Replicating Indexes In R With Style Analysis: Part I

In the quest for clarity in portfolio analytics, Professor Bill Sharpe’s introduction of returns-based style analysis was a revelation. By applying statistical techniques to reverse engineer investment strategies using historical performance data, style analysis offers a powerful, practical tool for understanding the source of risk and return in portfolios. The same analytical framework can be used to replicate indexes with ETFs and other securities, providing an intriguing way to invest in strategies that may otherwise be unavailable.

Imagine that there’s a hedge fund or managed futures portfolio that you’d like own but for one reason or another it’s inaccessible. Perhaps the minimum investment is too high or the fund is closed. Or maybe you prefer to build your own to keep costs down or maintain a tighter control on risk. If the returns are published, even with a short lag, you can still jump on the bandwagon by statistically creating a rough approximation of the strategy’s asset allocation via style analysis.

Any index, in theory, can be replicated, which opens up a world of opportunity. Even if you’re not interested in investing per se, decomposing key indexes through style analysis offers valuable tactical and strategic information. As one example, deconstructing key hedge fund or CTA benchmarks published by BarclayHedge.com provides the basis for quasi-real time analysis of investment trends in the alternative investment space. In turn, the analysis can provide useful perspective on the evolution of manager preferences for asset classes in global macro or managed futures strategies.

Let’s run through a simple example of how to estimate weights for an index through style analysis. To illustrate the process clearly in Part I of this two-part series, I’ll start by reverse engineering an index that’s already fully transparent: the S&P 500.

From a practical standpoint there’s no need to decompose the S&P since its components are widely known and you can readily invest in the index through low-cost proxy ETFs and mutual funds. But let’s pretend that the S&P 500 is an exotic benchmark and its design rules are a mystery. All we have to work with: the S&P’s daily returns and a vague understanding that 11 equity sectors (financials, energy, etc.) drive the S&P’s risk and return profile.