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 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).
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:
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:
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.