diversification across price, time, instrument etc.

The only reason I didn’t share it here is because the idea came from a trading friend of mine and I didn’t want to share someone else’s ideas. But again, it’s nothing special, just more variation on top of the mean reversion methodology shared in this article series.

With all that said, the backtested and live performance aligns very well. It’s normal to have a little bit of variation. Given all the subtle tweaks I made over time to better nest this mean reversion mini-portfolio into my overall portfolio, I’d say my backtest assumptions hold up pretty well to a live trading environment.

Execution Reality and Live Trading:

Order Management Workflow:

Let me walk you through the daily routine I follow to trade this mean reversion mini-portfolio because I bet some people imagine this is way more time consuming than it actually is.

It only takes a couple of minutes to trade every day. I use RealTest (outputs orders) with Order Clerk (reconciles and places orders with broker). The two tools work together to make the process of trading the mean reversion mini-portfolio (along with the rest of my portfolio) very straight forward.

I’m not sitting there manually calculating position sizes and entry levels and placing 30 staggered entry orders every day because these mean reversion systems scale into positions. All I do is click a few buttons. The system generates the orders, I spot check them, and I click submit.

On a busy day, all four mean reversion systems are sending orders for almost all ETF assets traded. Anywhere from 20 to 40 orders all getting placed in one day. On a quiet day, it’s maybe 5 to 10 orders for just a couple of different ETFs. But both scenarios are the same amount of work for me.

Today was a moderately high order count day:

The mean reversion mini-portfolio runs in the same Interactive Brokers account as my other systems. Long term trend and momentum systems hold the bulk of my exposure. The mean reversion mini-portfolio fills in the exposure cracks and takes up the rest of my open capital.

When mean reversion orders get filled, I sometimes go into margin. I’ll hold that margin for a few days until the price reverts, then exit the mean reversion position and go back to nominal portfolio exposure.

The crossing orders problem:

So, there’s one small issue that arises from time to time with the mean reversion mini-portfolio that is slightly annoying. It doesn’t happen too often, I only just recently noticed it.

It has to do with placing so many orders at staggered prices on the same instrument. The issue is that sometimes one system wants to buy a position and another wants to sell a position and you have an order crossing and Interactive Brokers cancels one of the orders.

Basically, if the price closed in the right spot, one system would want to sell and another would want to buy and, from the perspective of the broker, you would effectively be selling the position to yourself. The broker doesn’t like that, so they cancel one of the orders.

This really doesn’t happen that often, but it can be exacerbated if you trade other systems on the same ETFs as the mean reversion mini-portfolio. I have a couple seasonality trades on bonds I’ve implemented using the same TMF ETF as the mean reversion mini-portfolio. I’ve noticed when the seasonality system kicks on, I sometimes get trade rejections on the TMF ETF. It’s annoying, but I deal with it because it hasn’t been anywhere close to detrimental enough to meaningfully harm the system.

It goes back to the whole diversification across many assets, entry/exit levels, entry/exit times etc. If the order of one sub-entry from one system on one asset within the mean reversion mini-portfolio gets canceled, it really doesn’t do much at the mini-portfolio level. That’s the mindset I take with this rare situation.

With that said, if there is something I can do about it I will. If I am working from home that day or if I get home from work early, I’ll check in on the trade and see if any of the conflicting orders are unlikely to get filled. If so, I’ll cancel the side that is more unlikely to be filled and re-place the order for the side of the trade that is more likely to get filled. That 5 minutes of work every once in a while solves the issue.

And even so, most of the time when this order crossing issue happens, neither order would have been filled anyway, so many times it doesn’t even matter. If I can’t be home near the market close to modify the order, I just let the cancellation be, and move on.

This is an 80/20 solution. It’s not perfect, but live results still track close enough to backtests. This is the interim solution until I build/find a better solution. I accept the imperfection for now.

What It’s Actually Like To Trade:

Hopefully the introduction to this article provided a good framing for the bad side of trading the mean reversion mini-portfolio.

It’s important to share the good and the bad.

Because, as I learned, you need to size for the bad if you want to experience the good over the long term. So, let me walk you through what live trading this mean reversion mini-portfolio actually feels like.

The equity curve on a weekly or monthly chart looks smooth. Up and to the right in what seems like a straight line.

You look at it and think:

“I can handle this.”

But the day to day feel is a different story.

I got burned by this exact thing. The high timeframe equity curve looked so smooth that, as I mentioned, I oversized my allocation to the mean reversion mini-portfolio. I was excited to trade it. It was new, stable, and very uncorrelated to the rest of my systems.

I overlooked the shorter timeframe volatility, the day to day spikes. These are what we actually feel as traders. We don’t feel the zoomed out 10 year backtest performance, we feel the day to day and week to week performance, which is a lot more choppy.

Mean reversion inherently means you’re buying into drawdowns. You’re adding to positions when the market is dropping. Negative skew is baked into the system dynamics.

The systems buy when most people are most fearful and when most traders emotional states say:

“Stop! no more!”

But the mean reversion systems say:

“Keep buying, continue the scale-in with signal strength as designed”.

The hardest psychological moments are on Fridays. It feels like every time the markets sell off it’s on a Friday and I end up fully loaded on mean reversion positions, holding that risk through the weekend. These uncomfortable moments are why you get paid for trading this system.

Holding the risk nobody else wants to.

Providing liquidity to people trying to de-risk going into the weekend.

Holding that risk over the long term should pay off. But from time to time you’ll get whacked for it. You’re stuck in a scary situation for two days and you can’t do anything about it. That’s just part of the game.

The experience I discussed at the start of this article was uncomfortable enough that I went back in and lowered my allocation after. The lesson was to zoom in and consider the day to day volatility and consider worst case impacts.

It’s very easy to get into an uncomfortable position when you allocate too much, especially with leveraged ETF products. I got greedy and sized for the upside instead of the downside.

I know I always preach to size for the worst case scenario, but even I still make mistakes. Mistakes are how I learn. I always learn everything the hard way. In fact, I prefer learning the hard way. It makes me better and really solidifies the learning experience so I don’t do it again.

I’ve come to have peace with losing money if it means I got a good learning experience from it. It honestly happens to me all the time. It’s just me paying my market tuition.

What I Would Do Differently:

Size More Conservatively From the Start

I already mentioned this, but it’s worth repeating again because it’s the single biggest lesson I learned.

Size smaller than you think.

The reality is you live day to day. You don’t experience the monthly or weekly equity curve. You experience the daily swings. Shorter term fluctuations and volatility are what you actually feel. Don’t let the smooth high timeframe equity curve trick you into oversizing.

My thought process would be to size for a drawdown that’s double what the backtest shows. If the backtest says 15% max drawdown, allocate as if you’ll see 30%. Because when you’re living through it, it feels twice as bad as the number on the screen.

As an example, say you’re allocating a percentage of your overall portfolio to this mean reversion mini-portfolio. Maybe you don’t want to see more than a 10% drawdown from this mean reversion mini-portfolio when viewing from the overall portfolio context. If the mean reversion mini-portfolio has a 15% max drawdown, that means the max allocation would be 10/15 = 66% allocation.

But let’s be safe and assume the real worst case drawdown of the mean reversion mini-portfolio is 2x what the backtest says, i.e. 30%. That means portfolio level allocation to the mean reversion mini-portfolio would actually be 10/30 = 33% allocation. This is a simple yet effective way to think about allocation to the mean reversion mini-portfolio, or any system really.

Building Confidence and Scaling Up

It’s been about two-thirds of a year since I launched the mean reversion mini-portfolio. At this point I am starting to feel real confidence in the systems.

But that confidence took about nine months of live trading to build.

It didn’t happen after the first week.

It didn’t happen after the first good month.

It happened gradually, as the live equity curve kept matching what the backtest said it should do.

Starting a new system or set of systems is scary. No matter what the out-of-sample or robustness tests show, there is always an unknown. We never know what’s around the corner. So if you’re like me and are adverse to mean reversion systems, start smaller than you think.

Not only size for 2x the worst case drawdown, but add even more padding on top of that, at least until you start to get confidence with it.

Maybe even start with one or two of the systems instead of all four. Then add the others as you gain experience, understand how it works, get a grip on what the day to day feels like, and get the live trading operational side of things down.

As confidence builds, add more systems or scale up size to the 2x max drawdown allocation size. No need to go all in at once or go full size all at once. You can ease into it.

Don’t do what I did and go crazy with sizing just to be scared to death because I’m holding more risk than I ever have before.

Conclusion:

Part 1 introduced the four systems and the entry and exit logic. Part 2 showed how they combine into a portfolio with ranking, correlations, and return analysis. Part 3 proved the robustness of the method and the truths of trading it live. Hopefully this provides a good framework and understanding of what it takes to go from backtesting to live trading and what to expect along the way.

The portfolio effect is the only holy grail. You’ll notice not a single one of these individual systems is amazing. That’s by design. I would rather have four mediocre but robust systems that combine into something strong than one perfect looking system that fails because it was curve fit.

IS/OOS validation across multiple windows (2010 to 2018 in-sample, 2018 to 2025 forward out-of-sample, pre-2010 backward out-of-sample on unleveraged ETFs, 2025 to today live results) confirms the edge is stable in time.

Robustness testing confirms the system is in a stable parameter region and the system can withstand noisy data because the markets will only get more noisy with time. Also, live results since August 2025 track backtest expectations, which confirms the most important aspect about a system, that it works with real money (at least thus far!).

The biggest lesson learned was to size more conservatively than you think. Allocate for 2x the drawdown you expect. Don’t let the smooth equity curve fool you. The drawdowns tend to be short lived but they can be very steep. And start small and build up slowly as confidence grows.

Disclaimer

The information and services provided by the Systematic Trading with TradeQuantiX newsletter are for educational and informational purposes only and do not constitute financial advice, investment recommendations, or guarantees of trading performance. Any information provided is general in nature and does not take into account your individual circumstances. Trading involves significant risks, including the potential for substantial financial losses, and past performance is not indicative of future results. The information is provided ‘as is’ without warranty of accuracy or completeness. All decisions and actions based on the information provided are the sole responsibility of the reader. You should seek independent professional advice before trading. The Systematic Trading with TradeQuantiX newsletter is not liable for any losses, damages, or outcomes resulting from the use of this information or our services.

Robustness Test Excel Sheets:

These excel sheets are also in the GitHub, along with the noisy datasets, and the systems used in the robustness tests.

Read more

Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader.

I recently launched a portfolio tracking website (updated daily) that tracks my systematic trading portfolio performance, along with many supporting metrics. You can check in on my personal systematic trading portfolio performance anytime here: TQX Portfolio Tracker

Introduction:

In Part 1, we covered four independent mean reversion systems, each measuring oversold conditions in a completely different way.

Z_Reversion: uses z scores.

Vol_Reversion: uses volatility bands.

Vol_Reversion_2: enters and exits at different times and with different methods than Vol_Reversion.

RSI_Reversion: utilizes pre-calculated RSI entry levels and enters with a different timing mechanism than the other three systems.

Each system scales into positions across three sub-entries, and all four systems trade a multi-asset ETF universe spanning equities, bonds, gold, and bitcoin. This takes an “All Weather Portfolio” like approach to the trading universe.

If you haven’t read Part 1 yet, see the link below.

So, what happens when you stop evaluating systems in isolation and start combining them into mini-portfolios?

As I hinted at in the part 1 article, we will be combining these four systems into a mean reversion mini-portfolio.

Why use the term “mini-portfolio”? (warning, I use the term “mini-portfolio” a lot in the next few paragraphs)

Well, because I like to think of my own systematic trading portfolio as a portfolio of many smaller portfolios.

• Trend mini-portfolio

• Momentum mini-portfolio

• Mean reversion mini-portfolio

• Hedging mini-portfolio

• etc.

The portfolio effect is super powerful when it comes to creating superior risk adjusted returns. One strategy may have mediocre performance on its own, but combined into a portfolio of many other strategies, that portfolio of mediocre strategies can look fantastic.

I like to look at mini-portfolios of similar methodologies first. I’ll get all the allocations and volatilities properly adjusted relative to each other. Then I’ll combine the mini-portfolio into the overall systematic trading portfolio. This just helps me build up my portfolio one block at a time. This is why I use the term “mini-portfolio”.

Take any one of these four systems and run it standalone. The stats look okay, nothing special. That’s fine. Because the real story isn’t the individual systems. The real story is what happens when you put them together to make the mean reversion mini-portfolio.

This part 2 article covers the mini-portfolio construction of these four mean reversion systems. I’ll show how four similar systems combined together beat one. Even though these are all mean reversion systems on a similar universe, because they all enter and exit positions using slightly different measurements and and methods, you can still get some powerful diversification benefit.

In this article we will cover:

• The mechanics of how the combined portfolio works.

• System correlations.

• A system ranking mechanism that adapts allocations over time.

A Note For Paid Members:

If you are a paid member and have not joined our Discord community, you can do so with the link at the end of the article.

Also, we launched a GitHub to cleanly store all our strategies and tools. When you join the Discord I’ll give you access to the GitHub (or if you don’t use Discord, just message me and I’ll give you GitHub access).

Part 1 Quick Recap - Sub-Entry Scaling Design:

In Part 1, I mentioned that each of the four mean reversion systems use three sub-entries to scale into positions. A couple readers asked why three sub-entries specifically, and why equal sizing across all three entries. So, let me address that here before we get into the mini-portfolio creation.

Why 3 sub-entries?

Why 3 sub-entries, not 2 or 5 or 10? Well, two sub-entries is really not that many more than just one entry, which is what every other system uses. Sure, two is still better than one and you’ll see lot’s of improvement going from 1 to 2 sub-entries to scale into your systems positions.

But, three is like that 80/20 principle where you start to get a genuinely more continuous measurement of oversold conditions without that much extra work.

You could go to five, but you need enough capital allocation to trade five sub-entries with meaningful size and you’ll probably need automation because placing 5 trades to scale into a single position would be very tedious manually.

As the account grows, I will increase sub-entries from 3 to 4 to 5 or more, and keep adding more mean reversion systems to this mini-portfolio. Three sub-entries is the sweet spot for my current capital base. It’s enough granularity to capture the average oversold price, but not so many that each sub-entry is “too small to matter” and I get eaten up by commission costs.

Why equal 1/3 allocation per sub-entry?

Why equal 1/3 allocation per sub-entry? Why not some biased allocation where you scale in more in the first entry and less in later entries, and vice versa?

Think of each sub-entry as a fractional allocation of the total signal.

• Sub-entry 1 is a one-third signal strength.

• Sub-entry 2 brings you to two-thirds signal strength.

• Sub-entry 3 is the full signal strength and the full position size.

Equal weighting is deliberate. It may make intuitive sense to weigh later entries more heavily (buy more at better prices), but you have to be very careful with this. Optimizing for different sizing allocations on different sub-entries is a quick path to curve fitting.

Equal allocation for each sub-entry is the simplest, most robust approach. It scales linearly with the strength of the signal without introducing another optimizable parameter. It’s simple and it works well.

I am not against using non-equal weight scale-ins (to be honest, I’ve done it before), you just have to be super careful how you do it and not use that lever to curve fit the backtest to look better.

Remember, we care about future returns, not backtested returns. Keep in mind which approach is more robust and make sure that a non-equal weight scaling approach proves with absolute certainty to be just as robust as a stupid simple equal weight scaling in approach.

The Portfolio Effect: Why Run All Four Systems:

This is where a lot of systematic traders get tripped up. They look at the individual backtest results and think:

“System X has the best performance, why would I waste capital on the other three? I’ll just trade the best one.”

This is system level thinking. We need portfolio level thinking.

If you are only trading the system with the best backtested results, there is a high likelihood that something about those results is curve fit. It may not be wildly curve fit, but every system is curve fit to some degree.

If you only trade the best backtested system, sometimes it’s hard to know if it’s the best because it is actually better, or if it’s actually just the most curve fit.

The best way to get consistent, reliable live trading performance is to spread your risk across multiple different ideas, entries, and measurements. That means you are also inherently trading systems that do not backtest as nice as your best one. And that is okay.

Not only does this spread risk across the time axis (space entries over time) and price axis (space entries across different prices), but also the third hidden axis; which in this case is diversification. Diversification can be thought of as diversification of assets, but also diversification of ideas and implementation.

Spreading your trading across multiple ideas within multiple systems reduces the impact to the overall portfolio if one system underperforms. This basically is mitigating the impact of system failure risk.

Careful portfolio construction account for all these axis. Who cares what each individual system does. What matters is how they all fit together and how they spread risk across time, price, assets, ideas, and systems. The mean reversion mini-portfolio is just applying that same philosophy at a smaller scale.

The smooth, attractive equity curve you’ll see later in this article is a direct function of the portfolio effect in action. To get the portfolio effect with these four mean reversion systems, we will:

• Combine multiple semi-uncorrelated strategies together.

• Where each one looks at oversold conditions in different ways.

• Where each one scales in over time and price in different ways.

• Using a diversified basket of ETFs.

• And scaling in to get the average oversold price.

When you combine a bunch of intentionally different strategies together, you can end up with an amazing looking portfolio.

The portfolio effect is the only holy grail in systematic trading.

This article is just applying the portfolio effect at a smaller scale with mean reversion specific strategies, creating a mini-portfolio that then plugs into your overall portfolio at a scaled down allocation so the broader portfolio benefits too.

An example of the Portfolio Effect in action:

Now let me give you a real example of the portfolio effect and it’s benefits in action. The Z_reversion mean reversion system has struggled on bonds (TMF) recently. The portion of this system that is allocated to bonds is in a significant drawdown.

Bonds have performed terribly with this system while the equity, gold, and bitcoin ETFs have done much better. But bonds stay in the basket of tradable ETFs and within the mean reversion mini-portfolio because it is an uncorrelated asset to everything else.

One day, bonds may save this mean reversion mini-portfolio when everything else is struggling. And when you look at the combined four-system portfolio as a whole (next section in this article), the bond drag barely even shows through to overall results. Today’s laggard may be tomorrow’s star. I intentionally selected this basket of ETFs to be diversified across assets.

The whole point of being diversified across assets is such that when one performs poorly, the others make up for it. That’s the “All Weather Portfolio” approach.

Removing bonds just because it has performed poorly recently is nothing more than pure curve fitting; and it also defeats the purpose for why these assets were selected in the first place.

The image below shows the equity curve of trading bonds with the first sub-entry of the Z_reversion mean reversion system.

Looks terrible right? I agree.

It worked for awhile, but has recently started to not work too well. But, we have three sub-entries, not just one. How are the others performing?

See below for the equity curves of all three sub-entries of this Z_reversion mean reversion system on bonds.

Sub-entry two (purple) is down recently too, but not nearly as bad. Sub-entry three (red) is actually still up and to the right and is not in a drawdown. While sub-entry one looks terrible, sub-entry two and three look significantly better.

So, simply using the three sub-entry scaling mechanism for entry time and price diversification is already very helpful. You could think of these sub-entries as the first three components of the mean reversion mini-portfolio.

The next image shows the three sub-entries equity curves one bonds in context with the three sub-entries on all other instruments this Z_reversion system trades.

You can see sub-entry one on bonds on the very bottom of the plot (blue), underperforming everything else. But there are many other assets and sub-entries way outperforming the bonds first sub-entry equity curve.

Once we combine all of these individual equity curves of different assets all being scaled into across three sub-entries into a “mini-mini-portfolio”, we end up with the Z_reversion system itself.

You can think of the Z_reversion system as like a mini-mini-portfolio of different assets with different entry times and prices all within a mini-portfolio of other mean reversion systems; which will eventually get plugged into the overall portfolio. That’s portfolio inception if you ask me.

The image below shows the Z_reversion mean reversion system equity curve once you add all the other assets the Z_reversion system trades and their three sub-entries into one final system equity curve.

At this level it looks pretty good. In recent times, the system is in a ~7% drawdown, but that drawdown just started and overall the system looks unphased by the poor bonds trades.

This is the portfolio effect starting to creep in.

The system is diversified doing different things at different times. Also, each individual position size is small so if one or two underlying sub-entries on a singular asset look poor, it hardly matters as there are many other assets and sub-entries to pick up the slack.

The image below shows the drawdown equity curve of the combined Z_reversion system as a whole (dark blue) compared to the bond first sub-entry (light blue) drawdown.

While the first sub-entry on bonds drawdown (light blue) respective to itself is in an ugly drawdown, the combined system drawdown plot (dark blue) is completely unphased. The combined system drawdown plot is just doing its own thing and seems to not care at all that the first sub-entry bond system is hemorrhaging.

This is the portfolio effect in action at the mean reversion system level. Each system is like a mean reversion mini-mini-portfolio of different assets and different sub entries.

It then will become the mean reversion mini-portfolio in the next article section where all mean reversion systems get combined together.

You’ll see after all mean reversion systems get combined, the performance of one sub-entry on one asset within one system really doesn’t matter at all. There is so much diversification across time, price, assets, and systems that the underperformance of the first sub-entry on bonds is, frankly, irrelevant.

The Combined Mini-Portfolio:

I just spent a bunch of time showing you the portfolio effect on a tiny system-specific scale. Now let’s look at what happens when all four systems are actually pulled together into one mean reversion mini-portfolio (code to do this is at the end of the article and on the GitHub).

This equity curve shows the results of the four mean reversion systems combined together trading the leveraged ETF versions of its trading universe.

Like I mentioned, at this level one specific underperforming asset within one system on one or two sub-entries doesn’t even matter. The combined mean reversion mini-portfolio is so diversified across:

• Price

• Time

• Assets

• Systems

• Oversold measurements

• System failure risk

• etc.

that the entire mean reversion mini-portfolio as a whole is super robust to some underperformance on specific assets / sub-entries within itself.

To see what this mean reversion portfolio looks like on the non-leveraged ETFs, check out the equity curve and drawdown plots below. Non-leveraged ETFs allows us to test further back in time since leveraged ETFs became available around 2011, but the un-leveraged versions have been available since the early 2000’s.

Still looks great to me. 2000 had a somewhat bad drawdown, but that’s just the game we play with the negative skew of mean reversion. The system recovered and continued to perform beautifully after that. Oh, and I’ll talk about this more in the part 3 article, but pre-2011 and post 2018 is all out-of-sample.

If I show all the individual equity curves that comprise the non-leveraged mean reversion mini-portfolio, it looks like what’s shown below.

It’s worth noting the pink and green lines way above everything else are the bitcoin ETF results. The same ETF is used for the un-leveraged and leveraged backtest because the market is already super volatile and a leveraged ETF doesn’t exist with solid history.

If I remove the bitcoin results from this equity curve plot so you can better see the rest of the equity curves across all the systems and sub-entries, it looks like the following.

Most equity curves look up and to the right. Exactly what we want to see. Some curves are choppy and have many ugly spots, but when you combine it all together it all averages out to something pretty smooth.

Monthly and Yearly Return Heatmap

Let’s look at the combined mini-portfolio’s monthly returns laid out in a grid. This is one of my favorite ways to understand the performance of a portfolio because you can immediately see the consistency (or lack of it) across time.

Leveraged ETF monthly/yearly returns:

Unleveraged ETF monthly/yearly returns:

Not a single losing year in the in-sample or out-of-sample time period (in-sample is from 2011-2018, everything else is out-of-sample). This system does not have just a few massive months carrying the whole portfolio. Instead it is a slow but steady drip of positive months across different market environments.

I like how this mean reversion mini-portfolio is very consistent, which is different than all of my other trend/momentum/hedging systems. All my other systems have long drawdowns and flat performance periods.

This mean reversion mini-portfolio is the opposite. It has very short periods of flat performance and quick drawdown recoveries. It slots into my portfolio well and provides me with great portfolio level performance benefits.

Correlation Matrix

So I just spent 1.5 articles telling you that these four systems are genuinely independent and that combining them gives you diversification. Let’s look at the correlation table and see if that is actually true.

Below is the correlation matrix of daily returns and drawdowns between the four systems. I could not get this entire correlation matrix into an image that was actually readable so you’ll have to rely on the colors. I’ll upload this excel sheet into the GitHub for you to check out if you’re interested.

I did however add a summary correlation table showing the average correlation of each system relative to all the other systems, this table is more digestible and I can fit within an image in the article.

Combined Mean Reversion Mini-Portfolio Returns Correlations:

Combined Mean Reversion Mini-Portfolio Drawdown Correlations:

The average drawdown correlations are all ~0.34 and lower, that’s awesome from a diversification standpoint. This is why the combined equity curve of the mini-portfolio is so smooth.

The returns average correlations have a wider range, between 0.06 and 0.79. Still relatively uncorrelated on average.

This is the quantitative proof behind “why run all four systems and not just the best one?”. It is not just a feel-good argument about diversification. These numbers show that there is massive benefit to running as a mini-portfolio and take advantage of all the different measurements of oversold into account on different assets. This makes it so return streams that don’t move in lockstep.

Excluding Systems - The Ranking Mechanism:

There is an interesting dynamic layer within the mean reversion mini-portfolio code that I have not discussed yet. The portfolio has the ability to rank all individual equity curves (an equity curve being one sub-entry on one asset within one system) using a risk-adjusted return factor.

The ranking formula looks like this:

StratFactor = ROC(S.Equity, 252) / (StdDev(ROC(S.NetPct, 1), 252) * SQR(252))

This is the 1-year return divided by the annualized daily volatility of returns. Essentially ranking based on a rolling 1-year Sharpe ratio per equity curve.

This ranking method preferences equity curves which are increasing at the steepest slope with the least amount of volatility. This makes particular sense for mean reversion because when you are catching a lot of bad trades, the negative skew plays out and the equity curve gets very volatile as you catch falling knives.

Referencing equity curves with low volatility and high returns is essentially filtering out the ones currently exhibiting that negative skew. The ones with the best returns and least volatility are the ones cleanly catching bounces, rather than bleeding from extended drawdowns.

You could use other ranking mechanisms. This one is not uniquely correct, but it makes sense for the given context.

The rankings of the systems are updated quarterly. Why quarterly, not monthly or shorter? Mean reversion systems do not take that many trades. You need a long enough window to accumulate meaningful data before deciding which systems are outperforming and which are underperforming.

A shorter timeframe (monthly or less) means you are possibly ranking on noise. Systems could only have a handful of trades and the ranking excludes it based on a small sample size and you get whipsawed. One year simply felt too long because a lot changes in twelve months. One quarter was the comfortable middle ground. Enough trades to form accurately measure recent system performance, but short enough to still be responsive.

Did I spend a ton of time optimizing and testing this assumption? To be honest, not really. This was more based on gut feel and intuition of how I want it to work. The quarterly cadence was not tested against monthly or semi-annual alternatives. It was picked as a reasonable way to do things that makes sense, and then left alone.

The 252-day Sharpe and quarterly rebalance were chosen as sensible defaults, not optimized parameters. Adding optimization on top of already-optimized systems creates layered curve fitting risk. A 1-year Sharpe ratio is a common-sense metric with a common-sense lookback.

That is deliberate: the ranking overlay is not another optimizable surface. The more optimizable surfaces you add, the more surfaces you have to overfit. With that said, feel free to spend some time here playing around.

Just be super cautious with curve fitting. You do not want to layer curve fitting on top of this portfolio by being super specific with the system ranking mechanism. This is the exact reason why I intentionally picked something that intuitively made sense and just kept it without a ton of optimization and fitting. I have four robust systems, I don’t want to break them with a curve fit ranking layer.

How the system ranking works mechanically

This is a little confusing, but each strategy has a parallel Tracker (hidden) and benchmark system that are used to compute the strategy rank. The SetupSkip rule checks if this strategy’s rank is worse than the lowest allowable rank.

The ExcludeWorstX parameter (default 0) lets you drop the N worst-ranked strategies from taking new trades. Setting ExcludeWorstX to 10 would prevent the 10 worst-performing strategies from taking new trades.

TotalNumSystems: 72	// Total strategy count across all 4 systems (includes benchmarks and tracking systems for ExcludeWorstX usage) 
ExcludeWorstX:	10      //Dont trade the worst 10 systems
MaxStratRank:	TotalNumSystems - ExcludeWorstX

Template: Track
	Tracker:	Hidden 
	// If this is a tracker, never skip. Otherwise, check if the tracker version
	// of this strategy is ranked below the cutoff.
	SetupSkip:	if(IsTracker, 0, Extern(@tracker, StratRank > MaxStratRank))

If the strategy rank is below the threshold, it skips that systems entries.

This is what makes the portfolio dynamic, not just four systems bolted together. It provides an adaptive layer that reduces allocation to strategies that have been underperforming recently, without you having to manually decide which system or asset to drop.

Again, this is completely optional. To be honest I don’t use it at the moment, but I have it commented out into my mini-portfolio code just in case I do want to enable it someday.

Sensitivity analysis: how performance changes as you exclude more equity curves

I ran the system ranking on the mean reversion mini-portfolio and slowly excluded more and more strategies based on the Sharpe based ranking method and the quarterly ranking timing.

The table below shows the results for excluding 0 equity curves up to excluding the 50 worst performing equity curves (and when I say equity curve, that’s one sub-entry, on one ETF, within one of the four mean reversion systems):

The images below show the mini- portfolio results when you exclude some of the worst equity curves within the mini-portfolio. I show four examples so you can get a feel for how robust the ranking and selection logic is for excluding poor performing equity curves.

Exclude worst 50 equity curves:

Exclude worst 35 equity curves:

Exclude worst 15 equity curves:

Exclude worst 0 equity curves (none are excluded):

To see the equity curve rankings over time, simply update the tracking code from “Hidden” to “Visible”.

Then go to the “sdRank” tab in plots.

See the image below for all equity curve rankings over time.

See the image below for a down selected view of all equity curve rankings over time.

The default ExcludeWorstX of 0 means all equity curve within the mean reversion mini-portfolio trade. Excluding the worst-ranked equity curve generally makes performance slightly worse (you use less exposure and potentially miss out on some recovery trades from temporarily underperforming equity curves that got turned off before recovering), but it helps control total mean reversion mini-portfolio exposure.

This is a lever more for managing how much capital the mean reversion portfolio deploys at any given time; rather than a performance enhancement tool. It’s a way to make the mean reversion mini-portfolio more capital efficient by skipping the underperforming equity curve.

When would you increase ExcludeWorstX in practice?

1. You hate the idea of running systems that are underperforming and want a systematic way to turn them on and off dynamically.

2. It may provide a phycological safety net to know that the weakest-ranked systems are not trading. Doing this systematically and automatically is a much better approach than randomly turning off systems or reducing allocation across the board with a discressionary decision in the heat of the moment.

3. When you want to be slightly smarter about capital allocation and not waste exposure on systems that are underperforming right now.

4. Maybe you’re already running hot on portfolio margin and you want to be smarter about how you allocate to this mean reversion mini-portfolio

Don’t go crazy with it. Don’t optimize the lookbacks, Don’t optimize the ranking method. Pick a sensible value or leave it at 0.

The moment you start optimizing backtesting different lookbacks and ranking methods and trying to pick the best one, you’ve added another layer of curve fitting on top of everything else. Everything else is already robust by design, don’t ruin it with a curve fit top layer. That defeats the entire purpose.

Conclusion

Four systems beat one. Not because any individual system is exceptional, but because when you combine four genuinely uncorrelated approaches to measuring “oversold,” the portfolio effect takes over.

The correlation matrix shows that even though all these systems are buying dips on similar assets, there is still major diversification benefit to trading all four systems. The systems all fire at different times, using different signals, at different prices, and exit with different mechanisms. This produces a return stream that is smoother than any individual system could create on it’s own.

The quarterly ranking mechanism is what turns the four standalone systems into an adaptive portfolio. It’s not required, but it is a nice way to exclude the worst equity curves if trading “losing” sub-components of systems bothers you (like the first two sub-entries on bonds in the Z_reversion system).

Be very careful not to use the ranking overlay as another optimization surface. Use sensible defaults, check similar methods/parameters also produce similar results, and avoid anything super specific to prevent multi-layered curve fitting.

ExcludeWorstX really is more of an exposure management lever rather than a performance optimizer. Simply use it not to waste capital on underperforming systems (if you want) to make the mean reversion mini-portfolio even more capital efficient.

The whole point of this mini-portfolio is that no single strategy, sub-entry, or asset class carries it. The smooth returns come from the combination of all these things, and the optional adaptability comes from a ranking layer.

The full code for the combined mean reversion mini-portfolio script is in the appendix below.

In Part 3, I’ll get into:

• In-sample vs out-of-sample validation.

• Robustness testing.

• What it has actually been like to trade this live since August 2025.

So, see you in Part 3 and in the mean time, have fun with these systems and please ask any questions you have.

Disclaimer

The information and services provided by the Systematic Trading with TradeQuantiX newsletter are for educational and informational purposes only and do not constitute financial advice, investment recommendations, or guarantees of trading performance. Any information provided is general in nature and does not take into account your individual circumstances. Trading involves significant risks, including the potential for substantial financial losses, and past performance is not indicative of future results. The information is provided ‘as is’ without warranty of accuracy or completeness. All decisions and actions based on the information provided are the sole responsibility of the reader. You should seek independent professional advice before trading. The Systematic Trading with TradeQuantiX newsletter is not liable for any losses, damages, or outcomes resulting from the use of this information or our services.

Discord and GitHub Access:

Read more

Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader.

Introduction:

I’ve spent a lot of time in the past trying to build mean reversion systems on the entire US stock universe. I figured if I could find that perfect signal, it should work across everything. People say the US is a very mean reverting market, and maybe that’s the case, but I’ve always struggled to develop a system I’ve determined to be robust.

Every single mean reversion system I built would die on recent data. It didn’t matter what signals I used or how I tuned the parameters. I genuinely started to question whether mean reversion even worked on US anymore (Spoiler: it does. I was just looking at the wrong sub-universe).

The breakthrough came when I shifted to ETFs and large cap stocks. The stability was honestly night and day. And once I had that figured out, I didn’t stop at one system. I built multiple independent systems, each using completely different signals to identify when an ETF is stretched to the downside.

In this article, we will cover four of the mean reversion systems I personally trade within my own portfolio. Every system scales into the position across three separate sub-entries, so you’re never fully committed on the first signal. The idea is simple, get the average oversold price instead of trying to guess the exact bottom.

This is Part 1 of a three part series.

Part 1 covers:

• The four individual systems

• Why ETFs work better for mean reversion (at least for me)

• The design philosophy behind the systems

• And a detailed walkthrough of each system

Part 2 will cover:

• How the four systems combine into a mean reversion mini-portfolio

• Discuss a portfolio level system ranking mechanism

Part 3 will cover:

• In sample and out of sample validation

• Robustness testing

• What it actually feels like to trade this mean reversion mini-portfolio live.

Here’s the combined live performance from my actual live trading account attributed to my mean reversion systems. This equity curve is the combined result of all the ETF mean reversion systems I trade (including the ones shared in this article, along with a few other variants I have).

A little lumpy, a little bumpy, but real results. Being able to take the ups and the downs is just part of the game we play. So far, I’ve been very happy with the performance from these systems which I deployed live in August of 2025.

A Note For Paid Members:

Just before we get into the article, if you are a paid member and have not joined our Discord community, you can do so with the link at the end of the article.

Also, we launched a GitHub to cleanly store all our strategies and tools. When you join the Discord I’ll give you access to the GitHub (or if you don’t use Discord, just message me and I’ll give you GitHub access).

Why ETFs Work Better for Mean Reversion:

ETFs have structural properties that make mean reversion cleaner and more reliable than trying to do the same thing on individual stocks.

The first and most obvious one is there’s no idiosyncratic risk. No earnings surprises, no company specific events, no CEO getting arrested at 2am (the kind of headline that ruins your morning coffee).

When an ETF like SPY drops hard in a day, that drop reflects the entire market or sector selling off. There’s no “oops, they missed earnings by a penny” risk that can destroy the mean reversion trade on instrument you’re holding. Sure equity ETFs are comprised of individual stocks, but that idiosyncratic risk washes out when you go to the index ETF level.

The second reason is a passive flow thesis I have. Large institutional passive flows into major ETFs create a structural bid underneath the price. When the SPY or QQQ dips, the passive bid from retirement accounts, 401(k) contributions, and large funds provide a floor. This is why dip buying in large cap ETFs has been structurally sound for decades.

These equity ETFs are literally created for dip buying and passive flows. The mean reversion mechanism isn’t crowded out because these instruments are designed for mean reversion “buy the dip” type buying.

While large equity ETFs are great for mean reversion properties, ETFs are beneficial in another way too. ETFs can easily give you cross asset diversification. Unlike individual stock mean reversion (which is always equities), ETFs let you easily trade mean reversion across bonds (TLT/TMF), gold (GLD/UGL), crypto (GBTC), and other assets alongside equity indices.

This ease of ETF asset diversification can be leveraged to help build an “All Weather Portfolio” philosophy into the ETF mean reversion systems. This helps to a avoid correlations converging to 1 in a crisis because these asset classes have genuinely different drivers.

This cross asset diversification is extremely important in mean reversion trading because when everything sells off hard and you bought the dip and it keeps dipping, this is exactly when you get hammered from mean reversion. But with some asset class diversification, we can try to mitigate some of that risk because not everything will necessarily correlate to 1 during the next equities selloff.

As a side note, if you’re going to do mean reversion on individual stocks, stick to large and mega caps. These stocks have the institutional backing, rebalancing flows, and retirement accounts trickling in. The same structural bid that makes ETFs work well for mean reversion also exists in large cap stocks. When these stocks hit deep oversold levels, big money comes in to buy the dip. ETF’s like QQQ or SPY are comprised of these large cap stocks, so this structural bid propagates through into those ETFs as well.

On the other hand, small cap mean reversion trading has always been a struggle for me. They don’t have the same structural flows, and when they start selling off, may times there’s simply no big bid to catch them. A stock can just keep tanking because there’s nobody with big bucks stepping in to buy it.

I’ve spend probably 100’s of hours trying to find a mean reversion method that worked for me. Most of those hours were spent trying to make mean reversion work on the full US stock universe. I though that was the only right way to go about it.

It wasn’t until I let myself try different universes and shifted specifically to large caps and ETFs where I finally found some success. The stability was dramatically better, and the reason behind this mechanically makes sense: institutional backing and herd “buy the dip” mentality creates the bounce.

Then, on top of that, I built in an “All Weather Portfolio” like asset class diversification to better diversify the ETF mean reversion mini-portfolio. I’ll explain more about the design philosophy of these systems in the next section.

Design Philosophy:

Before we look at the four individual mean reversion systems, let’s discuss the thought process behind them first. All four systems share the same high level design philosophy, but all four of the systems are measuring mean reversion differently. Below I outline all of the main thought process that went into creating these systems, and why I did what I did.

As you’re reading this section, you’ll probably get a familiar feeling to why I built it the way I did. It takes a similar approach as the concepts discussed in the Luck By Design series:

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Luck By Design - Part 1

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a year ago · 29 likes · 4 comments · TradeQuantiX

Why four systems instead of two or six?

As I mentioned, this article will cover four (yes four!) mean reversion systems on ETFs. You may be wondering, why four? Well, that’s because four mean reversion systems will get you pretty dang close to where you want to be.

Going from 0 mean reversion systems to 1 is a big benefit.

Going from 0 mean reversion systems to 4 systems is a massive benefit to your overall portfolio.

After four systems, the increased benefit starts to dissipate. Four I felt was the sweet spot that would give most readers the biggest bang for their buck in their own portfolios.

It’s simply the 80/20 rule applied to a mean reversion portfolio construction. There’s nothing magical about four. It’s just a fantastic starting point (and honestly, four mean reversion systems is way more than most people have).

Ideally, over time you keep adding more mean reversion systems spanning more unique ways to enter, more ways to exit, traded across more ETFs. Four becomes six, becomes eight, becomes twelve etc.

You should think of this the same way you think about any other portfolio. Think of it as something you’re continuously building and adding uncorrelated mean reversion approaches on top of these existing four.

Back to the 80/20 rule, that last 20% of results comes from the next 20 Mean reversion systems you stack on. But that first 80% can be achieved by what I’ll share a little later on in this article.

Multiple independent entry mechanisms.

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Introduction:

Well, we’ve all been there. You spend a weekend coding up a new trading system. You run the backtest. The equity curve is going up and to the right. The Sharpe ratio looks decent. The drawdown is manageable. You’re already thinking about how much capital to allocate.

But here’s the question you should be asking before any of that: how do you know if it’s real?

Most traders I talk to apply one, maybe two robustness checks and call it a day. They’ll run an out-of-sample test or eyeball a parameter sensitivity plot and move on. I used to be in that camp early on (if I even ran a robustness test at all...).

But after building and testing 100’s of systems, I can tell you that each robustness test catches something different. Missing even one of them means you might be missing the exact reason your system fails once real money is on the line.

This purpose of this article is provide the how to for robustness testing, and includes some goodies as well in terms of tools to help you do it.

I’m going to walk through five robustness testing methods that I use on nearly every single system before it gets anywhere near my hard earned capital:

1. Parameter Sensitivity Analysis (+/- 25%)

2. Multi-Market Validation

3. Trade Skip Monte Carlo

4. Noisy Data Monte Carlo

5. Entry and Exit Delay

Each one tests a different thing. Each one can expose a different weakness within the system that’s maybe not obvious on the surface.

I’ve also built a free Excel template that helps automate the visualizations and calculations for all five tests.

You paste your backtesting output in, and it generates charts, summary stats, histograms, and percentile rankings automatically. I’ll walk you through how to use it before we get into the tests themselves.

Let’s get into it.

Why Each Method Tests a Different Thing:

Before we get into the specifics, I want to make sure the big picture is clear. These five tests are not redundant. They are not five ways of asking the same question. Each one is probing at a different vulnerability within your system.

• Parameter sensitivity: did I accidentally happen to pick the one lucky combination of parameters that works, or is this a stable region of performance?

• Multi-market validation: is this edge specific to one market and does the underlying mechanism exist more broadly? Or did I just curve fit to noise.

• Trade skip Monte Carlo: does the system depend on a few lucky trades and is the system curve fit to a specific sequence of trades? Or does the system robustly capture different trading opportunities when needed?

• Noisy data Monte Carlo: if the prices were slightly different (which they always will be going forward), does the system still work? Or is the system curve fit to noise.

• Entry/exit delay: does the system require perfect fills? And how precise are the entry and exit mechanisms the system is capturing? Some systems need that precision, others don’t. This robustness test isn’t applicable to all systems, but it’s a great test for where it is applicable.

This is not an all exhaustive list, but it is enough to help us learn a lot about the durability of a system.

These robustness tests generally come after the system is fully developed on both in-sample and out-of-sample data. You’ve built the system, you’ve validated it out of sample, and now you’re stress testing it from every angle before committing capital.

That said, there’s nothing stopping you from running these tests on just your in-sample data during development to get a preliminary feel for system stability. If parameter sensitivity looks terrible on in-sample alone, there’s no point continuing to the out-of-sample phase.

I want to make something clear before we move on: the point of robustness testing is not to find a perfect system. There is no perfect system. The point is to calibrate your confidence in an imperfect one. These tests help you understand exactly how imperfect your system is and whether you can live with it.

Let’s start with the tool that makes all of this easier.

The Robustness Testing Excel Template:

Before we walk through each test, I want to introduce a tool I built specifically for this article (but now I’m going to start using it and expanding it over time, I’ll share it with you as I do, consider this the v1.0 of the tool).

It’s an Excel workbook that takes the raw output from your backtests and does a lot of the robustness analysis automatically. No formulas to write, no charts to build manually.

You paste data in, and it gives you everything you need to evaluate your system. At least that’s the idea.

Maybe it doesn’t show everything yet, but over time I’ll get it there and share updates as it gets built.

You can download the Robustness Testing Template workbook attached to this post.

How It Works:

The workbook has 13 tabs, organized by color:

• Orange tabs (INPUT): This is where you paste your backtesting output. There are five input tabs, one for each robustness test. Each one accepts up to 1,000 rows.

• White tabs (Analysis): These auto-populate with tables, histograms, and summary statistics based on whatever you pasted into the corresponding input tab.

• Blue tabs (CONFIG and Instructions): The CONFIG tab lets you choose which metrics you want to analyze. The Instructions tab walks you through everything step by step.

Setting Up Your Metrics:

The CONFIG tab is where you tell the workbook which metrics matter to you. By default, it comes loaded with 13 metrics that I consider on every system: ROR, MaxDD, Volatility, UI, Trades, PctWins, AvgWin, AvgLoss, WinLen, Expectancy, ProfitFactor, Sharpe, and AvgExp. You can add up to 20 performance metrics total.

None of the performance metric column values are hardcoded. The workbook is smart enough to lookup each metric by its header name.

So, if your backtester outputs columns in a different order, or uses slightly different names, or you have your own custom metrics, you just make sure the header names on your CONFIG tab match the headers you pasted in. Then that just flows through the rest of the excel sheet.

Pasting Your Data:

Each INPUT tab has a blue header row at the top of the paste zone. Here’s the steps to input your data for a robustness test:

1. Run your robustness test in your backtester (RealTest, AmiBroker, custom python code, whatever else you use…)

2. Export the results to a CSV

3. Open the CSV, copy the header row, and paste it into the blue header row on the INPUT tab corresponding with the robustness test you ran

4. Copy your data rows and paste them below the header row

That’s it. The analysis tab for that test will auto-populate with everything: summary stats (min, max, median, percentile of your baseline), and histograms showing the distribution of results with your baseline system results highlighted in dark red.

Setting Your Baseline:

For four of the five tests (Parameter Sensitivity, Multi-Market, Noisy Data, and Entry/Exit Delay), you’ll see a “Baseline Row #” cell at the top of the INPUT tab. Enter the row number of your baseline system. This tells the workbook which result to highlight in the charts and which to calculate the percentile against.

For Trade Skip Monte Carlo, the layout is slightly different. Your actual backtest result goes in the top section (rows 6-7), and the Monte Carlo simulation results go below (starting at row 11). The workbook then shows you where your actual result falls in the distribution.

What You Get:

For each test and each metric on your CONFIG tab, the analysis tabs generate:

• Summary statistics: min, max, median of all results, plus the percentile rank of your baseline system and the delta between baseline system and the average/median result from the robustness test. The Baseline Percentile row gives you the quick answer: where does my system sit relative to everything else?

• Histograms: bucketed distribution of results across 10 bins, with the bin containing your baseline system results highlighted in dark red. The histograms show you the shape of the distribution. Is it a nice bell curve centered around the baseline? Or is the baseline sitting out on the right tail? The shape matters because it tells you whether the parameter surface is a plateau (normal or uniform distribution) or a spike (skewed distribution with your baseline on the edge).

The percentile is the key number. For example, if your baseline system’s ROR, volatility, Sharpe etc. are all in the 50th percentile of the parameter sensitivity results, that’s a good sign.

It means you’re in the middle of the distribution, not perched on a lucky peak. If it’s at the 95th percentile, that should make you nervous. You accidentally picked parameters near the top of the range, and the only direction from there is down (and that’s usually where live results end up too… down).

With the tool introduced, let’s walk through each test.

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Introduction:

A very common question I hear from systematic traders is:

“How do you know when your system is broken and how do I know when to turn it off before it’s too late?”

The short answer to that question is: generally you can’t know for sure if something is “broken.” Usually it’s too late before you actually know for sure.

But this answer is a bit lazy.

Maybe we can get some system degradation warning signs before the system completely dies. There are some things we can examine to understand if the system is degrading over time.

While there is no way to know for certain that the degradation will continue (maybe the system comes back to life), at least knowing that some degradation appears to be present is good information for us systematic traders to make decisions around.

Maybe if we could see degradation within a system, we could:

• Allocate less capital to it as the confidence in the system persisting slowly decreases with degradation. Then, if the system comes back to life, we can increase capital allocation again.

• Or maybe you put the system in a probation period.

• Or maybe you just keep the knowledge of degradation in the back of your mind and are ready to pull the plug at a moment’s notice.

These are some of the tricky parts of systematic trading. These are the parts that require discretionary decisions, which we never like. But if we use some informed and unbiased data-driven approaches, then maybe that discretionary decision around “Is my system broken?” becomes a little more systematic.

Why Is It So Difficult To Know When Your System Is Broken?:

Knowing when a trading system is broken is hard for a few reasons:

1. We don’t know the future. Who’s to say the markets are just experiencing unfavorable conditions for the system and the system will start working again once the markets start to cooperate again.

2. Systems tend to ebb and flow, moving in and out of drawdown. Who knows if this seemingly normal drawdown is the one that never recovers?

3. Some drawdowns feel worse than others. Deeper, faster, or more aggressive than any historical drawdown. This can lead to doubt and the feeling that something fundamental changed.

Psychologically, the decision to turn off a trading system due to the belief of it being broken is hard as well because:

1. We fear that if we keep the system running and it breaks, then we will lose money as the system crashes and burns.

2. On the contrary, we fear if we turn the system off and it starts working again we will miss out on the gains as the system rips out of drawdown.

3. We put all this work into researching and developing the system, accepting all that hard work is no longer valid is frustrating and annoying.

Take, for example, the TSX (Canadian) momentum system we developed as part of the Portfolio Development Series. This system has had many difficult periods of time.

The system has had deep drawdowns, flat spots, and volatility. Consider the flat performance between 2014 and 2021. I don’t think anyone would fault you for thinking the system stopped working during that period. Only then for it to come roaring back to life in 2021 and 2024 (and keep in mind, 2019 onwards was used as out-of-sample for the development of this system).

TSX Momentum System:

Knowing if this system was broken or just experiencing normal drawdowns and sideways action is hard.

Very hard.

If this was the only system you were trading, that would have likely been very frustrating at times.

This is one reason why it’s always best to trade a portfolio of many diversified systems together. Then, when this TSX momentum system went sideways for years, you still would have had many other systems pick up the slack.

One of the best ways to know if a system is broken is through a deep understanding of how the system works. For example, this TSX momentum system obviously trades high momentum stocks.

So, if the TSX market does not exhibit traits of momentum for long periods of time, it would be reasonable to think the market conditions are simply unfavorable for this system; rather than the system just stopped working.

TSX Market Index - SPTSX:

Notice how the TSX market index has large drawdowns and sideways periods at the exact same times as the momentum system struggled. So, just through basic reasoning of how this system works, we may be able to convince ourselves it’s the market rather than the system.

A system can only take what the markets give. If the markets are not providing momentum, this momentum system cannot extract returns from the market.

Understanding the underlying system dynamics and why/how it makes money is important to understanding if the system is broken; or instead are the markets just not providing the conditions for this system to extract returns.

On the other hand, if you have a more esoteric strategy and you are not really sure why the system makes money; then it is a lot more difficult to know if it’s market conditions driven or if the system is actually broken.

A system comprised of “indicator soup” that looks nice in a backtest is cool, but going forward in time we have no understanding of why the system works and if the current drawdown is temporary or a full system failure.

We don’t understand what this “indicator soup” system is harvesting. So we have no concept of knowing if the lack of performance is due to the markets simply not being cooperative or if the system was curve fit to begin with, and is now falling apart.

Anyway, the first step in knowing if your system is broken or not is to answer and understand the following things:

• Understanding what effect its harvesting.

• Understanding why the system should work.

• Understanding what market conditions need to be present for the system to work.

• Understanding when those conditions tend to exist.

• Understanding if the system capturing returns like it’s supposed to when favorable conditions exist.

Once you’ve had a critical thought about your system and can answer those questions, you can move on to the next section where we explore a tool I crated to look “under the hood” of your trading system.

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Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader.

Introduction:

You may have heard of the holiday effect in markets. It’s the idea that leading into federal holidays, the markets tend to rally. This had me wondering if this effect is real and, if so, whether it can be captured.

I mentioned in a note that 2026 is the year of researching “small” and “dumb” edges. Things that I can quantify and prove to myself have a very high likelihood of existing. Ideas that are different from the traditional trend and momentum type systems I trade a lot of and which we have explored in previous articles.

I figure if I can research and implement many of these different edges, it will provide a unique and non-correlated return stream to my other trend and momentum systems.

Not only does this diversify my portfolio return streams, but the more unique strategies I add to my portfolio, the more I reduce and spread the risk of individual strategy failure. Having two strategies and having one fail would suck. Having 50 strategies and having 4 or 5 fail would hardly even leave a mark.

Hence, researching market effects, like the holiday effect, and seeing if it’s something that can be exploited seems like the perfect “small” and “dumb” edge to help build up a fortress of trading strategies to diversify my portfolio return streams.

Let’s get into it.

Reason For The Effect:

The question we need to answer is:

“Okay, allegedly the holiday effect exists, but why would something like that exist in the markets? Is there a good reason for this effect to exist or is it likely a data-mined myth?”

We can attempt to answer the “why this effect might exist” through reasoning (but we can never actually know the true answer). A few decent reasons why this effect might exist would be the following:

• Good Sentiment:

  • Holidays simply make people happy, more optimistic, and less focused on work. When people are optimistic, they may be less averse to risk. This “holiday spirit” or euphoria may lead investors to buy stocks (or at least avoid selling), pushing prices higher. Happy investors process information less critically and expect better future outcomes. Studies often cite this as the dominant explanation, with investors in a good mood being reluctant to sell or potentially more willing to hold/buy.

• Lower Trading Volume and Liquidity:

  • Many traders, including institutional ones, reduce activity or go on vacation before holidays, leading to thinner markets. Lower liquidity can amplify price moves in either direction. Combined with good sentiment from happy investors, it could result in temporary upward drifts.

Price-insensitive buying during less liquid markets would be a good reason for an effect to exist. When investors/traders are buying or selling regardless of price, that leads to inefficiencies that we can exploit.

While these seem reasonable and plausible, we will never know for sure what the true reason(s) for the effect are. That’s just the markets, they’re opaque. But the good news is we at least have a decent educated guess at the causes.

The reason understanding the likely causes is important is because if there were no reasons why we would think this effect would exist, it would be harder for me to trade such an effect. This is because I would fear it was just a data-mined result. Also, if the effect went away in the future and I didn’t understand the cause of the effect, I wouldn’t be able to assess whether the causes had changed to understand if the idea was actually dead or not.

There could be times when an effect like this temporarily underperforms. When that happens, if I understand the effect I can ask myself whether I see a reason for the cause of the effect to have changed. If so, I can reason the effect is dead. If I can’t see a reason for the cause of the effect to have changed, then I’d continue to trade the system, expecting the underperformance to revert soon.

The part of the question about data-mining we cannot answer yet. The rest of the article will be used to answer that question through a bunch of analysis. And, if we are lucky, we’ll end up with a trading system to harness the holiday effect.

Research Phase:

Let’s kick off the analysis of this potential market effect by understanding the baseline returns from the S&P 500 SPY ETF. On average, the S&P 500 has an upward drift. I don’t think there is an argument against that.

Knowing what the average upward drift gives us a threshold for understanding whether the holiday effect has returns above average market returns, or not. If the holiday effect is real, I would expect to see that the returns during the days leading up to the holiday are higher than the average market return.

Below is a scatter plot of close-to-close SPY returns. Grey dots are daily close-to-close observations. The orange line is the average daily SPY return.

Average SPY Daily Gain/Loss (1993 to 2026):

The scatter plot shows the daily return can vary a lot, but on average is positive expectancy. The average SPY close-to-close daily gain is: 0.03998% (from 1993 to 2026).

This value makes sense. The SPY returns on average ~10% a year and if I multiply 0.03998% by 252 trading days a year I get 10.07%. Said differently, I could have just divided the SPY average return per year by the number of market trading days per year and found the same result.

Therefore, 0.03998% (or 0.04% for simplicity) is our line in the sand. Any return less than or equal to 0.04% per day is just market beta. But if we can find a consistent and repeatable effect with a return greater than 0.04% per day, well that’s alpha (or at least that’s how we will define it for these purposes).

Okay, we determined a threshold to use to define market beta vs. alpha. Now let’s see if we can measure the holiday effect to see whether it has a repeatable and consistent return above the market average.

To do this, I had to gather the dates of every federal holiday since 1993 (which is when my SPY ETF data starts). I considered all US federal holidays:

• New Year’s Day

• Martin Luther King Jr. Day

• Presidents Day

• Memorial Day

• Juneteenth National Independence Day

• Independence Day

• Labor Day

• Columbus Day

• Veterans Day

• Thanksgiving Day

• Christmas Day

I then looked at the market returns leading up to these holidays. I did this measurement in a couple different ways. The first way is shown below, where I measured the market return 5, 7, 9, 11, 13, 15, 17, 19, 21, and 25 days before a holiday. This would simply measure:

“If I bought x days before every holiday, and then sold on the close of the last trading day before the holiday, what returns would I see on average?”

I measured the returns for every holiday, buying x days before the holiday and selling at the close on the last market day before the holiday. I then averaged all of the results together to understand the average return.

I also repeated this same process but instead of buying before holidays, I instead measured the average result of buying SPY during random periods of time; holding for x days, then selling. This is like our benchmark for this type of measurement. If the holiday effect is real, I would expect to see outperformance from buy x days before a holiday compared to the returns of randomly buying SPY for the same length of time.

Average Return Leading Up To A Federal Holiday vs. Average Market Return (1993 to 2026):

The blue dots show the average percent gain from buying x days before a federal holiday. The orange dots show the average returns of the SPY if you randomly bought and held for the same length of time.

You’ll notice that buying before holidays appears to have almost 2x the returns as the average market return. Or at least this is true from 5 days out to 17 days out from the holiday. Measuring from 19+ days out from the holiday, the returns seem to collapse back to the average market return.

This result tells us two things:

1. The holiday effect is showing very promising potential right from the start. Buying SPY leading up to a holiday seems like it may be a decent idea.

2. Buying closer to the holiday, within about 15 days or so, is better than buying further away from the holiday.

The chart above shows the average return for each set of days away from the holiday. But we can decompose that information further to better understand what’s going on beneath the surface.

I decided to look at the average returns for each day leading up to the holiday, decomposing down to the day-by-day returns. I measured this from 20 days out all the way to 1 day out from the holiday date. What this entailed was measuring the market returns of day 20 before a holiday, day 19, day 18 etc. I did this for all holidays and then averaged the result to understand the average return for each day leading into a holiday.

This will tell us exactly what drives the holiday effect. Is the effect solely driven by the returns of SPY the day before the holiday? Or maybe all of the alpha resided between days 3 and 7, for example.

Decomposing down to the day-by-day returns will help inform us of exactly where the effect resides.

The bar plot below shows exactly this. It shows the average SPY return from 20 days out to 1 day out from each federal holiday from 1993 to 2026.

Day-To-Day Returns Leading Up To A Federal Holiday (1993 to 2026):

The left side of the bar plot shows the average SPY return 20 calendar days away from a federal holiday; the right side shows the average SPY return for 1 calendar day before a federal holiday. You’ll notice the left half of the plot (further from the holiday) looks noisy and unpredictable with random up and down days on average. But the right side of the plot (closer to the holiday) from calendar day ~11 right up until 1 calendar day before the holiday looks consistently positive.

This is exactly what we want to see. Long before a holiday the results look like average market noise. But as we get closer and closer to the holiday, the market returns start to look much more predictably positive.

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Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader.

Introduction:

Over the past few months, the most common question I have been asked in terms of systematic trading is:

“How do you allocate capital to your strategies when running a multi-strategy portfolio?”

If you have one trading system, capital allocation is pretty simple: 100% of capital is allocated to the system.

If you have two trading systems, maybe you just opt for a simple 50/50 split of capital.

But, once you have multiple trading systems, capital allocation can become much more daunting.

Is equal weight allocation the best?

Is there some secret sauce to portfolio capital allocation I don’t know about?

What if I miss something, mess up my allocation, and my portfolio suffers as a result?

There is a lot of second guessing that happens during portfolio level capital allocation. To help with this, I want to walk through an eight step process that provides a sensible, simple, yet very effective approach to portfolio capital allocation.

Example Systems Used In This Article:

I am going to walk you through each of the eight capital allocation steps with an example portfolio. Thus, I need some example systems.

For this article, I leveraged five systems that we developed as part of the Portfolio Development Series; which we spent a lot of time on in 2025. Within that series I did cover portfolio capital allocation, but in this article I want to dive much deeper.

I will give a more in-depth, step-by-step framework on how to perform portfolio capital allocation which blends everything together that was discussed within the Portfolio Development Series.

To get more information about portfolio construction, consider checking out these two articles:

Let me introduce the five systems I will use to build a portfolio. The five systems are:

• System 1 - US Mega Cap Mean Reversion

• System 2 - US Mega Cap Momentum

• System 3 - ASX Small Cap Trend Following

• System 4 - TSX Momentum

• System 5 - Long Volatility Hedging

You can see the results for each of the systems in the images below. I’ve also linked the articles where we developed these systems if you want more background.

System 1 - US Mega Cap Mean Reversion:

System 2 - US Mega Cap Momentum:

System 3 - ASX Small Cap Trend Following:

System 4 - TSX Momentum:

System 5 - Long Volatility Hedging:

Portfolio Allocation Steps:

Let’s get right into the step-by-step framework for sensible capital allocation within a multi-strategy portfolio. Like I mentioned, this implementation is straight forward but very effective.

Don’t get bogged down in super intense optimizations or super complex techniques. We want simple and effective, not complex an confusing.

We do not work for large hedge funds.

We do not have a team of PhD’s to work out the absolute optimal perfect allocations.

We are generally independent retail traders who just need the simple, yet effective, 80/20 solution. And that’s exactly what we are going to cover here.

The eight step multi-strategy portfolio capital allocation framework is summarized below as follows:

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Welcome to the “Systematic Trading with TradeQuantiX” newsletter, your go-to resource for all things systematic trading. This publication will equip you with a complete toolkit to support your systematic trading journey, sent straight to your inbox. Remember, it’s more than just another newsletter; it’s everything you need to be a successful systematic trader.

Introduction:

In the previous article, we took a very simple trend-following system idea and dissected it down to its core components. We learned what causes the system to make money and what rules are the key drivers of performance. We also uncovered some concerning features about the system that need to be addressed as well.

At the end of the part 1 article, I listed some ideas to test in an attempt to improve the system or increase its robustness. In this article, we are going to try implementing those ideas and see what we come up with.

Mindset In System Development:

My goals are to make a system with as few rules and parameters as possible. Simplicity is key; a rule really has to show a significant effect on the system in order to convince me to keep it. Also, a simple rule with slightly worse performance almost always trumps a complex rule with slightly better performance. It’s almost guaranteed the more complex rule is overfit.

Remember, a singular system doesn’t matter that much; it’s just one piece of the portfolio. Hence why we want robustness over performance. Robustness keeps the portfolio from failing; the performance comes from many non-correlated robust systems working together, each mediocre on their own, but extremely powerful when combined.

That is the mindset I am approaching this system with: simple system concepts and a portfolio-level view. If you don’t have a portfolio-level view, it’s very easy to throw away perfectly good systems. Of all the systems I personally trade, I wouldn’t trade a single one in isolation. I would only trade them together within a whole portfolio.

When you think about systems in this way, it’s much easier to look at system performance and design more objectively. The ideal portfolio-level thought process should be:

“That drawdown in 2008? I could curve-fit it out by tweaking the index filter, but wait, I just remembered I have a hedging system that makes money during 2008-like events! Okay, fine, I’ll leave it alone. The next market crash will likely behave differently anyway, so curve-fitting to remove one bad event won’t change the impact a future bad event would have on the system.”

Going into system development work with a portfolio mindset is crucial as it helps remove the urge to curve-fit. See this article for more details on the portfolio-level mindset.

That’s enough of me blabbering about mindset. Let’s get to the good stuff. Let’s see what we can do with this system. As always, no promises it gets better; I write these articles as I do the investigation, so it’s true real-time learning for both you and me.

System Improvement Investigation:

As I mentioned in the part 1 article, there were a few ideas I listed to test for potential improvement of the system. To recap, those ideas were:

• Add an entry rule to require a minimum amount of momentum prior to entry.

• Ensure the stock has recently crossed the 200-day MA + two standard deviations for the entry signal.

• Ensure volatility (standard deviations) is expanding to prove the stock is currently breaking out. Right now, a stock could calmly drift past the 2 standard deviations mark, which may mean that stock does not exhibit much momentum.

• Remove the -2 standard deviations band from the exit rule. Just use the 200-day MA as the exit, or potentially add a trailing stop loss as well.

• Allow the system to take more positions than 5.

• Dynamically adjust volatility-based position sizing to help with those massive drawdowns.

If you remember, these ideas were not randomly pulled out of a hat. Instead, we tore the system apart to understand exactly what every component was doing, we looked at some example trades, and we ran some robustness sensitivities. Only from those observations were we able to come up with sensible ideas to test, rather than just random guesses based on a hunch.

To refresh what the in-sample results of the system looked like, below I have the system equity curve in green (benchmarked to the S&P 500 in red), followed by the performance stats of the system, and then the drawdown plot.

Baseline System Results (In-Sample):

This will be what we compare back to for many of the tests we will perform throughout the rest of the article. So burn those results into your memory… or just scroll back up in the article from time to time; that works too.

Let’s jump into the first system improvement idea (and remember, improvement doesn’t always mean better performance; it can also mean more robust!).

Change Number of Positions Held:

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Introduction:

The other day I was perusing the internet for some trading ideas for new systems. I tend to find lots of ideas laying around, but most don’t really pique my interest. The ideas I like the most are:

• Simple in nature (simple tends to be more robust)

• Based on real market phenomena

• Are actually testable

Simple ideas are the best because they tend not to be fragile. Complex ideas on the other hand are extremely easy to curve fit and, in general, hard to test (have you ever tried to backtest a discressionary traders rules? You usually can’t, because there are 1,000 caveats!). Also, when a simple idea is based on some market effect that is proven, that’s even better.

That’s when I stumbled upon an idea that was so simple, I had to investigate it. The system was easily testable with only a few simple rules, and was based on a real market effect: momentum.

In this article let’s dive into the system. I want to attempt to replicate the results and then tear the system apart to better understand its innerworkings. Then, using what we learn about the system in this article, there will be a part two where we attempt to improve the system; where improvement can mean two things (and ideally means both):

1. To make more robust

2. To make have higher performance (though to make more robust is more important, higher performance should be the second goal after making a system more robust)

Anyway, let’s not get too in the weeds yet. Let’s jump into the system and try to code and understand it.

Replicating The Trend System:

So you can follow along, the link to where I found this system idea is listed below:

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Introduction:

Let’s continue working on the system we took a deep dive into in the previous article. To recap, I had found a random system buried in my files that had positive forward-tested out-of-sample results. I then took that system, tore it apart, then built it back together slightly simpler and with position sizing updates.

In this article, I want to move on to running some robustness tests on the system to ensure the system does not show signs of curve fitting or risk of future degradation. The robustness tests I will run are:

• Parameter Sensitivity Tests (focusing on the out-of-sample time period)

• Entry Rule Monte Carlo

• Slippage Sensitivity

• Different Universe Tests

Then, I would like to take the learnings from the robustness tests and do what I like to call “building robustness into the system”. This is the technique I have been implementing into every new system I develop prior to going live with the system.

From my experience, this technique has helped with system stability and forward live out-of-sample performance. It also inherently allows me to sleep better at night knowing I am trading more robust systems that are less prone to single points of failure.

As a refresher, this is the current result of the system we are working with:

Alright, let’s dive in and see where this system shines and where the system has flaws. Ultimately, we need to decide if the system is worthy of the portfolio or not. So, let’s begin some robustness tests!

Parameter Sensitivity:

The first robustness test to assess is a parameter sensitivity. If you remember from the part 1 article, I ran a parameter sensitivity on the in-sample. Now, I want to run the same parameter sensitivity on the out-of-sample. I want to focus specifically on the out of sample because I want to understand a couple things:

• Is the out-of-sample time period more “fragile” or sensitive to parameter values than the in-sample?

• Did the out-of-sample get “lucky” in terms of positive performance

It’s 100% possible to have a lucky out-of-sample result that only had positive performance due to shear luck. The parameters chosen in the system could be on an out-of-sample performance peak and just happened to make money during the out-of-sample period. But going forward in time, that performance peak will eventually collapse or shift, leading to poor or negative results. This is what we want to check for.

Hence, I ran a +-25% parameter variation on all parameters within the system, specifically on the out-of-sample time period. The table below shows the percentile the default system parameters reside in terms of performance.

For all metrics, the system was basically right in the middle of the road, in fact the system performance was slightly less than the average result. The only exception was Percent Wins being 67%, but for all other metrics, the system was below the 50th percentile.

Assuming all results within the +-25% parameter space are positive, this is exactly what you want to see. You do not want the systems default parameters to be in a super high percentile. That would be evidence of selecting a performance peak that just hasn’t shifted yet, i.e. a lucky out-of-sample result.

The fact that this system is in the middle of the road basically means as the optimal parameters shift around over time, this system is right in the middle of the road and has the wiggle room to handle the noise in the parameter surface.

Visualize it this way, it’s much easier for a new driver to drive a car down the middle of the road than right on the edge. When driving down the middle of the road, there is plenty of room on either side to account for the new drivers poor driving skills. When driving right on the edge of the road, one side has no margin, one wrong move and the car is in a ditch. Kind of a dumb analogy, but that’s how I think about it.

Now, let’s compare some of the results from this +-25% optimization. I’ll show the default system parameters out-of-sample performance first, then I’ll show the best and worst results in terms of Calmar ratio (ROR/MaxDD).

Default Parameters Out-of-Sample:

Next I’ll show the equity curve of the best result in terms of Calmar ratio from the +-25% optimization.

Best Result (Based on Calmar Ratio):

You’ll notice this parameter set happened to miss Covid, then go on a steep upward slope, making new high after new high. It’s good to see results significantly better than the default parameter set.

I would never complain if the parameter surface shifted in this direction and the default parameter system started seeing performance like this. If the markets shift and the default parameters start performing better than they do currently, it’s nice to see this type of performance is possible.

Worst Result (Based on Calmar Ratio):

Above is the results of the worst equity curve based on Calmar ratio. You’ll notice these results have very few trades (125 vs. the default systems 580). Basically this parameter set within the +-25% range is choking the system performance. The oversold measuring parameters become very low, and the ADX parameter is very high, leading to a very restrictive set of conditions which would result in a trade. Basically, this was the most stringent possible parameter set within the +-25% results.

On one hand, this is an ugly result. On the other hand, even though this variation of the system had an overly strict parameter combination, the system still worked its way up and to the right. This is a good sign that even under very stringent scenarios, the system rules still resulted in a positive outcome.

Let’s now check out a more realistic worst case result from the +-25% parameter variation. The above parameter set only had 125 trades during the out-of-sample period while the default parameters have 580 trades. Let’s again sort the results of the +-25% parameter variation by the worst Calmar ratio, but check out a system with slightly more trades, say 350 trades. This will let us see the results of a “poor performing” parameter set that does not choke the system.

Realistic Worst Result (Based on Calmar Ratio):

Okay, this parameter set had 349 trades, close enough to 350. As you can see, with a parameter set that is not as restrictive, even the results on the worse end of the +-25% parameter variation are pretty good. I would trade this parameter set, even though it’s in the bottom 4% of parameter values in terms of Calmar.

Overall, the out-of-sample +-25% parameter set variation shows promising results. The system appears to be in a very stable range of parameters which is exactly what we want to see. All +-25% parameter variations make money in the out-of-sample time period and every equity curve that has a reasonable number of trades is profitable and tradable.

Entry Rule Monte Carlo:

A neat Monte Carlo you can run to test the systems ability to choose good trades is via Entry Rule Monte Carlo. I’ve seen many systems fail this test which is why I like this test a lot.

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Introduction:

I was digging through my folders the other day when I stumbled across a handful of mean reversion strategies that I had forgotten about. It was like finding buried treasure, except it was buried deep in my folders rather than in the ground. I couldn’t remember when I developed these strategies or where I had gotten the ideas from. Luckily the files were timestamped, which showed it has been over a year since these strategies had been touched.

There were two strategies in particular that I found to be quite interesting. In this article I want to focus on one of those two strategies (maybe in a different article we can focus on the other strategy).

What I want to accomplish in this article is:

• Share the current starting point of the strategy and what the forward tested out-of-sample incubation looks like.

• Then I want to tear the strategy apart to understand its core components

• I want to ensure there are not any misses or new learnings that need to be incorporated into the strategy.

• Then I want to try to improve the strategy further (if possible)

• Then we’ll piece the strategy back together

Hopefully when it’s all said and done we have a new strategy that we can add to our database.

The Hidden Treasure Strategy:

The strategy that I stumbled across was a short-term mean reversion system. The strategy trades mega-cap stocks, only buying oversold conditions on stocks that are trending.

The system enters positions using a limit order. The system exits when the high is above the previous day’s high, or the position has been held for 10 days.

The system holds up to 10 positions. If more setups exist than the 10 slots, the system ranks and prioritizes stocks that have increased the most over the previous year.

See below for the detailed list of system rules:

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Introduction:

Let’s wrap up this portfolio development series with the final article, part 11. In this article, we’ll construct a U.S. equities only portfolio. Hopefully, you can leverage the systems and ideas presented here to enhance your own systematic trading portfolio.

There are multiple systems that will be in this portfolio.

There is a momentum system which targets U.S. large caps, specifically the S&P 100, NASDAQ 100, and Russell 1000.

There is a trend system which also focuses on U.S. large caps, particularly the NASDAQ 100 and S&P 100, incorporating trends from both a low volatility and momentum effect perspective.

There are two mean reversion systems. The first mean reversion system concentrates on NASDAQ 100 and S&P 100 stocks. This is complemented by a second mean reversion system on a diversified basket of leveraged ETFs spanning equities, gold, bonds, and Bitcoin.

There is also a tactical asset allocation system. This system allocates to a collection of diversified ETFs with the goal of achieving steady, smooth returns.

On the short side, there are three distinct systems: a breakout momentum type shorting system, an ETF mean reversion shorting system, and a long-volatility hedging system.

This portfolio is going to comprise of many different system types, and as I’ve preached many times before, a portfolio with multiple different system types is the key to exceptional portfolio performance.

System Summaries:

Let’s briefly summarize the equity curves and performance statistics of the systems that will be included in the U.S. only portfolio. This summary will refresh your understanding of each system’s individual performance.

None of these systems are amazing on their own, but once we combined them into the final U.S. only portfolio, you’ll see how the combined performance is greater than the sum of its parts.

• System 1: The U.S. large cap mean reversion system:

• System 2: The set of U.S. large cap momentum systems:

• System 3: The set of U.S. hedging systems:

• System 4: The U.S. ETF tactical asset allocation system:

• System 5: The set of U.S. large cap trend following systems:

• System 6: The U.S. ETF mean reversion system:

U.S. Only Portfolio System Allocations:

The system allocations for the U.S. only portfolio are summarized below:

• System 1: U.S. large cap mean reversion: 30%

• System 2: U.S. large cap momentum: 25%

• System 3: U.S. hedging systems: 30% (each)

• System 4: U.S. ETF tactical asset allocation: 30%

• System 5: U.S. large cap trend following: 35%

• System 6: U.S. ETF mean reversion: 35%

I tried to make all strategies contribute to the overall portfolio performance relatively equally. Meaning no one system is dominating the return profile, each system has a similar say in the returns of the overall portfolio equity curve. It is not perfect because different strategies start their backtests at different periods of time, but it’s close enough to show the power of this U.S. only portfolio.

You’ll notice these allocations sum to over 100%. That is intentional and we will discuss that shortly.

The combined portfolio is the dark blue line in the equity plot below. The other lines below the combined line are the contributions from each individual system.

This U.S. only portfolio is very intriguing. While I’m a strong advocate in trading multiple markets globally for diversification, this U.S. focused portfolio is highly tradeable.

This returns of this portfolio outperform buy and hold strategies by several percentage points, and the drawdowns are significantly lower than buy and hold. With a maximum drawdown just under 12%, compared to over 50% for a passive buy and hold approach. If I had a choice between trading this portfolio and passively investing in the S&P 500, I’d choose this portfolio any day.

One critical factor to consider is the portfolio’s exposure over time. The exposure plot for the combined portfolio shows that, for the first 10 years of the backtest, the portfolio is relatively underexposed, peaking at around 60–70% exposure.

This is because some systems lack historical data during this period and haven’t yet “activated.” But, by the early to mid-2000s, once all systems have data to work with, exposure ramps up to 100% and occasionally enters margin, reaching a maximum of 138% exposure.

While I’m comfortable with brief periods of margin use, as shown in the exposure plot, this is a key consideration for traders without margin accounts. If you’re trading in a cash only U.S. equities account, you’ll need to scale down system allocations to avoid margin usage.

As I mentioned above, the allocations to all the systems sum to over 100%, yet the exposure of this portfolio tends to be around 100% or lower; with only very occasional margin use. This shows the power of combining non-correlated systems.

Not all of the systems are activated of fully exposed at the same time. Some systems are on, others are off, others are partially allocated. It’s a constantly evolving dynamic of sharing capital back and forth. For example, the shorting systems only kick on during bear market events. During this time, all the long trend/momentum strategies are actively selling, freeing up capital for the shorting systems.

Portfolio Comparison To Benchmark:

The benchmarks to beat are the S&P 500 and the traditional 60/40 portfolio. Over the past 20 years, the S&P 500 has returned approximately 9.5% annually with a maximum drawdown of 55%, while the 60/40 portfolio has delivered around 8% returns with a maximum drawdown of 31%.

It’s astonishing to me that investors settle for such performance when, with a bit of effort, we can far surpass these metrics. By combining non-correlated systems that analyze the market from different perspectives, we can create a portfolio that’s greater than the sum of its parts.

Individually, the systems within the portfolio are volatile and imperfect, but together they produce remarkably smooth portfolio-level performance.

In the equity curve comparison, the U.S. only portfolio (blue line) significantly outperforms the 60/40 portfolio (green line) and the S&P 500 (pink line).

The U.S. only portfolio’s trajectory is nearly linear, contrasting sharply with the volatile paths of the two benchmarks. It shines particularly during turbulent market periods, where the U.S. only portfolio tends to move sideways while the S&P 500 and 60/40 portfolio suffer steep drawdowns.

This outperformance is further evident in a rolling volatility plot. The 10-day rolling volatility of the U.S. only portfolio (dark blue) is significantly lower and more stable than that of the S&P 500 or 60/40 portfolio. This again shows how the U.S. only portfolio experiences a significantly smoother return profile compared to traditional buy and hold approaches.

Capital Requirements Of The U.S. Only Portfolio:

You might be wondering:

“I have $25,000 to allocate, is that enough to manage this portfolio?”

That’s a great question, so let’s explore. Every system in a portfolio requires a minimum capital amount to operate efficiently due to real-world trading costs and constraints.

For example, if a system is allocated $10,000 and holds equal weight 20 positions simultaneously, each position is worth just $500. If the system needs to buy a stock priced above $500, it may skip the trade or select a cheaper stock, leading to inefficient and suboptimal capital use. The system said to buy a certain stock, but we didn’t because we didn’t have enough capital, that’s not ideal. This can harm performance.

Another issue is commission drag. With a small allocation, if a system earns $20 per trade on average, but pays a fixed $2 in commissions, that’s 10% of profits lost to fees. However, with a larger system allocation resulting in an average profit per trade of $1,000, that same $2 commission becomes just 0.2% of the profit, a much more manageable cost.

These two example situations illustrate why knowing the portfolio minimum capital threshold is essential for efficient trading.

To investigate the impact of portfolio size, I ran the portfolio with allocations of:

• $10,000

• $25,000

• $50,000

• $100,000

• $250,000

• $500,000

• $1,000,000

The table shows the performance metrics begin to converge around a capital amount of $50,000. This is the capital amount where the portfolio overcomes commission drag and can position-size optimally. Beyond this point, additional capital still yields some performance improvements, but they are minor.

A common myth is you can start trading with $2,000 and grow your account to millions in a short period of time. This study shows that there is significantly more capital required to properly manage a well diversified portfolio of multiple systems; with $50,000 appearing to be the minimum for this specific setup. And even so, it’s going to take a long time before $1,000,000 is in the cards. All good things require patience.

Adding ASX and TSX Systems:

Although this is a U.S. only portfolio, let’s have some fun and experiment by adding the Australian (ASX) and Canadian (TSX) systems to see their impact. We’ve already made these systems in previous articles, so we may as well add them to the portfolio just to see what happens.

As a refresher, the ASX system is a trend following strategy on small caps, and the TSX system is a rotational momentum strategy, also on small caps.

I adjusted the portfolio to scale down the allocations to the U.S. systems, making room for the ASX and TSX systems to be added. I set the allocation values such that each system contributes roughly equally to the portfolio’s returns, aligning each systems equity curves more or less on top of each other.

The results of this expanded portfolio are very interesting. Nearly all metrics improved: returns increased from 14.3% to 16.8%, drawdowns decreased from 11.8% to 10.6%, and risk-adjusted metrics like the Calmar and Sharpe ratios rose (Calmar from 1.21 to 1.58, and Sharpe from 1.48 to 1.82).

This demonstrates the value of incorporating non-correlated markets/systems into a systematic trading portfolio. While this article focuses on U.S. only trading for those with limited market access, these results serve as a compelling call to action. If you’re currently trading only U.S. markets, please consider exploring non-correlated markets, like the ASX and TSX, to significantly enhance your portfolio’s risk-adjusted performance.

Conclusion:

This U.S. only portfolio illustrates the power of systematic trading, combining momentum, trend, mean reversion, and hedging systems to deliver superior returns with significantly lower drawdowns than traditional benchmarks like the S&P 500 or the 60/40 portfolio.

By carefully blending non-correlated strategies, we’ve created a portfolio that’s not only robust but also resilient, maintaining stability even during market turbulence.

This portfolio is a testament to the idea that thoughtful design and disciplined execution can transform your investment outcomes. Now it’s your turn to take these ideas and implement them into your portfolio in the best way you see fit.

Well this is officially the last article in the Portfolio Development Series. I hope you enjoyed these articles and now have a better understanding of how to create a systematic trading portfolio from scratch. As always, let me know if you have any questions.

Also, all code for every U.S. system is documented below. I also added the combined script that aggregates all U.S. systems together so you can run combined portfolio backtests. Enjoy!

Do you have ideas/suggestions for future articles? Let me know what you want to read about by clicking the button below and submitting your suggestions. Your suggestions are greatly appreciated as they help tailor this newsletter to what you want to read about.

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Disclaimer

The information and services provided by the Systematic Trading with TradeQuantiX newsletter are for educational and informational purposes only and do not constitute financial advice, investment recommendations, or guarantees of trading performance. Any information provided is general in nature and does not take into account your individual circumstances. Trading involves significant risks, including the potential for substantial financial losses, and past performance is not indicative of future results. The information is provided ‘as is’ without warranty of accuracy or completeness. All decisions and actions based on the information provided are the sole responsibility of the reader. You should seek independent professional advice before trading. The Systematic Trading with TradeQuantiX newsletter is not liable for any losses, damages, or outcomes resulting from the use of this information or our services.

Real Test Code:

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Introduction:

I’ve received a request from several readers to convert the portfolio we developed is part of the Portfolio Development Series to focus solely on U.S. markets. While I’m a big believer in global diversification and trading as many markets as possible, there are reasons to create a U.S. only portfolio.

For one, some investors are restricted to trading only U.S. equities. Retirement accounts, for example, are often limited to U.S. only equities, and many major U.S. brokers also impose similar U.S. equities only trading restrictions. Given this, I can understand why there’s significant demand from U.S. investors for a U.S. only systematic trading portfolio.

In this article, let’s take a look and see what we can develop in terms of a U.S. specific systematic trading portfolio.

What Systems To Add To The US Only Portfolio:

Let’s start by reviewing what we’ve built so far in the Portfolio Development series, specifically for U.S. markets. Thus far, we’ve created the following U.S. specific systems:

• A U.S. large cap mean reversion system:

• A set of U.S. large cap momentum systems:

• And a set of U.S. hedging systems (three total):

These three systems provide a solid foundation for a mildly diversified U.S. only systematic trading portfolio.

But let’s expand further.

In previous articles (before the Portfolio Development series), I’ve explored other systems for the U.S. market that may be worth adding to this U.S. only portfolio, including the following:

• A U.S. ETF tactical asset allocation system:

• And a set of U.S. large cap trend following systems:

If we start by taking the three U.S. strategies developed as part of the Portfolio Development series and combined those with the two systems from previous articles, we’re working toward a robust five-system portfolio.

And remember, some of these systems contain sub-systems on different markets, or sub-systems looking for different market conditions to be met, so really its like an 11 system portfolio.

But let’s pause and assess what system types we have and what system types we might be missing.

We’re pretty well-covered on the hedging side, with three different shorting/hedging systems to protect us during adverse market events.

On the trend and momentum side, we’re in good shape with two trend following systems on two different large cap universes; and one momentum system across three different U.S. large-cap universes.

However, when it comes to long side mean reversion, we only have one U.S. mean reversion system. All other major system categories (trend following, momentum, hedging/shorting) we have at least two different systems; but for long side mean reversion, we only have one system currently.

This suggests that long side mean reversion is a category where our portfolio may be lacking. So, let’s develop another mean reversion system to enhance and diversify this portfolio further.

Planning The Mean Reversion System:

The existing mean reversion system buys oversold stocks in the Nasdaq 100 and S&P 100. Personally, I’ve never found much success trading mean reversion on small caps, especially in recent years. From my experience, mean reversion systems on small-cap equities have significantly degraded in recent times, with many systems failing outright, particularly during 2022 and 2023.

It could just be me, maybe my ideas are not good enough, but I can’t seem to create a stable system on small caps. I know many other systematic traders who have experienced the same as well. Hence, why up until now I have focused my mean reversion development on on large cap stocks.

I have a theory that the passive flows from large funds find their way into large cap U.S. equities, which tends to make them more mean reverting. With flows buying nearly every dip. There’s always a large institutional bid, hence why they tend to always rebound after a sell off.

Leveraging the same theory, large cap equity ETFs should follow a similar phenomena. Hence, I have just recently started to explore and develop mean reversion systems on U.S. ETFs. I have found a lot of success here and have been able to develop multiple systems with very stable results.

When developing ETF trading systems, there are a few traps to avoid. One issue I see with many ETF mean reversion systems is that they’re often built around only a single ETF, like an S&P 500 mean reversion system, a NASDAQ 100 mean reversion system, or a Bitcoin mean reversion system, etc. I take issue with this approach because it’s easy to overfit a system to a single time series.

If the behavior of the ETF shifts in the future, then the system could suffer significant losses. It’s also extremely easy to overfit to the limited data in just one ETF time series. Hence, why single ETF systems make me nervous.

To help avoid this risk, I prefer to develop ETF mean reversion systems that trade a basket of ETFs. This ensures some level of diversification and reduces the risk of curve-fitting as I have more data points to develop the system with.

After I’ve chosen the basket of ETFs I’d like the system to trade, I like to develop the system using just a few of the ETFs, from say 2000 to 2018. Then, I’ll validate the system on the unseen ETFs and on the unseen timeframe. Then I’ll trade the final system across the entire basket of ETFs. This provides more out-of-sample data for validation and adds diversification within the system.

I also avoid choosing ETFs that all belong to the same asset class. For example, I don’t want to trade only large-cap stock ETFs like the S&P 500 or NASDAQ 100, as these are highly correlated (though they do mean revert well, likely due to the passive flows theory I mentioned a few paragraphs ago).

Instead, I take more of an all-weather portfolio or tactical asset allocation approach. This ensures the ETF basket covers a broad range of asset classes. I include ETFs for assets like bonds and gold for example, to avoid overexposure to a single asset class.

The danger of focusing on one asset class is that during crises, correlations within equities tend to converge to one. Going all in on equities during the COVID crash, for instance, could be catastrophic if the systems timing is off.

By including other asset classes, which behave differently during adverse market moves, the system is more diversified and will likely not be “all in” during a major market crash. For example, equities may be crashing, while gold may be bouncing to the upside, resulting in a winning gold trade and losing equities trade, smoothing the equity curve.

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Introduction:

Up until this point in the Portfolio Development series, the following broad high level topics have been explored:

• Planning out what types of systems will be included in the final portfolio

• Developing those systems with high quality development techniques

• Combining those systems into the final portfolio and determining allocations.

These are the general concepts that one needs to understand to create a systematic trading portfolio.

But there are other very specific small details that one needs to consider to really get the most out of their systematic trading portfolio.

In this article, I'm going to go into the nitty-gritty considerations. These are the considerations that should be carefully mapped out to ensure your portfolio performs at its best. Thinking through these topics now will help reduce the number of issues that occur after you launch your newly developed systematic trading portfolio.

This article is not necessarily going to be the most entertaining or action-packed, but it is going to be one of the most important.

I will discuss multiple different high-level concepts that you’ll need to understand and consider. These concepts are:

• Practical portfolio design considerations

• Non-quantifiable portfolio allocation considerations

• Quantifiable portfolio allocation considerations

• Portfolio external capital considerations

• Portfolio expansion over time

• Unforeseen portfolio risks

• Portfolio live execution considerations

If you do not consider and find solutions for the topics I am going to discuss, then your portfolio will likely suffer.

Practical Portfolio Design Considerations:

The first genre of aspects to consider is practicality. This includes things like time zone considerations, currency conversions, regulatory items, and mental capacity.

Time Zones:

Let’s start with time zones. If you decide to trade a market different from your home market, realize that there will be a time zone difference. This stock market will open and close at a different time than your home stock market.

It's possible that the market may be in a time zone that does not align with your schedule, making it difficult to run a trading system on said market. For example, if you live in Australia and want to trade the US markets, the US market opens around midnight Australia time and closes around 6 am Australia time.

I don’t know about you, but I don’t prefer the night shift. Depending on how the trading system operates, it could be an absolute nightmare to trade.

There are ways around this, though. What I do is place all of my orders during times when the market is closed. The orders sit with my broker and get executed market-on-open when the other country’s market opens. This allows me to place orders when I have the free time to do so; rather than staying up late to place orders exactly when the market opens.

This method works if you trade the daily timeframe, but if you’re trading intraday, then you either need to stay up all night to babysit your system trading the foreign market, or you need to develop very robust automation.

Remember, while you are developing trading systems, the backtest may look great, but if it’s a nightmare to trade, you may not be able to stick with it.

Personally, I trade the USA, Canadian, and Australian markets. I have found a time that works for me when all of these time zones align such that all of the markets are closed. This allows me to process and place the orders for the next market session. I would recommend you open a time zone converter online and look at the time differences across all the markets you plan to trade; then plan out how you intent to account for the time zone mismatches.

The more markets you add across multiple different countries, the more difficult it's going to be to find off-market times. You may find you have to process and place your trades multiple times a day across all the different markets. That could be pretty annoying to do everyday.

Currency Conversions:

Another thing to consider is currency conversions. If you trade a market other than your home market, it is likely there will be a necessary currency conversion to place that trade. Whatever position size your system spits out must be multiplied by the current currency conversion rate to ensure you end up with the correct exposure.

While a currency conversion isn't difficult, it can be an annoying nuance to do every day if not automated. It's also an aspect that is commonly overlooked, leading traders to be either massively under or overexposed in their position sizes compared to what they should be. So, be sure not to forget about currency conversions.

Below is a plot of USD/CAD. Assuming your base currency is USD, when the price goes up, that means you can buy more CAD with your USD; meaning the value of CAD has dropped. I also have a 1-year rate of change plotted at the bottom as well.

Imagine holding a trade between 2014 and 2016, unhedged from currency fluctuations. CAD dropped nearly 50% in value in relation to USD! If you were holding a trade on the Canadian market, the value of that trade would have also dropped 50% in relation to USD.

Regulatory Items:

Another practical nuance to look out for is regulatory items. These are another minor headache to tackle. Be sure that whatever market you plan to trade, you are legally able to trade.

For example, I am from the United States, and therefore, legally, I cannot trade the Indian markets, even though I would like to. If I had not known this ahead of time, I may have potentially bought data for Indian markets and spent a lot of time developing systems just to be frustrated when I found out that these systems were unusable.

Another example would be developing a shorting system on a market that doesn’t allow you to short. You can't short 95% of the stocks on the Australian market. You're lucky if you can get shorts for the top 50 stocks. So, spending lots of time creating an ASX short system is likely going to result in subpar live results and frustration.

There could also be special tax considerations applicable to trading other markets. For example, the London Stock Market charges a tax on all trades of about 0.5%. If I had created a trading system that had low expectancy on the London markets and I did not consider this tax being taken out of my P&L, this could transform the system from being wildly profitable to a system that loses money. So, spend time upfront figuring out if there is a special tax situation to account for before you spend a bunch of time developing your portfolio.

Here’s an example system where I assume no taxes are applied to every trade (but slippage and commissions are applied):

And here is that same system with a 0.5% tax on every trade per the London Stock Exchange’s rules:

Imagine not knowing that the market you plan to trade has this tax, and your system can’t overcome these extra fees, then its performance is severely degraded. Never assume fees are negligible.

Psychological Considerations:

The last set of practical considerations are psychological ones. You could develop a killer system that has amazing performance, but the only downside is it's extremely difficult to execute.

If you have a busy life and a demanding day job, adding a very demanding trading system into that mix could result in disaster. This is why I personally focus on the edges that are relatively easy to exploit so that I do not have to spend a lot of time worrying about execution.

I'm very grateful for this on busy mornings when I wake up late and need to rush out the door to get to work for my first meeting. The fact that I can crack open my trading systems, generate the orders, and place them with my broker in less than 5 minutes makes my morning trading routine a breeze. This is because I don't use convoluted systems to trade.

I designed the systems such that they work synergistically with my life and routine. I don’t bend my life to fit around how a system needs to be traded. So, consider how you’re actually going to be required to trade your portfolio every day and plan the system design accordingly.

Another consideration is if you do not have any sort of automation, but you decide to trade 10+ trading systems, this could lead to overwhelm and mistakes. With every new market you add, you are essentially adding that much more work to your daily trading process. After awhile, there will come a tipping point where the amount of work required to run your systematic trading setup will be so much that you’ll start becoming prone to errors.

This is why some sort of automation is key. Having a batch script to run all your systems and generate your orders is a relatively simplistic thing to create, but it can have a massive impact on your systematic trading every day. Creating some sort of automation will generally save you time, stress, and reduce silly errors. I have a handful of small utility scripts that I use every day to make my life 10x easier and less prone to error.

Non-Quantifiable Portfolio Allocation Considerations:

In this portfolio development series, we have spent a lot of time discussing how to combine all your systems into a final portfolio. We quantified our allocation decisions, but sometimes there are allocation decisions that are non-quantifiable.

Portfolio Allocation (Over)Optimizing:

Once you have a set of trading systems and you go to combine them into a portfolio, it's very easy to think that simply optimizing the allocations to each system and picking the best result is the way to go. Why would you not want to trade that best set of allocation parameters, right?

I'm gonna tell you this is the wrong way to go about it.

Similar to when we develop trading systems, we don't just pick the best parameter for a certain trading rule. Portfolio construction should be treated the same way.

If you were to simply run an optimizer to find the best allocations to each system, what that would result in is an overallocation to the best backtest and an under allocation to the worst backtest.

On the surface, this sounds fine, but this method of blindly finding the best system allocation percentages has a lot of hidden dangers that need to be considered.

Consider: is your best backtest the result of a genuinely well-designed trading system that exploits an edge extremely efficiently? Or has overfitting found its way into the backtest of this system?

Say I built a small portfolio of three strategies:

• Strategy 1: amazing performance, likely an overfit strategy

• Strategy 2: okay performance, likely not an overfit strategy

• Strategy 3: okay performance, likely not an overfit strategy

When I ran an optimization of allocation parameters, the best results based on this optimization were between a 75%-100% allocation to Strategy 1, and a 0%-25% allocation to Strategies 2 and 3. But that’s not ideal; that removes all diversification.

Also, if Strategy 1 fails in the future, and it probably will because it’s likely curve-fit in this example, that’s going to really hurt because we are overexposed to it.

Whereas if we traded all three strategies with a more equal allocation, we would have a much more robust portfolio. In this instance, if one strategy failed, yea, it might suck, but the entire portfolio isn’t going to zero, because there are two other strategies picking up the slack.

Now, when I say overfitting, that doesn't necessarily mean that the system will completely crash and burn during live out-of-sample. It could, but really what I mean is the backtested performance is overstated.

If your backtest says the system should have a 20% return with a 20% drawdown, but in reality, it's slightly curve-fit, and going forward, the return is more like a 15% return with a 30% drawdown, then you're going to be overstating the returns and underappreciating the risk involved in that system.

Assuming this system had the best overall performance in relation to the other systems being considered in the portfolio, then the results of your portfolio optimizer would heavily over allocate to this slightly curve-fit system. Then, during real-time trading, your live results would suffer due to the degradation from curve fitting.

Not only do you get worse results because the system was slightly curve-fit, but it’s being exacerbated by the fact it was also heavily overallocated to. This is why we can't blindly optimize allocations. Sure, optimizing allocations can be a decent starting point to get an idea what allocation to start with, but we need to add another layer of critical thought on top of this.

Geopolitical Risk:

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Introduction:

In the previous article in this portfolio development series, we finally combined the four systems we created and evaluated the portfolio’s performance. Even with just four systems, the portfolio performance was very solid, yielding a a fantastic starting portfolio to build from.

While the portfolio didn’t fully meet all the objectives we originally outlined, it came extremely close. Considering the portfolio consists of only four systems, I am not concerned, there is still plenty of room to build on top of the four system portfolio. To further improve the portfolios performance, it was decided that the next step is to add a hedging system, to benefit from adverse market events.

Why Adding Short Side Exposure Is Important:

Currently, the portfolio is long-only, so it’s expected to outperform during bull markets, but go flat or enter drawdown during bear markets. Consider a time period such as the 2008 bear market: many systems within the portfolio went into drawdown, and remained in a drawdown for years.

When looking at a backtest over 30 years, we loose perspective of how long the systems were in a drawdown. Going forward in time into the future, we do not have the luxury of knowing when we will hit new equity highs. We have to remember we are going to live that equity curve everyday, in real time. Would you be able to continue to execute the orders of your system for years while your system remains in drawdown?

Therefore, creating the smoothest equity curve possible is desired. Having short side systems to profit during adverse market events will help with that smoothing effect; as shorting systems are typically uncorrelated to long systems.

So, what kinds of systems could we develop to benefit from adverse market events? There are likely many solutions, but I categorize them into a few different types of approaches.

The first is a system that shorts the market during a downtrend. This could involve shorting via breakouts to the downside or mean-reversion strategies which short local relief rallies within a larger downtrend.

Another approach is to use what I call long-volatility strategies. During adverse market events, volatility typically spikes. A system that goes long volatility can be highly profitable during volatile bear markets. However, these systems are like insurance policies. You pay a premium every month, slowly bleeding cash, until a crisis hits, only then do you receive a payout.

Long-volatility systems work similar to buying insurance. During normal market conditions, you may lose money gradually, but when a crash inevitably occurs, the system spikes with profits, capitalizing on the surge in volatility.

In this article, I’ll explore all three of these concepts. We’ll implement a long volatility system, a system that shorts breakouts to the downside during bear markets, and a system that shorts relief rallies in bear markets using mean reversion.

I can almost guarantee these systems won’t look pretty on their own, but that’s not the point. The goal is to smooth portfolio equity curve during periods of time when the long side systems underperform.

Short Side Mean Reversion:

The first system we’ll cover is a short-side mean-reversion system on equity and bond ETFs. This system trades the SPY, QQQ, and TLT ETFs on the short side.

If you recall the mean-reversion system from Part 3 of this series, we used the concept of scaling in to the position to obtain an average price during oversold conditions. For this short mean reversion system, we’ll follow a similar approach but scale into an overbought position.

The system works by measuring the RSI and placing limit orders at various overbought RSI levels, scaling into the position over a few days. This technique provides more stable results and is less prone to curve fitting, as it doesn’t rely on a single set of parameters that we hope will remain optimal into the future. Instead, it diversifies across multiple parameter sets.

You can also think of this as scaling in by signal strength. As the overbought signal strengthens via the RSI increasing, the system scales in more aggressively, increasing position size with the signal’s intensity.

As a simple way to emulate this scaling in, I developed four versions of this RSI mean reversion shorting system. Each uses a different RSI value for entry and exit. See the end of this article for the code.

You can see the equity curve for this system below. Note the four equity curves on the bottom of the plot are the four different variants of this system using different RSI values. The resulting equity curve of these four variants combined together is the dark blue line.

Short Side Mean Reversion System:

You’ll notice the returns of this system are low, but the time periods where it makes returns is what’s important. The system makes money during 2000, 2008, and 2022 which are all bear markets where the current portfolio struggles. This system is also relatively low risk, as shown by the drawdown, with a max drawdown of only 4.4%.

Because this system is comprised of four sub-systems, the exposure can scale up and down based on signal strength, as discussed above. As the ETF shorting signal increases, the position size increases and thus the exposure.

You’ll notice in the exposure plot below that a large majority of the time, this system is off, yielding zero exposure to the markets. When the system is in a position, generally it is only at 25% to 50% allocation. Only a few times is this system at 75% to 100% allocation. See the exposure plot below.

If you were okay with taking on a bit of leverage from time to time, you could bump up the allocation to this system such that more equity is used more often. Just keep in mind there will be a day where this system asks for leverage if you do that. Personally, I use a small amount of leverage in my portfolio, so that doesn’t bother me but it’s dependent on every individuals risk profile and goals.

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At this point in the portfolio development series, we have created four unique trading systems across three global equity markets. In this Part 7 article, I will start assembling a portfolio of systems so we can see the portfolio effect in action. What we will find when we build the portfolio is that, even with just four trading systems, phenomenal performance can be achieved at the portfolio level.

In this article, I will cover a handful of topics, including:

• Recap the performances of the four original trading systems.

• Review the portfolio level goals laid out in the first article in this series.

• Combine the 4 trading systems into a portfolio.

• Understand the portfolio's strengths and weaknesses.

• Outline next steps.

Ideally, this article will show you why having multiple systems working together within a systematic trading portfolio is the only true Holy Grail. There is no such thing as the Holy Grail at the trading system level.

The only Holy Grail that exists is the result of combining multiple different and uncorrelated trading systems into one unified systematic trading portfolio. This article will show you how to do just that.

As a sneak peek, here is where we end up: a portfolio of four trading systems, with allocations set such that each system contributes similarly to the overall equity curve. This shows the power of developing a systematic trading portfolio. Just four uncorrelated trading systems can create a magical result.

A Quick Recap:

First, let's start by recapping where we stand up to this point. We have developed four unique trading systems across three different equity markets. Each trading system has its own unique performance profile.

No individual system is amazing on its own. The good news is that no system has to be amazing on its own; what matters is the effect on the portfolio as a whole.

Below are the backtested equity curves and performance metrics for each of the four systems we have developed thus far:

System 1 - US Mega Cap Mean Reversion:

System 2 - US Mega Cap Momentum:

System 3 - ASX Small Cap Trend Following:

System 4 - TSX Momentum:

Next, let’s quickly outline the performance goals of the systematic trading portfolio. These goals were laid out in the second article in this series. We will see if the four-system portfolio is sufficient to meet these goals. If it does, great! If not, we will discuss methods to meet these goals in the Next Steps section.

If you missed the article that outlined these performance goals, you can check it out here:

Portfolio Performance Goals:

• Portfolio CAGR Goal: >20%

• Portfolio Max Drawdown Goal: <25%

• Portfolio Max Drawdown Length Goal: <1 year

• Portfolio Average Drawdown Goal: <10%

• Portfolio Volatility Goal: <10%

• Portfolio Sharpe Goal: >2.0

If the portfolio falls short of these goals, we will simply have to keep working toward them over time. We don’t have to be perfect from the beginning. A systematic trading portfolio is a never-ending improvement project anyway. You should always be striving to make the portfolio better.

These performance metrics were chosen loosely based on my own personal situation. I'm in my late 20s, looking for strong absolute portfolio performance to quickly compound my capital. I do not want to work in the corporate world my entire life, so I need a high CAGR to compound my capital quickly.

While I am willing to take on some risk to achieve a high CAGR, I do not want to take on so much risk that I am constantly stressed and can’t sleep at night. Hence, the drawdown tolerance at the portfolio level is moderate, at 25%, but not absurdly high.

Risk and reward are proportional. If I want more returns, I generally have to take on more risk. Therefore, I’ll accept downside risk up to 25% to achieve a CAGR of 20%.

Equal Weight Portfolio Allocation:

Now, let's start digging into the assembly of the systematic trading portfolio. But, before we start, let’s discuss some of the assumptions surrounding how this portfolio will work:

• All systems will share capital from one account.

  • The systems do not operate in silos; they all work together and share the same capital from one account. If System 1 makes money, that capital is equally distributed across Systems 2, 3, and 4.

• System allocation and position sizing are based on the net liquidation value of the account. This value is updated every day.

  • Every day, the allocations to each system are recalculated based on the net liquidation value of the account. These allocations are then used to position-size new trades within the system, but existing trades are not updated based on the day-to-day allocation fluctuations.

  • Open trades are not rebalanced based on changes in the account's net liquidation value; unless there is a specific rule in the system to rebalance periodically (some of the systems have a rule to rebalance monthly or if the trade size is significantly different from the current ideal size).

• The starting account balance of the portfolio backtest will be $100,000.

  • There will be no deposits or withdrawals from the account over the entire portfolio backtest period. Only compounding of the original $100,000 will be shown.

Think of this portfolio as a team. If one member of the team is performing well, the entire team benefits. The dollar allocation to each system builds or reduces based on the performance of every other system, but the percentage allocation remains static.

There are many unique ways we can allocate capital to each trading system. I want to pick a few allocation methods and experiment to see which capital allocation method is the best to achieve our portfolio goals. The capital allocation methods I want to test are:

• Equal weight allocation

• Equal volatility weighted allocation (risk parity allocation)

• Equal return weighted allocation (return parity allocation)

Each allocation technique has its own pros and cons. For example, equal weight allocation may be naively simple, but it ensures equal exposure to each system and/or market, which may be desired.

Let’s dive into each of these allocation methods, see how they behave, and decide which is best for this portfolio. We may even decide we don’t like any of these allocation techniques and instead go a hybrid route. There’s no correct answer; it’s all about experimentation and picking something that suits your goals.

One of the most important things is to pick an allocation style you can stick to without constantly changing allocations or quitting trading the portfolio altogether.

You may find that one of the allocation methods has better results on paper (however you define “better”), but it may not be something you would actually be comfortable trading live. For example, maybe the allocation method has amazing returns but too much risk for your liking. Thus, you modify the allocations to allocate less to some of the more volatile systems to create more of a hybrid allocation approach.

Portfolio allocation is more of an art than a science. You’re going to be the one who has to ride the equity curve of this portfolio every day, so allocate in a way that makes it a ride you want to take.

Equal Weight Portfolio Allocation:

We will first start with the simplest allocation method: an equal allocation percentage given to each system. Since the portfolio has four systems, each system receives 25% of the total portfolio capital.

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Introduction:

Welcome to the part 6 article of the Portfolio Development series. In this article we are going to head up north to the Canadian market. Thus far, we've developed a couple of systems on the US market, a system on the ASX market, and now we are going to add the TSX market.

Having diversification across multiple world equity markets can provide massive benefits to a systematic trading portfolio. Think about it, different economies perform better during different times. The US market may be going sideways, the Australian market may be in decline, and the Canadian market may be growing. You never know what the economic situation will be, and so having exposure to multiple different economic environments can be extremely powerful.

On the Canadian market, I'm going to develop a momentum trading system. To be honest, I'm pretty nervous about developing this system. I have attempted to develop momentum systems on the Canadian markets a couple of times in the past, and every attempt has failed out-of-sample or robustness testing.

I'm actually starting to write this article before I even develop the system. That way I fall into the sunk cost fallacy and work really hard to develop a system that actually passes out-of-sample testing and is robust. So wish me luck.

In this article, I'm going to focus on parameter optimization during the in-sample development phase. I'll share the final system results, but the majority of the article will focus on robust optimization practices and setting yourself up for success in out-of-sample.

The worst feeling is when you spend hours developing using in-sample data just to check out-of-sample and the system completely falls apart. It's demoralizing and feels like you've wasted an entire day, and then the rest of your day you just feel defeated.

This is why I want to focus on robust parameter optimization techniques so that you set yourself up for success for the out-of-sample test. There's no guarantee, obviously, that the out-of-sample will pass, but it will give you a better probability of passing when you implement these techniques, as opposed to not.

Common Optimization Pitfalls:

It's very common for systematic traders to throw a bunch of indicators on a chart, they then say:

“That looks good, all it needs is some optimization!”

Then they run a brute force exhaustive optimization on a million parameter combinations and pick the very best result. This is a faulty practice and is nearly guaranteed to fail in out-of-sample.

A better practice than picking the best parameter is to pick the most stable parameter. This is why I think optimization confuses people. The word "optimizing" is the wrong word. It should be called stability searching, or something of that nature.

Generally we need to find a parameter with a stable performance surface, meaning all parameters surrounding the chosen parameter have similar performance. This allows for the markets to shift a little bit and the system still work into the future.

Now, it’s not always this easy. Sometimes parameter optimization surfaces are bumpy, sloped, and noisy. There is a lot of nuance that goes into how I pick parameters during these scenarios. Those examples will be outlined in this article.

Picking the best parameter (the performance peak) allows no wiggle room for future market shifts, and thus is more likely to fall apart in the future. Performance peaks generally are not real, instead, they are noise within the data.

The reason why systematic traders are prone to pick performance peaks and overfit rather than create robust systems is because robust systems aren't as pretty. Overfitting results in beautiful backtests. It's very easy to fall in love with how your backtest looks. But a backtest is just that, there's no guarantee of future performance, and the more fragile and overfit your backtest is, the less likely you are to have any positive performance in the future.

Instead, this is why we need to focus on robust backtests, which are uglier backtests, but they're real. These backtests are much more likely to have continued positive performance into the future. Ask yourself, would you rather:

• Trade a system with a lumpy and bumpy equity curve with drawdowns and periods of underperformance that is robust and continues to make money over the long term for years into the future?

• Or trade a system that has a perfectly straight equity curve and is prone to catastrophic failure during the next market shift due to overfitting?

I know what I would pick, the uglier but more robust system. Robustness is like the 2005 Toyota you've had in your garage for 20 years. Yeah, it's ugly, it's old, and it's not going to turn any heads, but it's going to run forever.

Let’s go over a silly, but real example of overfitting. I say real because I have seen people do this kind of thing before. Say, for example, you're optimizing a system to only trade one day a week. You run an optimization to see which day the system performs the best. You find Monday, Tuesday, Thursday, and Friday all have about the same performance, but for some reason Wednesdays have 20% better performance.

Now the question is, why? Is there something special about Wednesdays? If you were running a system on crude oil, then yeah, Wednesday is when the weekly crude oil report comes out, so it would make sense that Wednesdays may have more profit opportunities. But if there's no fundamental reason as to why Wednesdays are the best, then it's likely just a random anomaly within the data.

If you were to really dig in and dissect the data, you may find that there just happened to be a couple of random Wednesdays in the backtest that were really big winners-no rhyme or reason to it; it just happened to be on a Wednesday. Picking Wednesday in this scenario, when there's no fundamental reason why Wednesday should be better, is just curve fitting to noise. This is just a performance peak that will likely not persist into the future.

A better way to actually prove if Wednesdays are better would be to run a rolling optimization like a walk-forward analysis. This would help determine if the Wednesday anomaly persists over time or if it's just due to a few random Wednesdays that had a big winner in the past.

This was an example of what not to do. Don’t just start digging through the data and plucking out random anomalies, they’re likely noise. Instead, think through fundamentally why that anomaly should or shouldn’t exist. If there is no reason to think Wednesdays are better than any other day, then it’s likely not. I'll digress from this example as I think you probably get the point.

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TSX Momentum System Rules Outline:

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Introduction:

This is the first article in the Portfolio Development series focusing on a market outside the US market. While most traders and investors concentrate on the US markets due to its liquidity and maturity, the US market is not the only viable market to trade. The Australian stock market, known as the ASX, offers diversification opportunities for a systematic stock trading portfolio.

As I’ve mentioned in all my articles, each piece in this series focuses on a specific aspect of the system development process to keep things fresh and engaging. In this article, while I’ll briefly cover how the system works and its in-sample and out-of-sample results, the main focus will be on robustness testing.

In this article, I will develop a long term trend following strategy for the ASX market. This trend following strategy will use moving averages in a way that reduces the dependency on just one single parameter combination.

As I always preach, the more we can leverage and be exposed to the entire parameter space, the better. Hence, this strategy will use a technique similar (but a little different) to what was outlined in the article below, to determine the entry and exit signals.

As a sneak peak, this is the system I will develop and then robustness test in this article. Not too bad for a long term trend following system!

Why The ASX?

The ASX has distinct advantages over the US market. The US market is relatively efficient, with many large institutional players extracting alpha everyday, leaving little for retail traders, like us. The ASX, on the other hand, is less institutionalized, providing more opportunities for retail traders to find an edge.

This is a double-edged sword, however. A mature, institutionalized market tends to be highly liquid, whereas a less mature, less institutionalized market like the ASX is typically less liquid. While smaller markets like the ASX may offer greater edges to exploit, the reduced liquidity can be a challenge.

Depending on your trading style, this lower liquidity may or may not be an issue. If you trade systems with long-term time horizons (holding trades for weeks, to months, to even years) in a less liquid markets, you’ll likely be fine. This is because the increased expectancy due to holding positions for long periods of time can overcome the extra slippage caused by lower liquidity.

However, if you’re trading a fast mean-reversion system on the ASX, like the one we developed for US markets in Part 3 of this Portfolio Development series, your profits could be eroded by excessive slippage due to illiquidity. This isn’t to say there are not stocks in the ASX which are liquid, there are quite a few very liquid stocks on the ASX, there are just fewer than in a more mature market, like the US market.

In summary, smaller markets provide larger edges for retail traders to exploit, but these edges are generally best captured on longer timeframes to mitigate the impact of slippage due to lower liquidity. It’s also worth noting that commissions on the ASX are higher, likely because it’s a smaller market with fewer brokers, thus there is less competition to drive the commission prices down. Higher commissions and lesser liquidity leading to more slippage is a disaster for short term trading systems, hence we are looking longer term.

This is why I’m developing a long-term trend-following system for the ASX market. Being long-term, the system’s expectancy should be high enough to remain robust to significant slippage and commissions. The system will focus on small-cap stocks, as smaller stocks on smaller markets tend to offer larger edges for us retail traders to exploit.

Institutional investors often can’t easily trade smaller stocks due to liquidity constraints, making it easier for us retail traders to compete. Running a long-term trend-following system on ASX small-cap stocks is like playing poker against your drunk friends instead of a professional poker player.

The ASX Trend System Rules:

I personally run multiple trend-following systems in my systematic trading portfolio. Rather than leveraging an existing system I already have, for this article, I wanted to create something original. I went a completely different direction than I would normally go for trend following. While the indicators and filters I used are not original, I think the way I used them is original and also adds robustness.

I’m a big believer in always pushing yourself to coming up with new ideas, no matter how goofy they may seem. You never know, one of those ideas may work. This is exactly what I did here, I forced myself to go outside the normal way I define trend following, and the results were pretty interesting.

I built the system on an in-sample dataset from 2000 to 2018, with out-of-sample testing ranging from 2018 to mid-2025 (today). The rules I finalized for the system are as follows:

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Introduction:

This is an article I was not expecting to write as part of this series; hence it being called part 4.5. I made a mistake in the previous part 4 article of this Portfolio Development series.

After I posted the previous article about creating a US momentum trading system, a subscriber was kind enough to point out to me a very subtle survivorship bias within the system. Now, don’t freak out, I have fixed the system and it still works just fine, the updated code will be provided at the end of this article.

Since I am in this awkward position, I figured I should make the most of it and use it as an opportunity to discuss mistakes in system development. In this article, I want to:

• Discuss the mistake in the system

• Discuss why it matters

• Discuss how it could have been avoided

It’s important not only as a learning opportunity but to also point out that even someone who has been doing this for years can still make mistakes!

If you missed the previous article, check it out here. There is still a lot of informative content aside from the mistake!

The Survivorship Bias Mistake:

The coding mistake within the momentum system was within the breadth filter. The current breadth filter logic is as shown below:

BreadthFilterThreshold: 0.5	
BreadthFilter1:	#Sum InOEX
BreadthFilter2:	#Sum C>MA(C, LongTermLookback)
BreadthFilter:	BreadthFilter2 / BreadthFilter1 > BreadthFilterThreshold

In English, this code was meant to:

1. Sum the number of stocks currently in the S&P 100 index

2. Sum the number of stocks in the S&P 100 currently above the 200 day moving average

3. Only take a trade if 50% of stocks in the S&P 100 are above the 200 day moving average

The survivorship bias issue occurs in step 2. I missed a conditional to only sum the number of stocks above the 200 day moving average if they are a constituent of the S&P 100 at that point in time in the backtest. Accurate historical constituency is key.

Instead, this rule was checking for 200 day MA uptrends in all stocks currently in the S&P 100, previously in the S&P 100, and to be added in the future to the S&P 100.

This issue is a mix between what's called survivorship bias and a future leak. The breadth rule was using data in the calculation that would not have been available at that point in time.

This is obviously no good, hence why I need to fix it. This can severely skew results, and survivorship biases and future leaks are generally some of the worst biases in backtesting. Luckily, the impact to the system is minor, but more on that in a bit.

It is why it is extremely important to have an accurate index constituency time series. This makes it so a strategy can know what stocks were in the S&P 100 every single day of the backtest. In this case that is what the InOEX function does in the RealTest code.

Survivorship bias and future leaks can wreak havoc on live trading results. A backtest with survivorship bias/future leak may look fantastic, but once you go live your results are slowly going to degrade over time.

This is because during live trading we don't know what the future holds, so the system is only going to be using the current data. But as time goes on, the system will be subtly adjusting it's historical performance as new future information is known. The history of the backtest will be “repainted” as some call it.

You’ll notice that some of your live trades inexplicably change. You may also notice that your live results look a lot worse than the backtested results over the same period. It’s a slow and subtle degradation in between live and backtested performance.

For example, let’s say a handful of new stocks were added to the index in 2021. With a future leak/survivorship bias, the breadth filter calculation is going to include the stocks that were added to the index in 2021 for all years prior to 2021 as well. But before 2021 we would not have known those stocks were going to be added to the index yet. The system was making decisions based on unknown future data.

The equity curve will essentially be constantly changing with every stock that is added to the index. The back test will not be static, it will be a constantly moving target that is impossible to hit because you don't know the future; but the backtest does.

Luckily The fix is relatively straightforward. All I need to do is add the conditional to check index constituency in the rule that calculates if the close is above the moving average.

BreadthFilterThreshold: 0.5	
BreadthFilter1:	#Sum InOEX
BreadthFilter2:	#Sum If(InOEX, C>MA(C, LongTermLookback), 0)
BreadthFilter:	BreadthFilter2 / BreadthFilter1 > BreadthFilterThreshold

These are the subtleties in back testing that are really easy to mess up. I've been doing this for over 5.5 years now and I still sometimes make subtle mistakes like this, everyone does.

Luckily the mistakes have reduced over time but obviously from time to time they still creep in. This is why it is extremely important to double check your work and if you have a second pair of eyes to look over your system code, that never hurts as well. Especially when the mistakes are not obvious, such as this one.

Removed Survivorship Bias Results:

After implementing the fix to remove the survivorship bias/future leak and ensure a proper historical index constituency, I re-ran the backtest. Shown below are two backtests comparing the original results with the survivorship bias free results.

Original US Momentum System - Survivorship Bias In Breadth Filter:

US Momentum System - Fixed Breadth Filter, Survivorship Bias Free:

Luckily, the results actually got better after removing survivorship bias. This is not common, I’ll reiterate that we got lucky. Returns increased by 1% and drawdown decreased by 5%.

The results got better likely because he breadth filter was being flooded with the price action of irrelevant stocks. A stock that joined the index in 2015 was being used to calculate breadth in 2000. Basically there was a lot of non-useful information being fed into the breadth filter, making its result more noisy.

Yes, future data was being used, but in this case that future data wasn’t actually that helpful to the system. It’s like cheating on a test by getting a hold of the answer key, but the answer key was for an outdated version of the test.

I decided to check and see if the breadth filter was even needed. I ran a quick optimization on the breadth filter threshold. Breadth threshold being defined as the percentage of stocks above the long term moving average within that index. The results are shown below:

Sharpe vs. Breadth Threshold Value:

ROR vs. Breadth Threshold Value:

Max Drawdown vs. Breadth Threshold Value:

Number of Trades vs. Breadth Threshold Value:

The Sharpe and rate of return are basically unchanged until the breadth threshold becomes 0.5 or so. Then the Sharpe and ROR drop off in terms of performance. Max Drawdown also follows a similar trend. Also, if you look at the number of trades, that drops off a cliff at the same rate.

This tells me the breadth filter is essentially just choking the system. It doesn’t do anything until after a threshold of about 0.5. Then for values higher than 0.5, it’s just reducing the number of trades, decreasing ROR and Max Drawdown proportionally. Thus, I am inclined to remove the breadth filter all together, it doesn’t appear to be adding to the system.

Avoiding This Issue In The Future:

There's actually another step that could have been taken that would have prevented this mistake from happening in the first place. In my system development process, I have a step where I ensure the significance of each rule in the system.

After I’ve finished developing the system, I go rule by rule and ensure that its contribution to the system performance actually matters and that the rule deserves a place in the system. For whatever reason, with this particular system, I forgot to do this step. I apologize for that.

What I’ve realized is that this breadth filter rule actually doesn't contribute that much to the system performance. The index filter and the breadth filter more or less perform the exact same function, and really I only need one within the system.

So, I could completely remove the breadth filter and the system would still work fine. In my eyes, this would be a great solution because it would remove needless complexity from the system.

As I always say, a system should be the simplest viable solution to capture the market effect you're aiming for. In this case I can get more or less the same results without the breadth filter. Removing it makes the system simpler and less complexity leads to less chance of error; and this whole article has outlined how error has already snuck into the system.

So, removing the breadth filter from the system results in the equity curve performance as shown below.

US Momentum System - No Breadth Filter, Survivorship Bias Free:

As you can see the system still performs just fine without this filter. I personally would just trade this version of the system without the breadth filter.

But, in case you want to explore the breadth filters impact more, I have both versions of the code below, with and without the fixed breadth filter. Maybe you’ll be able to find a better way to model it such that it has a more significantly positive impact on the system.

Conclusion:

This article is a great lesson in not only double checking your work but having a second pair of eyes to examine your systems. Luckily, in this case the survivorship bias/future leak in the system actually didn't have too much of an impact, but generally we don't get this lucky.

After fixing the survivorship bias/future leak and then examining the results with and without the breadth filter, it was determined that the breadth filter is needless complexity that doesn't add too much to the overall system performance.

Now that the system is fixed we can move on to the next article in the series which will focus on an ASX trend following system. Special thanks to the subscriber that pointed out this survivorship bias issue and working with me to resolve it.

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Corrected Real Test Code With Breadth Filter:

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