The Holy Grail and Tail Risk in Trading

 

In the article on Edge and Expectancy, we’ve learned that the foundation for making a profit in trading must be built on having an edge. Since the market is largely random, individual and short-term outcomes are unpredictable. A better approach is to evaluate a strategy’s performance over a large number of trades.

The process of discovering and building an edge in the market is a continuous, repetitive cycle. It begins with ideas, then turns those ideas into trading systems that can be executed in real markets, and finally involves testing the results and deploying them in actual trading.

One crucial factor to pay special attention to when building a strategy is tail risk. In financial markets, where fat tails exist, everything we observe and measure about the tail does not accurately reflect the actual risks we may face in the future. Tail risk refers to extreme events that occur more frequently than predicted by standard statistical models, and these events reside in the tail of a distribution, often distorting model outcomes. It’s possible that all our statistics on expected value and edge may be misleading—and in reality, a backtested strategy may have no actual edge. In the future, the emergence of a massive extreme event—far beyond anything we've seen in historical data—could cause the entire strategy to collapse.

Consider a turkey that is fed every day. Each feeding reinforces its belief that the general rule of life is that it is cared for by friendly humans and that there is nothing to worry about. But on the Wednesday afternoon before Thanksgiving, something unexpected happens that delivers a massive shock to the turkey. It is slaughtered, and all the happiness it has accumulated collapses. If Thanksgiving Day is excluded, the turkey’s expectation is a positive one—where its happiness and weight increase steadily each day.

If we take the set of trades from a given strategy, summarize the outcomes, calculate the probability of each outcome within the entire set, and then plot a probability distribution—just like we do with price data—we will obtain a probability density function. Depending on how the strategy trades, we’ll get different types of distributions. Two strategies may both have positive expectancy and exhibit stable equity growth, but when we examine how profits are distributed, their nature can be fundamentally different. Take a look at the chart below: we see the equity curves of two strategies, both with positive expectancy, and both tested over the same period from 2004 to 2024. Now, when we plot the distribution of trade outcomes for these two strategies, the results are shown in the chart below.

Looking at the chart above, in the distribution of the first strategy on the left (in red), we see that it resembles one half of a full distribution. There are many small winning trades and a few large losing ones. The chart has a long left tail, indicating the presence of tail risk. The expectancy of this strategy appears solid within the observed dataset. However, if applied in the future and faced with a tail event far more extreme than what was seen in the past, the strategy could be completely wiped out—just like the turkey mentioned earlier. Its equity curve may look smooth and consistent, but it will fail catastrophically when a fat-tail event appears.

Strategies that exhibit this kind of tail risk are often DCA (Dollar-Cost Averaging), loss-averaging, martingale, or use compounding-style position sizing. For a period—sometimes even decades—their expectancy can appear positive. But due to the embedded tail risk, they are doomed to blow up one day in the future.

If you search for a trading signal on mql5.com—the world’s largest platform for trading strategies and signals—you can easily find a strategy with this kind of tail risk. The strategy shown in the chart above displays very steady monthly growth and profits for over a year. Within this trading period, its expected value is clearly positive.

However, if you look more closely, you’ll notice this strategy is highly dangerous due to its exposure to left-tail risk. The reason is that the Equity line (green) remains consistently below the Balance line (blue) for most of the time, indicating it may be a short take-profit strategy, a DCA-style system, or one that avoids using stop-losses.

This suggests that its losing trades may have no defined limit. The strategy will appear effective—until the moment a massive tail event appears and wipes it out.

A type of strategy even more dangerous than one without stop-losses is the martingale strategy. Although it does use stop-losses, the core idea behind this approach is that you double your risk after every loss. In theory, if you had infinite capital, this strategy would eventually win.

However, in reality, losing streaks can last much longer than expected. There is no way to accurately measure the maximum number of consecutive losses you might face. If, in the future, a losing streak extends too far—say, 30 consecutive losses—your risk on a single trade would become enormous.

If you started with a $1 risk, after 30 losing trades, the exposure would be 2³⁰ = $1,073,741,824. That means you're risking over 1 billion dollars just to win 1 dollar. Clearly, this is not a wise way to make money.

One way to identify this type of strategy is by looking at its equity curve: you'll notice sharp drawdowns—steep drops—followed by rapid recoveries that quickly surpass previous highs. I’ve personally coded and built such strategies, so I understand very clearly how the equity curve behaves.

The problem with this type of strategy doesn't lie in the expectancy ratio, but in its position sizing and capital management. This kind of money management creates tail risk that cannot be measured or controlled.

Most of the signals on this website are built using such methods. Signal providers aim to generate attractive expectancy and steady profits, often by using only a small portion of the account’s capital, in order to attract copiers.

Their goal is to collect subscription fees from naive investors, without concern for the capital that may be wiped out by tail risk. Signal providers benefit from the fees while only risking a small amount in their sample accounts when things go wrong.

Take a look at the strategy with tail risk shown in the chart above. This is a strategy that does not use stop-losses and takes short profits. It has demonstrated excellent performance over a 15-year period, with positive expectancy and a smooth equity curve showing very few drawdowns. During that time, no major left-tail event occurred, which made the strategy appear highly effective.

However, this is purely a matter of luck. Just look at the chart below—when the same strategy is applied to a different asset over a longer time horizon, it becomes clear that it has no real edge. When tail risks occur more frequently, the strategy produces negative expectancy. There are extended periods—5 to 10 years—during which the strategy performs well and shows strong growth, but as soon as a tail event hits, all the accumulated profits vanish.

Its behavior closely resembles the turkey problem mentioned earlier. Because it does not use stop-losses and relies on flawed position sizing, the losses of this kind of strategy can grow without limit. If tail events become more extreme in the future, the strategy will perform even worse.

These types of strategies are the favorites of broker-affiliated signal sellers or those who monetize copy trading. They use the illusion of remarkably stable performance to deceive the uninformed. Over periods that can stretch beyond ten years, the strategy may show steady growth—allowing them to advertise and promote its profit potential. But that is not how real wealth is built. Once a tail risk strikes, all accumulated profits vanish.

Strategies with extremely smooth and stable equity curves are highly likely to carry tail risk—because in financial markets, stability either doesn’t exist or comes at a very high price. A strategy without left-tail risk, when applied in real markets, should exhibit a mix of growth and drawdowns. Its equity curve should look more like a price chart—this is the kind of strategy with the green profit distribution on the right side of Figure 2.6 mentioned earlier.

I believe this type of strategy is the true “Holy Grail” of trading. It carries no left-tail risk, has positive expectancy, and features a fat right tail. These characteristics make it uniquely powerful in real-world trading. It is capable of withstanding unseen tail risks, has statistical edge to grow profits, and can capture massive upside tail gains that haven’t appeared in historical data. In fact, its real-world performance can exceed what backtests suggest.

I tried searching for this type of strategy on MQL5, but found nothing. It’s likely that traders who have developed such strategies prefer not to share them. So, I uploaded one myself. The chart above shows such a strategy.

This strategy follows the principles I mentioned earlier: it uses strict stop-losses and does not set a profit target, allowing profits to run as far as possible. You can see that the account's Equity value remains above the Balance value for most of the time, indicating that this is a cut-loss-short, let-profits-run strategy.

Essentially, this approach cuts off the left tail of the profit distribution. It produces positive expectancy and does not carry tail risk. You can check it directly here.

The chart above shows how the strategy behaves during backtesting. The green line represents Equity, while the blue line represents Balance. You’ll notice that at certain points, Equity increases while Balance decreases. This indicates that the strategy is allowing profitable open trades to run while cutting losing trades.

The Equity curve above acts as a driving force, pulling the account upward, while the Balance curve below serves as a protective barrier, preventing the account from drawing down too deeply. This behavior is the exact opposite of the earlier tail-risk strategy—where Balance increases but Equity declines, showing that the strategy took profit early and let losing trades run.

When starting to build a strategy, beyond measuring expected value, we must also be mindful of tail risk. Any strategy that carries left-tail risk cannot have its expectancy accurately calculated or measured. The risk and edge metrics such strategies reflect in historical data—even over decades—are fundamentally misleading.

In practice, we can manage tail risk for such strategies by setting a stop-loss limit at the account level when drawdowns become excessive. This can help eliminate extreme left tails. At that point, the strategy may potentially become one with a genuine edge.

However, what’s crucial is that we must be able to measure the impact of that intervention on the overall performance across the full cycle. And that is often not feasible—because fat tails appear so infrequently within the observable dataset.

When unmeasured tail risk finally strikes, it can be so severe that all the profits we've ever made vanish—rendering years of trading effort meaningless. Worse still, if we don’t place limits on the account and stubbornly let losing trades escalate—such as continuously adding funds until we run out of money, or even going into debt to fund losses, or doubling down through DCA with increasing position sizes in hopes of recovering—we may end up bankrupt.

Trading a strategy with unbounded left-tail risk is like playing Russian roulette. The only difference is that our gun has more chambers. But if we play long enough, sooner or later, we’ll end up pulling the trigger on a loaded chamber.