System Portfolio Optimization

Gary s. antonacci

Portfolio theory principles and practices have important potential benefits with respect to computerized trading. Chief among these benefits is the value gained from careful and proper diversification. In fact, the closest thing to a free lunch in the world of investing is the performance-enhancing benefit from a well-designed diversification strategy. Nowhere is this more evident than in futures trading, where the ability to trade in unrelated markets can lead to significant reductions in overall portfolio volatility. This kind of diversification naturally takes place on the output side of our analysis. Here the investor determines which trading systems to use, as well as how many and which markets to trade. Yet diversification can take place on the input side, too, regarding the factors that make up computerized trading systems themselves.

Input Diversification

Many traders prefer to concentrate their efforts in trading a single market, such as the Standard & Poors (S&P) 500. These investors may receive some benefits by diversifying their systems input. The idea here is to gain value by trying to incorporate as much information as possible. If testing reveals the extra information has no value at all, then the investor can exclude it from use. Thus, traders can only gain by trying to incorporate as much information as possible.

In the academic world, building models is known as data mining, and in the world of practitioners it is usually called curve fitting. Criticism that is sometimes brought against the approach of seeking as much input as possible (and, in fact, against all forms of sophisticated model building) is that it can lead to overspecification and selection bias in ones model. This outcome is also referred to as overmining the data, and overfitting the curve.

Data overmining or curve overfitting is like shooting thousands of arrows at the side of a barn and then drawing a target around where many of the arrows land close together. This kind of questionable target practice has almost no value, since it is unlikely anyone will be able to hit the same target next time out. Similarly, when investors throw lots of factors at their trading models, some are likely to stick solely by chance but they have little or no predictive power.

A way around this potential problem is to start with a simple and effective core trading model. This model should "make sense" by being in tune with what one already knows about the market(s) that are traded. Any parameters that need to be optimized (and there should be few at this point), must be robust and stable. This means that they should perform well over a range of values. Otherwise, attractive looking results may be spurious. Most important, back-testing data should be split into in-sample optimization and out-of-sample validation sections. Parameter values optimized over in-sample model development data must hold up well when applied to out-of-sample validation data. It is relatively easy to develop models that give a good fit to past data. Books and commercial trading systems are full of attractive looking results based on doing just this. But the replication of attractive results on out-of-sample validation data is much harder to come by.

Once the investor develops a satisfactory core model in the manner previously described, then he or she can add model factors one at a time in a stepwise manner continuing with the same procedure as described earlier: each additional input should be in tune with what is known about each market. Parameters being optimized should be stable and robust; and, finally, each additional input must hold up under out-of-sample validation, as well as in-sample optimization.

I have used the preceding approach to effectively build and improve basic trading models through the addition of entry filters and alternative exit strategies. I have also found value in incorporating nonprice information, such as volume, open interest, calendar anomalies, and intermarket price relationships into many of my trading models by using the same approach.

By being careful and conscientious in model construction, traders can safely build elaborate and sophisticated models from valid, simpler approaches. This is how to add value using a "portfolio approach" toward informational inputs.

Output Diversification

What distinguishes futures trading from other forms of investment is the unique opportunity available to enhance system performance by diversifying in many different non-correlated markets. This is in contrast to trading in equities where cross-correlations, or tendencies to move together, between securities are quite high. In such cases, the benefits of diversification are not as great as with futures trading, since the overriding risk of the stock market itself cannot be diversified away.

Portfolio theory still extols the virtues of diversifying away nonmarket risk by holding well-diversified portfolios of securities. In fact, international diversification has gained importance in recent years primarily because of its diversification value in reducing overall portfolio risk, since foreign securities are less highly correlated to domestic securities than are other domestic securities. Yet nondiversifiable market risk still accounts for a substantial amount of volatility given the high correlations between individual equities.

In contrast, there is very little correlation, or comovement, between futures groups as diverse as energies, currencies, interest rate instruments, grains, or meats. To see how this can work to our advantage, let us contrast two examples. In the first, we hold a portfolio of securities where the correlation between them explains, on average, about two-thirds of their composite movement up or down. If each security has an expected annual return of 10 percent and an expected maximum drawdown of 20 percent, then an equal asset allocation among these securities would give an expected return of 10 percent (their average) and an expected maximum drawdown of perhaps 15 percent. The reason this is not 20 percent is because although most of our portfolio holdings would be down at the same time, it is unlikely they will all be down the maximum amount at the same time.

Holding an equally weighted portfolio of unrelated futures contracts, in which the expected cross correlations between them is close to zero, would also give an expected return equal to an average of their respective returns. This is no different from the stock portfolio. Yet the maximum expected drawdown of the futures portfolio would be much lower than the average individual futures drawdowns. This would occur because when some futures markets are down significantly, others could be up significantly, while others might be unchanged.

Of course, futures themselves might be more volatile than equities. However, this apparent volatility is a function mainly of the leverage inherent in futures contracts. Commodities in and of themselves are often less volatile than equities. Traders can modify the leverage of futures simply by adjusting the amount of funding used as collateral for futures trading. Institutional investors, for example, who wanted to participate in futures trading without any leverage at all, could place into their trading account the full value of each futures contract.

Other forms of Diversification

Not all the benefits of diversification come into play with respect to the diversity of markets available for trading. Trading the same markets using different frames of reference can also provide some of the benefits from diversification. For example, investors might trade bonds using systems based on daily, weekly, and intraday price patterns. Likewise, different kinds of trading systems can be applied to the same markets using the same time frames. The application of both different trading systems and different time frames means that market entries and exits are phased in and out, which often smooths out the ups and downs of performance in accordance with diversification principles.

Most traders, including professional trading advisers, ignore these other forms of diversification, preferring instead to trade all markets the same way using a singular method and/or time frame. The benefits of these additional forms are there for the taking; however, they entail much more research effort. A problematic aspect of this broad-based approach to trading is that the trader is forced to look at systems and methods developed by others to cover all bases. In doing so, the same principles of