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.
Trade-offs
Portfolio construction is largely an exercise in compromise. Further complicating matters is that critical decisions often need to be made based on limited data. Before the 2008 financial crisis, for example, equity-based hedge fund strategies often touted themselves as having low correlation to long-only equity indices. In the low-volatility markets of the mid-2000s, this often was true. But what wasn’t realized at the time is that this was based on a placid global environment. When market conditions became turbulent, a different relationship was exposed: These strategies were all predicated on being short volatility, meaning that any panic would be short-lived in time and bounded in magnitude.
In a short volatility world, mean reversion would restore order soon and, thereby (in a self-fulfilling feedback loop), reward the strategies whose profitability depended on its existence.
In 2008, however, disorder became the rule. As a result, long volatility strategies, such as trend-following, were the only programs to profit systematically because they were the only strategies that were able to short the global economy (see "Diversify with crisis alpha," February 2011).
The designer truly needs to understand the component strategies in the portfolio. But most track records are too short to have experienced the gamut of possible macro-economic conditions. Hence, the portfolio engineer must have sufficient knowledge of the portfolio’s constituent strategies. Once armed with this knowledge, the engineer can make the necessary trade-offs and maximize portfolio fitness.
However, not all trade-offs are created equally. Idiosyncratic risk is a rare example of an objective with a fairly painless trade-off. We define idiosyncratic risk as the potential for performance dispersion by a single program or small set of programs. For instance, within trend-following, most trend-followers’ monthly returns are correlated. There are times, though, where certain trend-followers do significantly better or worse than average. The root causes are often slight differences in time scales, sector allocations and the trade entry/exit directives. Also, many trend-followers have introduced modifications to their systems. As a result, CTAs have added features to their systems (sometimes unknowingly) that are actually counter-trend in nature or at least are non-correlated with the space. By understanding the finer details of the systems under consideration, a portfolio engineer can diversify away this idiosyncratic risk and arrive at a truer representation of the dynamics the portfolio is designed to exploit. The only downside is the cost to implement a sufficiently wide gamut of managers within the same basic style.
But sometimes the trade-off is intractable; mutually exclusive goals are, oftentimes, unknowingly chosen as distinct primary objectives by the portfolio engineers. "Hitting a triple" (below) shows three common objectives: Trend-following de-correlation, risk-adjusted performance and a positive skew of returns. In high-tech product engineering, there are three factors that are highly desirable: Low cost, high reliability and a speedy development time. The historical rule is that one can choose any two of these but never all three simultaneously.
For the portfolio engineer, the three-factor trade-off acts in an analogous manner. Numerous CTAs have proven empirically that solid risk-adjusted performance and good drawdown properties can be achieved with trend-following. In addition, a number of CTAs have achieved low correlations to trend-following along with good risk-adjusted, long-term performance. However, rigorous analysis reveals that such systems periodically experience larger drawdowns than trend-followers, owing to the system architecture needed to remove the trend-following correlation. Finally, systems can be constructed that offer both low correlations to trend-following and also positive return skew. But these systems tend to have very poor (even negative) risk-adjusted performance over long time scales.
Statistical analyses show that markets, on average, exhibit "trendy" behavior over 50-day (and greater) time scales. In other words, prices move more than that predicted by a random walk, even after allowing for the non-Gaussian distribution of daily returns. This explains why trend-following is profitable, but not why markets trend.
Programs exploiting such trends effectively are rowing downstream. By increasing portfolio risk after profits accrue (i.e., cut your losses and let your profits grow), positive return skew and reduced drawdown magnitudes follow as natural consequences. Conversely, constructing a program that is de-correlated to trend-following requires one to selectively take positions that oppose the prevailing long-term price movement. The inherent risk properties of such systems are less optimal; specifically, they tend to lack positive skew of returns and have higher kurtosis on multi-day time scales.
Optimize robustly
Over half a century ago, Harry Markowitz pioneered a cornerstone of modern portfolio theory. Markowitz, who in 1990 won a Nobel Prize for his efforts, developed the concept of the "efficient frontier." The efficient frontier provides a way to determine the mix of a set of investment choices such that the mean return is maximized for a given variance. It maximizes the returns of two or more programs by assigning optimal weights.
Markowitz’s mean-variance optimization is both a useful tool and also one that is overused unwittingly by many portfolio engineers. A natural, intuitive and practical approach is to choose a core program or set of programs that offers a strong historical record, then add peripheral programs in smaller percentages to complement the core. To measure the "goodness" of the overall mix, the risk-adjusted performance, or Sharpe ratio, often is used, and by maximizing this metric you immediately arrive at the efficient frontier.
In practice, this methodology is a useful starting point but may be sub-optimal when used in isolation. Considering the objectives pondered earlier, it may be critical to consider the depth and/or length of eventual drawdowns. It also may be important to minimize the correlation to trend-following strategies. In such situations, multiple objectives now must be satisfied simultaneously; the best compromise likely implies a portfolio mix that does not lie on the efficient frontier.
Still other potential pitfalls lurk. We have observed real portfolio optimizations fall prey to what we term inbreeding. For example, perhaps the designer decides he would like to build a robust portfolio that simultaneously maximizes Sharpe ratio, minimizes drawdowns and has a positive skew of returns. Thus, optimization software is built that measures all three variables as it churns through various combinations of the candidate programs. In the end, based on numerical computations, an optimal set of program weights is found, and this portfolio subsequently is deployed. Invariably the day arrives where all the portfolio constituents simultaneously perform poorly and render the program with a larger drawdown than would be expected based on backtesting.
So what happened? Essentially, the optimizer inadvertently was asked to find a set of correlated programs. As discussed in the previous section, trend-following strategies tend to satisfy all three of the stated metrics. By asking for a portfolio that satisfies these constraints, you essentially are forcing the optimizer to heavily weight programs that are substantially similar. Inbreeding occurs and the portfolio is now at risk because of its lack of fitness.
The combination of multi-objective optimization, the need to understand the candidate strategies and the requirement to understand the possible connections between various objectives renders fitness-based optimization difficult. There is no easy method to make this task a purely algorithmic exercise. However, we can provide a set of useful guidelines to assist with the process:
- Define the objectives: The portfolio engineer needs to articulate the portfolio requirements and differentiate want from need. Based on the objectives, determine the trade-offs that likely will be required. Be realistic about drawdowns and performance, and use statistical analyses to underpin expectations. Endeavor to understand which types of strategies are consistent with the portfolio objectives. Choose portfolio constituents accordingly.
- Attempt to minimize idiosyncratic risk: Be aware that trying to choose the best program of any one style may be impossible. The idiosyncrasy that worked well one year may be detrimental the next.
- Be aware of the "inbreeding" potential from correlated metrics: Develop multiple methods to generate optimal portfolio weights. Because of the complex nature of the problem, there likely are no methods by which to get a true optimal solution; every solution only will be approximately optimal. Therefore, as long as the objective remains the same, you should be able to generate similar results with a variety of methods.
Conclusion
Navigating beyond the efficient frontier is a challenging proposition because fitness-based optimization simply cannot be reduced solely to numerical computations. Rather, the heavy lifting must first be done in the mind of the portfolio engineer. The necessary pre-requisites are an understanding of each candidate program; a knowledge of how each candidate program has responded or is expected to respond to various stressors that the portfolio engineer deems important; and a concrete metric or set of metrics for which the portfolio should be optimized. However, once armed with a solid goal and a sufficiently diverse set of candidates, the process can proceed in a fairly systematic manner. And the potential payoff in terms of portfolio consistency and stability may well be worth the voyage.
Michael Mundt is a principal with Revolution Capital Management. He has built successful long-term and short-term trading strategies.
