Diversify or Die – The Benefits of System Diversification

System diversification is a great way to manage correlation between return streams. There are many different ways you can diversify to achieve improved risk-weighted returns including:

  1. instrument diversification…..ideally across asset classes whereby you look for uncorrelated instruments that allow you to achieve higher risk-weighted returns than what is achievable with a single instrument;
  2. timeframe diversification which also allows you to deploy uncorrelated return streams to optimize risk-return relationships; and
  3. system diversification in which you deliberately construct your return streams to offer uncorrelated relationships.

Of the different methods described above, system diversification offers additional benefits to that delivered by 1) and 2) in that you can actually design your uncorrelated return distributions to remain constant as opposed to leaving matters to prevailing market conditions. Where 1) and 2) become more problematic is that given the non-stationery conditions of a non-Gaussian market, there is no guarantee that the correlation between return streams remain constant. What may be uncorrelated at one point in time, may become correlated in other periods when market conditions change.

The way we look at systems designed to attack particular market conditions is that “No single system can be profitable across all market conditions, however a blend of uncorrelated systems has the ability to address a suite of market conditions”.

Now either you can deploy market condition filters to turn ‘off’ or ‘on’ your different systems to capitalise on conditions that respond to the strengths of each system….or alternatively you can develop very robust systems that outperform when conditions are favorable and manage capital stringently when conditions are unfavourable….and therefore keep each system turned on all the time. We prefer the latter technique as the deployment of market condition filters are inevitably lagging in nature and when you turn on your system, you may find that market conditions quickly turn unfavourable and there is a lag before you turn them off.

If you prefer the former ‘market condition filter’ approach, then one way to achieve this is to run live walk forward systems in demo mode in tandem with your live systems and when the demo accounts are entering drawdown, then turn off your live system trader until we see a reversal of drawdown fortunes where you then turn the live system on again…..but despite the theory you may be a bit disappointed with the outcome (given the lags described above).

In designing your portfolio of systems it can be helpful to think in terms of the following:
1. Classify your systems into two broad categories….whether they are divergent systems (capitalise on trending periods), or whether they are convergent systems (eg. mean reverting systems). Obviously these two broad system types are uncorrelated or anti correlated to each other. When one system is performing well the other is floundering and vice versa.
2. Determine which system you will use as your major bread-winner. This should be the system with the best risk-weighted performance metrics and have positive expectation. I tend to find the safest bet is to ensure the major bread winner is a divergent system with high positive skew (eg. many small losses with occasional large wins). This ensures that your total portfolio when constructed also is dominated by positive skew which assists in robustness tests.
3. Select a system from the alternative category which also has positive expectancy which is uncorrelated or anti-correlated with the primary system and adopt a lower allocation weighting to ensure that this additional system supplements as opposed to dominates the mix.

A Practical Guide to Implementation

Any type of trending strategy is likely to perform well when the market is trending….but likely to flounder and enter drawdown phase when market conditions are non-trending. Trend following or momentum following strategies owe their existence to the market principle of divergence where under certain market conditions, price takes an excursion away from a historic mean.

Non trending markets however can be broadly categorized into markets that do not diverge away from a mean but rather converge towards a mean. For example what some call counter-trend strategies may fall into this category or those strategies that operate on the principle that an overextended market will tend to converge back to a non-stationery mean (eg. sideways congesting markets etc.)

In back testing….contrary to what many might think… is not actually the sample size that is the most important factor in testing system robustness as market conditions can remain in place for indeterminate periods of time. What is the most important consideration in your testing is the degree to which your system performs over the greatest variety of different market conditions. This is a better statement of system robustness that using a defined sample size. Of course sample size is a proxy for this as the greater the number, the more chance you encounter a greater variety of different market conditions but it is no guarantee….so using a fixed number like a back test of 200 trades etc. to be representative of a more robust performer is a bit of a misnomer. If your system is a high frequency trader then that sample size can potentially arise in a single market condition. In testing your system under an array of different market conditions…..then the longer the test the better. There is no fixed number of assuredness.

The way to assess the strengths and weakness of your system is to plot how your equity curve (or system return distribution) performs under different market conditions. We do this visually by superimposing the equity curve generated by the system over market price for the same period and then identifying in what market conditions the system flourished and in what market conditions it didn’t. Having this understanding of the relationship between your system performance and the market provides powerful info that you can capitalise on. For example if you can define in what conditions it doesn’t perform, then this gives clues in system design how to develop a complementary strategy that outperforms during these poor conditions for your primary strategy…..and hence under a blended arrangement, the drawdown of your primary system will be reduced by the draw-up of your secondary system.

So start closely looking at equity curves (return distributions) of your different systems and how they blend when you merge them together. Correlation statistics give you a little bit of info…but equity curve comparisons tell you so much more in relation to correlation. In portfolio management, correlation of return streams (equity curves) is perhaps the most important thing to get your head around.

For example have a look at the equity curves and statistics of the two different systems below.

Momentum Trader (Divergent)

The chart above details two different systems. Let’s first focus on the first system first (being the divergent momentum trader referred to as “Momo Trader”)

The “Momo Trader” is a breakout trader (a divergent system) that performs very well when markets are divergent in nature (eg. trending). The strong equity growth between Jan 2013 to June 2013……and between Sep 2014 to Mar 2015 were when markets were volatile and had extended periods of trending behaviour where things took off. During these periods, drawdowns were eliminated (refer to drawdown profile of the charts above). Outside of these trending periods, the system was quite robust as despite unfavourable non-trending market conditions, drawdowns did not become pronounced and were restrained below 10%.

Now have a look at what this system achieves in isolation over the 7 year testing period.

CAGR: 28.34%
Max Draw: 10.71%
Skew: +1.00

The compound annual growth rate (CAGR) was 28.34%. Some years produced returns of >50% while others produced low returns of around 4-8%. The variation can be attributed to different market conditions over the period as we always methodologically apply the same strategy irrespective of the nature of market condition.

Also look at the maximum drawdown of the system of 10.71% which arose in August 2014 immediately prior to the system taking off into the stratosphere in Sep 2014.

Now look at the CAGR/DRAW ratio of 2.65. This is an important risk-weighted metric that you use for portfolio blending purposes. Also look at the skew of 1.00. Such high positive skew demonstrates that the strategy is designed to take many small losses but has the potential to achieve a few very large gains. This is attributed to its strict risk management policy while it lets profits run to capture potentially unlimited upside. This positive skew is a great weapon for robustness in protecting yourself against black swan events. In fact, the open ended profit nature of this strategy allows you to participate in exceptional white swan events (that would be a black swan for other systems).

The “Momo Trader” produces these results with a 1% trade risk taken on each trade. If we doubled this risk% to 2% by doubling the position sizing of each trade taken, I would generate a CAGR of approximately 56% over the period with a Max draw of approximately 21%. The MAR ratio would stay constant. Notice how we have scaled down my position sizing through my trade risk % to achieve a max draw we are comfortable with. The bottom line is that you can scale up or down any risk metrics of any system using position sizing….but with an isolated return stream you cannot avoid the relationship between increased return and increased risk no matter how you cut it…..but under portfolio management, where you blend return streams you can actually do something about this relationship…..and there lies the beauty of diversification.

Overall over the given period, the strategy has positive expectation. This is an important criteria as you can do things with positive expectancy under portfolio management utilising the free lunch principle of blending uncorrelated or anti correlated return streams. If two different return streams have high positive correlation then when in unfavourable market conditions, both systems perform poorly and vice versa for favorable market conditions. Trading two strongly positive correlated return streams therefore makes the combined return stream of both systems far more volatile….which is a bad thing.

If two different return streams are anti-correlated (opposite), then when one system is in draw-down, the other system is in draw-up. This is a great thing as the overall return stream of the combined systems is almost linear in nature. When this occurs you can magnify your position sizes to achieve far higher total return than what can be achieved by a single system with far lower drawdowns. This allows you to more efficiently utilise your finite capital to get far higher bang for buck. Achieving this holy grail of portfolio management (namely trading two perfectly anti-correlated systems) is a difficult endeavor to achieve as you not only need two different return streams in which both have positive expectancy but also correlations do change over time. Note however that through a knowledge of system design, you can manage this outcome with far greater precision than what can be achieved by instrument diversification of timeframe diversification.

So if you cannot muster an anti-correlated relationship…..then the next best thing is an uncorrelated relationship. What this means is that the two systems have no causal connection between each other and their individual return streams are effectively independent. What this allows for then is the ability to merge the return streams with the confidence that it is very unlikely that both systems will be in drawdown at the same time. The result therefore will be a composite return stream whereby the overall drawdown is diluted (given that each systems drawdowns are likely to occur at different times), yet you can summate the overall returns of both systems to achieve a far higher risk-weighted return.

Look at the MAR ratio (CAGR/DRAW) of EDTT. It is 2.65. Remember this result as we move on to the next Mean Reverting System.

Mean Reverting Trader (Convergent)

The supplementary system is a mean reverting long only trader (referred to as the “Boll MR Long Trader” that operates well as a convergent trading style.It uses a Bollinger band to identify when price appears oversold and will take a long position on the assumption that price will revert back to the median regression of the Bollinger band.

Go through the steps we just took with the the prior Momentum Trader to identify when this system over-performs and under-performs. Also refer to the key performance metrics:

CAGR: 7.63%
Max Draw: 10.96%
Skew: -0.56

On their own these statistics would not be very appealing but what is critical is the positive expectancy and how the equity curve is uncorrelated to the primary system. Refer to the system comparison chart again.

Look at the equity curve itself and cross compare this to “Momo Trader”. Refer to the areas circled in the equity curve chart. A yellow circle reflects an uncorrelated relationship which is good and the red circle represents a positive correlation relationship which is bad and leads to building drawdowns during unfavourable times) 

By visual comparison of equity curves you can see that it is very uncorrelated without even having to refer to the correl statistic which demonstrates an almost perfectly uncorrelated nature of -0.003. Remember that a positive correlation of 1.00 is bad and an anti-correlated relationship of -1.0 is fantastic. Well in this instance the relationship is close to 0 which represents an uncorrelated relationship.

Now Let’s Blend Both Systems

Look what is achieved with the blend and compare this against that stats of the single systems in isolation.

CAGR 40.13%
Max Draw 10.58%
CAGR/Max Draw 3.79
Skew 0.99

Lo and behold….through simply consolidating both systems into a single portfolio we have almost doubled the return of the “Momo Trader” in isolation with the same level of drawdown plus we have been able to retain the very favorable positive skew. Also now look at the MAR ratio and see how much higher it is compared to the individual system results.

If you can understand these simple principles…you will realise that the secret sauce in this game is not the efficacy of a single system, but rather the benefits that diversification brings to the game through magnifying your risk-weighted return. Understanding this principle may turn your fortunes around in trading. It takes you to a new place where you can focus on very simply systems that in isolation do not appear attractive….but under a portfolio can be very powerful beasts…..and it allows you to avoid the propensity to look for curve fit solutions that do not stand the test of time.

When you start practicing the art of portfolio blending you realise that a failure is not measured by the trades you take…..but rather in the trades you missed that turn out to be windfalls. Having your systems turned on all the time ensure that you can participate in the action when the market decides it is time to do so…..otherwise you find that you tend to over-trade to make things happen as opposed to allowing the market to decide when it will happen.

Trade well and prosper

Rich B

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