Portfolio Composition and Optimization
It's well established that one of the best ways to increase risk-adjusted returns is diversification. That's why most professional traders trade a portfolio of market systems, rather than just one market or one strategy. However, putting together a good portfolio can be more complicated than just combining your best market systems. For example, the performance of the portfolio will depend on how you allocate capital to each market system. And what if you have more market systems than you can reasonably trade? How do you select the best subset of available market systems to trade?
This article will address these questions. In particular, I'll start by presenting the equation for the number of combinations of market systems in a portfolio. The equation makes it clear that it's not practical to consider every possible combination except for small portfolios. I'll then present several objective methods for identifying candidate market systems to remove from a portfolio in order to reduce its size. I'll also demonstrate the process of optimizing the position sizing for a portfolio, which determines the allocations to the market systems. Lastly, I'll present out-of-sample tests to validate the portfolio composition decision and to estimate the bias from the position sizing optimization.
Combinations of Market Systems
Diversification is one of the only true "free lunches" in trading and investing. However, a large number of market systems can become too much of a good thing. While dozens of stock symbols might be manageable in a buy-and-hold investment portfolio, for trading, particularly for short-term trading, managing a large number of market systems is much more difficult. If you're an individual trader without a supporting team to help manage your trades, you might feel you can successfully manage only a handful of markets at the same time. Also, if two market systems are highly correlated, there could be little benefit to trading both unless, perhaps, they trade different markets and your position sizes are so high that you need the liquidity of both markets.
To be clear, what really matters is how the market systems trade with respect to each other, not necessarily whether the underlying symbols are correlated. For example, you could have a short-term strategy on the E-mini S&P futures and a long-term, trend-following strategy on the same symbol. Even though both strategies trade the same symbol, the market systems (i.e., the combination of the symbol and the trading strategy) could have a very low correlation to each other. On the other hand, you might be trading two different strategies with similar underlying logic on two different but correlated symbols. Even though the strategies and markets are different, the market systems might be highly correlated.