Following the last study on diversification using a “portfolio randomizer”, I wanted to further explore further the concept of hindsight bias in portfolio selection and how it can impact performance. This short post is an illustration of that concept.
51 Instruments, 40 Picks, How Many Combinations?
The answer is… a lot: there are 47,626,016,970 ways of picking a portfolio of 40 instruments from a total set of 51 (formula is: 51! / [40! x 11!]). Running so many simulations was not practical (!) so I decided to run a fraction of the possible combination (5,000 random iterations). We get a similar set of results as the last study:
This is still for a run of the 20/50 Moving Average cross-over system running from 1990.
Note that the results are slightly different from the run with 40 instruments from the last post, as the position size was greater here (and therefore the “cloud” of CAGR/MaxDD results has moved towards the top-right).
The average performance figures for the systems are as follows:
The next step was to isolate the worst and best cases (circled on the scatter plot) and identify the difference in portfolio composition between the two. Since this is a combination of 40 elements from a set of 51, there can only be 11 differences at a maximum between each portfolio.
Indeed, the “worst” and “best”portfolios share 32 of their 40 components but still exhibit a wide difference in their performance figures (the MAR ratio for example is 3.5 times better for the best case: 1.02 v. 0.29). For reference, the “good part” of the best portfolio (ie its instruments that do not overlap with the other portfolio) are:
- Cattle-Feeder-CME(Floor+Electronic Combined)
- CopperHG-COMEX(Floor Trading Only)
- Euro(Floor+Electronic Combined)-CME
- Gas Oil(Combined)-ICE(IPE)
- IBEX 35 Index-MEFF
- Natural Gas-Henry Hub-NYMEX(Floor+Electronic Combined)
- OMX Helsinki 25-EUREX
- Palm Oil-Crude-MDEX
On the other hand, the “bad part” of the portfolio is:
- Azuki Beans-Red-TGE
- DJ Euro STOXX 50 Index-EUREX
- EURIBOR-3 Mth-EURONEXT(LIFFE)
- Gold-COMEX(Floor Trading Only)
- MSCI Taiwan Index-SGX(SIMEX)
- Silver-COMEX(Floor Trading Only)
- Soybeans-CBT(Floor Trading Only)
To take the comparison to a further extreme, I ran the exact same system over both bad and good portfolios by themselves.
The difference in results is fairly striking:
Going from a CAGR / MaxDD combination of 26.73% / 34.9% to -3.20% / -63.3% is fairly drastic.
This is not a big surprise, knowing that 20/20 hindsight was used in picking both sets of instruments. But bearing in mind that the results above come from the exact same system and parameters, using the same number of instruments, it does illustrate the point even more clearly on portfolio selection and how they can impact performance results.
If anything, I believe this illustrates that testing over several portfolio sets might be a good way to identify robustness in system results. If the system only shows good results on specific portfolios, it might simply be a “lucky” outlier.
Finally, there were a few comments on the last post with regards to how to implement diversification. I had only focused on diversification from a portfolio point of view. However I believe that ideally one would diversify with a large set of instruments to trade, different systems covering different timeframes.
One problem is that diversification on all these levels bring on an increase in required starting capital (one likely reason why most Trend Following Wizards have a minimum managed account size in the millions).
So you might have to make a choice in how to apply diversification.
As diversification is really beneficial thanks to the non-correlation it brings, diversifying across different systems could also be a good idea, as systems can be more or less “engineered” to be un-correlated to each other (ie a Trend Following system with a Mean Reversion system).
It is also possible to “trade” a large portfolio without taking all the signals (by using filters or an overall risk/size limiter).
After all, this is something that the Turtles used to do (when they were at full position size they had to skip signals)
Some ideas to think about…
Credits: Thanks to Trading Blox forum member sluggo for the reminder of how the Turtles used to skip trades, and how filtering trades could enable small accounts to trade a large portfolio – on this thread.