We often hear the question, “what is the ideal sample size to use to test the robustness of your trading strategy?”. Well the question is a bit like the ‘how long is a piece of string?” question.
The reality is that the sample size is less important than the different array of market conditions encountered. For example in the High Frequency Trading environment, the sample size is huge (within a single market condition)….and strategies deployed in the very short term environment are very unlikely to still perform if conditions change (some exceptions here like order ‘front running’ bots). We use sample size more as a proxy to ensure we have a better chance of being exposed to alternating market conditions.
Certain classes of strategy (eg. divergent strategies) such as trend following and momentum methods ‘rely’ on non-stationery conditions and make their profits with market disruptions. Their performance results are a consequence of their style. They typically have Low win rates but relatively high risk to reward ratios….but perhaps more importantly they possess positive skew. A high positive skew means that you tend to have many small losers but occasional very large winners. This positive skew creates the volatility in their equity curves. This doesn’t mean they are ‘worse strategies’ or have ‘higher risk exposure’. In fact the outstanding track record of diversified systematic Fund Managers that embrace positive skew demonstrates that they are far more long lasting than their convergent cousins and there are a swathe of white papers to demonstrate the efficacy and long lasting nature of these approaches.
The times these class of strategy shine are during volatile less stable market conditions. At other times when the markets are more predictable in nature, they churn to simply keep their heads above water while waiting for markets to dislocate towards new equilibria. Statistically these strategies are deployed to catch ‘fat tailed’ events on either side of the probability distribution.
The key to success in the divergent space is your ability to endure disappointment and continuously manage the downside risk. For most long term successful divergent strategies approximately 90% of trades or so are taken simply to keep the head above water…but the anomaly (say 10% of trades) were what led to the overall strong performance metrics of this solution.
The possible reason that alpha (arbitrage opportunities) persists for trend following and momentum based strategies is that the game is very hard and requires intense discipline and patience. You simply are diversified and follow price….. again and again and again …….with the same recipe….and let the market decide when it gives you a windfall.
The flip-side however to this argument is that convergent systems that possess negative skew may have a hiatus in the sun over a short term interval…..but are very unlikely to last more than a few years duration. They rely on the leptokurtic peaks of the profit distribution for their bread and butter as opposed to the ‘fat tails’ like divergent traders.
Where divergent strategies come undone through death by a thousand cuts is when the fat tails are few and far between. On the contrary in a fat tailed environment, convergent strategies come undone very quickly.
Under a normal distribution, no strategy wins. Under a Non-Gaussian distribution you get two broad styles of trading strategy that can harvest arbitrage (the tails and the peak of the distribution).
Convergent styles of trading strategy work on the principle of reversion back to an equilibrium such as mean reversion styles of trading, counter trend trading, buying the dips and selling the tips, fundamental investing, grid trading and Martingale variants whereas divergent styles are forward looking and simply assume that conditions will change. Convergent styles are therefore backward looking and rely on prediction, namely that price has taken an excursion away from a stationary equilibrium….but in the future will revert back to this ‘known point’. The assumption typically used by this type of strategy is that the market becomes over-valued or undervalued and will revert.
You will identify a convergent trader by virtue of some of the comments you will hear such as…..this trend is overextended, it’s better to wait for a retracement in a trend before entry to get a better R:R etc etc etc. The statement is typically couched in predictive terms. This is great while it lasts but totally disruptive while it doesn’t.
A divergent trader on the other hand avoids any form of predictive statement and has no opinion on price other than ‘the current price is right’. They are simply relying on the future price being at a different place to where it is now and hence they simply follow price like a shadow with tight trailing stops designed to get them out quickly when price changes direction and they do not attempt to project a future price position.
Now despite the fact that we might hear that a trader is a trend trader, does not necessarily imply that they are a divergent trader. In fact divergent traders are few and far between and tend to occupy the professional fund management space. The way you tend to sort out the who’s who in the convergent or divergent space is based on the assumptions applied by each style of trading that are either predictive or non-predictive in nature.
The primary reason that we don’t find many retail traders occupying the divergent space is that to survive long term as a non-predictive trend trader, you cannot afford to pin your hopes on a single instrument, timeframe or applied system and hence you cannot afford to have favorites and you need to be diversified which tends to imply that you need a greater capital base (though times are changing and not necessarily the case anymore). As a divergent trader you just never know when the moments of alpha will arrive. You operate in the land of the Law of Large Numbers as opposed to the land of ‘preciseness’ and you mercilessly manage your exits for risk mitigation and to preserve your capital base. You therefore need diversification as a means to improve your chances of a lucky strike to survive the brutal assault of the thousand cuts to your capital. For that reason, you will find that the divergent trader is always heavily diversified and also approaches this game from the perspective of the overall portfolio result as opposed to the individual return stream generated by a single component of the strategy.
The chart below represents the Trend Following Index which comprises the equal weighted index of 54 diversified fully systematic trend following FM’s which apply divergent solutions in their trading enterprises.
The overall line of best fit generates a CAGR of 9.3%. The market conditions can in hind-site be attributed to central bank intervention during mean reverting periods, whereas the volatile market disruptions can be attributed to events such as Brexit, the GFC, oil shocks etc. The key to this diagram relates to how different strategies fair under different market conditions.
You can see from this aerial view (refer to chart above) that a single market condition such as a mean reverting environment can last for extended periods up to 10 years etc….however when conditions change, you get a massive disruption to participants where the prior equilibrium is disrupted and our mean reverting cousins become extinct.
If you only focus on the short term time horizon to derive your strategies, chances are you will skew your portfolio towards ‘convergent styles’ that bear far more intrinsic risk. They typically have high win rates but lower Risk to Reward ratio’s and they tend to also possess negative skew which is a sure sign that they bear intrinsic risk far greater than what is revealed by their ‘closed position’ equity curves. If you had access to their floating equity curve….you would see this intrinsic risk in action.
Other strategic styles that have negative skew are Martingale and Grid Trading variants. The symptoms of this style of strategy is that their equity curves look glorious for a period of time….until they don’t….and the account blow up comes without warning. You would think that you could turn off these strategies in time to save yourself from account blowup….but rarely is this the case as a degree of prediction is required to know when to turn them off.
Unfortunately when it comes to convergent strategies with negative skew (which work on the premise that market conditions are stable and price will revert back to a *known* equilibrium), the equity curve you experience during periods of exuberance when things work to plan is not the full story over extended periods where market conditions alter. That nice linear equity curve you are experiencing and the high win rate is a symptom of your strategy responding to the current market condition and this can last for extended periods. Sure it may be a great winner over these periods of stability, but you might be in for a rude shock when conditions change. The negative skew signature means that you frequently take small wins but occasionally take larger losses. When market conditions change you find that a small sequence of large losses is enough to blow your account.
You will frequently hear the statement from a convergent trader that the strategy is a winner….(and then in small print) provided you can keep away from trending periods. That is because they are hiding the big picture. Mean reversion works until it doesn’t and then it is usually game over unless you deploy risk mitigation methods that tends to interfere with those illusory straight equity curves and reflect the more realistic picture. Now this isn’t to say we cannot deploy some convergent systems in a diversified portfolio as it is a means to improve cashflow reliability, but it certainly means that you cannot afford to overly bias your portfolio towards convergence.
For divergent strategies, the antithesis is true. Divergent systems are forward looking and do not assume that price will revert back to a historic point of significance. Rather their philosophy is couched in uncertainty itself and the philosophy assumes that the past is no reliable guide for the future. In fact they bet on the principle that price will not respect a past equilibrium but rather dislocate from the current market condition and reach for a new *unknown equilibrium*. As a result, divergent systems plan for the unexpected and work on the principle that most times you will be wrong in your future assumptions that market conditions will change….but while conditions remain constant you stridently manage your risk taking numerous small hits….until the dislocation happens where you ride the transition to the new market equilibrium until it lasts…….which hopefully pays for the past sequence of hits and quickly brings you out of drawdown. You will never know the exact destination of the new equilibrium but you open your system constraints to at least follow the price movement while it lasts.
So how much data is enough data? In terms of the philosophy of this thread, then there is never enough data. The reason for this statement is that we want to test if our strategies stack up in as many different market conditions that we can muster, as we are not concerned with how profitable we will be in the future. We simply want to ensure we have covered our bases and have a robust model that has survived the storms of the past and are more likely to survive into an uncertain future.
To harvest the non-predictable beneficial offerings of uncertainty you need to be able to participate in the unpredictable moment and that requires you to be present at the right time (when the market decides). If you focus on the profit side of the equation without paying heed to the risk side of the equation (which is something you can actually do something about) you may have a brief life of exuberance….but chances are over time that you will end up in traders heaven.
Unfortunately this philosophy therefore encounters a problem with over-inflated expectations. For a strategy to survive over the very long term, you need to prepare yourselves for a shock. To survive in the long term, a single strategy must endure horrific drawdowns when compared to the returns they deliver. Long term robust strategies typically have average annual returns half the size or less of their maximum drawdown. This ultimately caps the aspirations of traders seeking an immediate ‘ticket to riches’…..but this is where so many pundits get it wrong. They send those strategies to the bin and system hop as a result, where in fact this was simply a realistic outcome resulting from the volatile signature of all stationery strategies.
So for example if you can endure 30% drawdowns then expect an average annual return of <15% per annum in the long haul. The relationship between Return and Risk is important here as it is scalable with leverage (eg. position sizing). What this means is that if you double the position sizing then expect a drawdown of 60% and return of <30%….but let’s keep going into unrealistic land and assume we want a 50% average annual return. Sorry, you have just blown your account.
What this in reality land of uncertainty means (given that this is an average) is that you have to trade with small risk exposure to survive over the long term and this dictates your earnings potential but in conjunction with this premise is that to survive over long term trading horizons you need to expect being underwater for long periods of time.
For those traders who have faced the long term, this symptom is one of the realities you need to face in your trading life. If you cannot accept this simple reality you are doomed as a long term trader…..however all is not lost provided you are prepared to diversify your systems, instruments and timeframes but to do this successfully needs you to shift your focus from the individual trade result and focus on the long term result and the bigger picture of the entire portfolio.
Trade well and prosper