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.