Portfolio Optimization and the Sharpe Multiplier: A Case Study on Managed Futures

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I’ve spent a great deal of time in past articles discussing the merits of portfolio optimization. In this article I will examine the merits and challenges of portfolio optimization in the context of one of the most challenging investment universes: managed futures.

Futures exhibit several features that make them challenging from a portfolio optimization perspective. In particular, there can be mathematical issues with large correlation matrices, and certain futures markets may exhibit high correlation in certain periods. However, for practitioners that are willing to make the effort, the extreme diversity offered by futures markets represents a lucrative opportunity to improve results through portfolio optimization.

Seeking diversity

Why are we convinced that diversity produces opportunity? We are motivated by the Fundamental Law of Active Management described by (Grinold 1989), which states that the risk-adjusted performance of a strategy is a mathematical function of skill and the square-root of breadth.

where IR is information ratio, IC is information coefficient and breadth is the number of independent bets placed by the manager. For our purpose we can substitute Sharpe ratio for information coefficient because we are focused on absolute performance, not performance relative to a benchmark. Information coefficient quantifies skill by measuring the correlation between a strategy’s signals and subsequent results.

Breadth is a more nebulous concept. Grinold described breadth as the number of securities times the number of trades. However, (Polakow and Gebbie 2006) raise the issue that, “The square root of N in mathematical statistics implies ‘independence’ amongst statistical units (here bets) rather than simply the notion of ‘separate bets’ as is most often implied” in the finance literature.

It is therefore insufficient to simply add more securities in an effort to increase breadth and expand one’s Sharpe ratio. Rather, investors must account for the fact that correlated securities are, by definition, not independent. This prompts questions about how to quantify breadth - the number of independent sources of risk or “bets” - in the presence of correlations.