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Trading Diversification: A Free Lunch?

diversified hats
 
The more I think about system design, the more I get convinced that diversification is a key to great performance.

As the cliche goes:

Diversification is the only free lunch on Wall Street.

This is a concept equally shared by Modern Portfolio Theorists and Trend Following Wizards, who usually emphasise the concept – and are often quoted as trading around 100 different types of instrument, if not more.

The State of Trend Following report contains a decent level of diversification with around 50 instruments and I wanted to use this as a base to check the impact of diversification on performance.

The idea is to run the same strategy using a subset of the portfolio (ie less instruments = less diversification) and see how it performs.

The problem, though, in selecting a subset of instruments out of the 51 in the original portfolio is that it could affect performance in the same way as any portfolio selection can (ie you could obtain vastly different results in trading the same system with two different sets of instruments, just by virtue of a “lucky” pick of strong performers).

Historical Performance

First, let’s get a reference point and look at the historical performance of the system chosen for this test: the 20-50 Moving Average system. Below is the performance back-test of that system over the last 20 years with the original portfolio:

equity-curve-log

Performance Stats
CAGR
29.68%
Max DD
43.60%
MAR 0.68
Sharpe Ratio 0.59
Trade Number 3629

 

Tests with Less Diversification

As mentioned below, the idea is to work on a subset of instruments and compare the results with the initial portfolio. To avoid any sort of data mining/hindsight bias in the portfolio selection, I decided to run a Monte-Carlo-like approach to test the system with multiple instrument subset combinations: instead of picking a single portfolio subset of 25 instruments, I’ll run the system over 1,000 different sub-portfolios, chosen randomly.

In order to get an idea of how gradually diversification affects the performance, I ran the test in three steps:

  • sub-portfolio of 15 instruments
  • sub-portfolio of 25 instruments
  • sub-portfolio of 40 instruments

All instruments are picked at random from the list of 51 instruments in the original portfolio.

Each of the 3,000 runs generated a full system performance record. Below are plotted the CAGR and Max Drawdown for each instance:

Click to zoom in

Click to zoom in

The original system is also represented as the yellow dot.

Note that the “portfolio randomizer” did not account for any logic in terms of sector allocation. The original portfolio is balanced over several sectors (currencies, energies, rates, agriculturals, etc.) and there is no account for correlation between the different instruments (obviously correlation plays a big role in diversification: there is not much point in having dozens of instruments if they are all strongly correlated). However, over the large number of simulations, the main ideas of the test still come through.

Another point is that the only difference between the different runs were regarding the position sizing of each trade (fixed fractional), which were adjusted to obtain results of similar magnitude in each test (a portfolio with less instruments will require a slightly higher position size to match the return/drawdown rate of a portfolio with more instruments).

Looking at the plot chart, there are two main observations:

  • We can see the gradual effect of diversification improving the system results by “moving” the cloud of performance points towards the left (less drawdown) and up (more return).
  • The other observation is that the more diversification there is, the lower the deviation in the system results – therefore providing more robustness and less chance of data mining impact from portfolio selection on your back-tests.

Diversification or Why the Coffee Cup Never Jumps

That last point makes me think of an example discussed by Nassim Taleb in his Black Swan explaining the averaging of randomness:

Yet physical reality makes it possible for my coffee cup to jump – very unlikely, but possible. Particles jump around all the time. How come the coffee cup, itself composed of jumping particles, does not? The reason is, simply, that for the cup to jump would require all of the several trillion particles to jump in the same direction, and do so in lockstep several times in a row. This is not going to happen in the lifetime of this universe

Every trade/instrument can be seen as a particle composed of a (large) random element and a smaller edge that we try to extract via a mechanical system.

A portfolio composed of too few instruments would be like drinking your coffee or tea from a cup made up of only a few particles: cups would be jumping around everywhere, making coffee drinking a perilous venture. Same concept applies to trading.

This is the way I see diversification: by adding a large number of mostly random elements, you can ensure that random moves have some cancelling effect on each other so that your “trading cup” never jumps. All that is left is to collect the small edge from all the instruments via your preferred trading strategy(ies).

In effect, this is how casinos operate – and with diversification you somehow get to be the house!
 
 
Credits: The use of a portfolio randomizer and the display of results in a CAGR/MaxDD scatterplot was directly inspired from user sluggo on this Trading Blox forum thread.
 
 

Hats picture credits: maiostra via flickr (CC)
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arrow20 Responses

  1. Paolo
    45 mos ago

    what are your thoughts about system diversification (trading different systems) versus instrument diversification (trading the same system with different instruments)?

    paolo

  2. 45 mos ago

    Paolo – I like them both!
    Seriously I think they complement each other
    Ideally I think one would want to trade a large diversified portfolio with a suite of systems, each trading different timeframes. Of course this would require a fairly high starting capital.
    I suspect this is what large CTAs do – and one of the reasons why some are set up as funds as opposed to managed accounts (BlueTrend for example, which has had impressive results since it started).

  3. 45 mos ago

    It would be interesting to conduct a similar study contrasting the benefits of adding additional trading systems based on small medium and large (static) portfolios to see what the relative benefit is. I guess you’d need a pool of different trading systems with differing, but positive expectancies. I think even adding inferior (but profitable) approaches certainly would improve the drawdown/return ratio. My own approach is to build as much instrument diversity with one good system before adding a second (yet to be done), then diversifying that. This approach is more instinctive though rather than based on testing.

  4. 45 mos ago

    Bevan – very true, although I like to think that the State of Trend Following report does that to some extent with the composite index, which is always much less volatile than its individual system components. Maybe an idea for a further post.
    Additionally, you might be interestd in this post I did a while back, mixing not systems but managers together. The resulting curve was very much benefiting from that diversification too with most funds underperforming that fund composite index.
    You can check it out there:
    http://www.automated-trading-system.com/trend-following-wizard-history/

  5. Pretorian
    45 mos ago

    I absolutely agree with the benefits of diversification. The problem is that the only way we have to choose assets for our portfolio for diversification purposes is through correlation, however correlation only has sense in a normal distribution not in a fat tailed fractal one (Mandelbrot pointed that out). That means that there is a limit for the free lunch, I think that is way many traders (Seykota, Eickhardt) suggest not beting the optimum size, becuase there is no way we can be sure about the distribution of our system.
    On another comment, I think is going to sound sacrilegious for this blog’s readers, but I think that the best way to diversify a Trend Following system is through an option selling system, I am studying this concept and it seems to work. Try even the most naive option selling strategy, it has almost a -1 correlation with Trend Following systems (based of Wizards performances). I actually met a CTA manager who is doing just that to diversify his system.

  6. Jing
    45 mos ago

    Hi, Do you consider the trading system parameter diversification? It seems the market is indeed changing, if we only use one set of parameters, it may not work well in future. But if we use many sets of parameters, they as a whole may continue to work. Take simple channel breakout for example, if we only use 25-day high/low(original turtle system), we may experience big drawdown/loss after 1990, but if we use 25-day, 55-day and 90-day together(short-term, medium-term and long-term), these parameters may handle future better and more robust.

  7. nqwr
    45 mos ago

    Can you confirm that you are running this simulation without accounting for commission or slippage (for entry, exit or roll) ? Looking at it myself, and only way I can get close to your numbers is by having zero transaction costs. Does not change the conclusion, but wanted to make sure I was not missing something else.

    Also, my experience is that while asset diversification is important, system diversification yields even greater benefit, and by that I mean not just several Trend Following strats, but other types of quant strats

  8. 45 mos ago

    @nqwr
    Yes, the simulation did not include trading costs – same as for the State of Trend Following report.

    @Pretorian, @Jing, @nqwr
    As mentioned in my earlier comment above: “Ideally I think one would want to trade a large diversified portfolio with a suite of systems, each trading different timeframes.”
    So yes, I think trading different systems (potentially including ant-trend following ones like option selling) and different timeframes is another great way of obtaining diversification.

  9. Pretorian
    45 mos ago

    It seems that we all agree then. I was also thinking about the possibility of building a very short TF system, using something like 5 min bars. Assuming the markets are fractal and we have good execution and low cost brokers it should work. The idea is to meet the long term expectancy of the system in a very short time, since the law of large numbers will work in our favor, the typical 1 year drawdown of a medium term system should become something like a 10 day drawdown here. What do you all think? I am asking this because the blog has some of the most knowleageble people around the trading blogosphere. Thanks!

  10. Jing
    45 mos ago

    Pretorian, I do think adding some short-term trend or counter-trend trading system can diversify the typical long-term trend following systems. It may work well when long-term trend following is in trouble. But I think the difficulty for short-term system is it relies on relative high winning percentage to be profitable. Because short-term system can’t make profit fly like long-term trend following, it requires a higher winning percentage than long-term system. The difficulty is the market is always changing especially in short term. The shorter the time frame, the nosier and more random in price movement. It is possible to design a high-winning percentage short-term system for a specific time period. But a few years later, this system may not work well after market changed. In my opinion, it is very difficult to design a Consistent high winning percentage short-term system, so the short-term system’s life may be shorter than long-term system. It seems the most consistent profit making systems are all long-term system. Short-term system may become super star in this year but may disappear a few years later. Just my opinion.

  11. Jing
    44 mos, 4 wks ago

    I think a key for trading system diversification is these systems need to be uncorrelated. Sometimes even adding a trading system that lose money may improve the original one if that system can make money when all others lose money because it can reduce the maximum drawdown, thus improving the risk-adjusted return. So one important consideration of trading system diversification is to maximize their non-correlation with each other.

  12. Paolo
    44 mos, 4 wks ago

    Jing, in theory I fully agree with you, in practice is a matter of how assessing/forecasting correlations going forward…

    paolo

  13. Jing
    44 mos, 3 wks ago

    Yes, it is much harder in practice. My observation is it seems most long-term trend systems lose money at the same time – ranging/choppy markets. Designing a range/mean-reversion medium term system may help. When market is in range, long-term trend system may lose money but this swing system can make money. We need some filter to limit its loss in strong trend market. Used together, the maximum drawdown may be improved. I think it is difficult to assess/forecast correlation going forward, but if a system tries to capture a different price pattern, such as short-term momentum, swing, pullback, volatility burst, or gap, it may provide better trading system diversification than just combining a channel breakout and moving average crossover. Also valid in theory, but difficult in practice.

  14. 44 mos, 3 wks ago

    Good discussion here…
    On the short-term system/winning percentage, It has been noted (by Trend Following Wizards for example) than robust systems have a low win% (or vice-versa) so I’d agree with Jing’s comment.

    Regarding correlation of systems, I think we have “some” control over it, even though we cannot fully forecast future correlations: a Mean-Reverting system should “in theory” have a low correlation to a TF system.
    Mixing several TF systems together is probably better from a diversification point of view (than using one TF system), but most systems will still probably exhibit a relatively high correlation (look at the State of TF report – as mentioned above I’ll actually run a report at the end of the year to compare the performance of individual components vs the index).
    Pretorian’s suggestion to implement an option selling system on top of a TF system to smooth out the equity has some merit I believe (although I have not tested that approach myself). It probably depends on your objectives (ie absolute performance vs volatility of returns, etc.)

    I am actually just back from a Ralph Vince workshop and there were a few ideas on how to mix/allocate systems together without relying on correlation. I’ll need to study the material further and will probably write a few posts on it.

  15. Jing
    44 mos, 3 wks ago

    Yes, I fully agree with Jez. I think actually there are two kinds of trading system diversification. The first kind is just combining several TF systems (with different parameters) together. As more and more people use the same parameter, this parameter set may suffer big performance degrade. If we only use one set of parameters, we are not sure whether it will degrade dramatically in future. That’s the benefit of TF system mix. We are sure at least some parameter sets/systems in this mix can make money. So I think an important benefit of TF mix is to prevent a specific system’s performance degradation. The “real” diversification comes from the second kind of diversification – mix mean-reverting system with TF system. In theory, mean-reverting system may make money when all TF systems suffer. We are looking forward for your posts about system mix/allocation. Thanks!

  16. 44 mos, 3 wks ago

    Hi. I also worked a lot in the past to apply a properly diversification but… one disadvantage I see that nobody is mention it: if you diversify too much, there is a very high probability that the exposure(allocation) to the different instruments will be very low and even if a few instruments start to perform very nice, we would not take full advantage because we are so diversified as such that we are light exposed in the instru. which are outperforming but our profit is low. Sry for my language.

  17. Paro
    44 mos, 3 wks ago

    How do you guys explain the super smooth shape of the equity-curve in the first a few years and the multi-year sluggish performance in 2005-2006 and 2009-2010?

    @Pretorian: sounds like a good idea! what underlying would you write options on?

  18. 44 mos, 3 wks ago

    @Trocio
    I agree but I think this is precisely the point in diversification: not letting your system be affected too much by performance in individual markets – both on the up and down sides – so that it gives a smoother equity curve. You could always overlay some other money management techniques to modulate the allocation for each trade (higher position size when small number of positions open).

  19. 44 mos, 2 wks ago

    As has been noted in this discussion and Ralph Vince’s paper, correlation works until you need it. Correlation is not a static number. We all know how correlations between various asset classes increased during the financial crisis in 2008 and 2009. That is not to say we should completely ignore correlations in trading system design but I think too much weight can be put on correlation based on my own experience.
    For my own trend trading system, I have found that using ETF’s covering various asset classes is the best way of achieving a somewhat smooth equity curve (i.e. minimal drawdown).

  20. 44 mos, 2 wks ago

    Fred – I agree. Correlation is a “volatile” concept and diversification is probably the best answer to this

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