DNA is life; it contains the blueprint for the creation of virtually all known living organisms. Genes are segments of DNA that act as fundamental building blocks, and hence maintaining the integrity of such genetic instruction sets is paramount to the health of an organism (or "fitness"). In much the same way that inbreeding can reduce genetic robustness and, thereby, increase susceptibility to illness and disease, an insufficiently diversified portfolio may be subject to an increased likelihood of uncharacteristically poor performance under a particular set of market conditions. Market environments that are stressful for one type of trading program, however, may be beneficial to another. It is exactly this type of divergent behavior that we wish to identify systematically and combine in order to construct a robust, resilient portfolio that bends but does not break.
Too often, portfolios are constructed with a single goal in mind: To maximize Sharpe ratio. Even when the portfolio engineer considers multiple objectives, many of those goals can be mutually exclusive, and improper attention to such constraints may compromise the fitness of the portfolio. Here we first discuss the variety of objectives that often are mandated for a portfolio of trading programs. We then consider how to prioritize objectives and understand the necessary trade-offs. Finally, we compare and contrast our portfolio construction process with more traditional techniques. We argue that novel, non-classical approaches are needed to systematically generate a high-fitness portfolio.
Defining objectives
Before starting, we must define an end goal. Commonly, the initial, singular objective is to maximize performance. This answer is legitimate but raises additional questions.
The first question involves consistency of performance. Certain strategies such as trend-following have desirable risk properties but are intermittent in their returns, while strategies such as option selling may tend to produce consistent returns over most periods but occasionally experience large, sudden drawdowns. Optimizing for performance typically implies that you are optimizing for the average performance over the sample period, but this metric doesn’t account for the year-to-year variability around the average. The importance of consistency depends largely on the time horizons of both the portfolio designer and the investors. Shorter time horizons demand greater consistency of returns.
Another question is that of style, or desired correlation to a benchmark. Alternatively, you may wish to minimize correlation specifically to a particular benchmark. Many portfolio designers seek to replicate the style of trend-followers, yet also improve on the risk-adjusted performance, i.e., they seek "alpha" as well as "beta" (see "Manager lingo," below). Other portfolios have become popular. For example, an index comprising short-term traders has been developed to reflect a uncorrelated return stream to standard trend-following benchmarks.
Additional and often overlooked objectives include optimizing for various return statistics, including skewness, kurtosis and drawdown measures. Such objectives can be difficult to incorporate into the optimization process accurately. For instance, even though many believe that drawdowns can be bounded a priori and that risk-management methodologies can be separated from the trading program itself, two primary determinants of drawdown magnitude are program style and time. Longer-lived programs generally will have experienced larger peak-to-valley drawdowns, reinforcing the adage: "Your worst drawdown is always ahead of you." Hence, optimizing for maximum drawdown is an exercise in futility.
Additionally, trend-following programs tend to have shallower drawdowns than other investment styles given equal Sharpe ratios. Generally speaking, return skewness, kurtosis and other statistical properties are linked inextricably to the program style and, therefore, cannot be optimized independently.