Imitation, Oscar Wilde famously observed, “is the sincerest form of flattery that mediocrity can pay to greatness.” The observation echoes the objective for using Professor Bill Sharpe’s style analysis to replicate investment indexes that, for one reason or another, can’t be purchased directly. If we can obtain an index’s returns, there’s a pretty good chance that we can reverse engineer the asset allocation and recreate the portfolio with publicly traded securities.

Earlier this month I reviewed a simple example of index replication by using 11 sector ETFs to recreate the S&P 500. But that was child’s play, not to mention pointless from a practical standpoint since it’s easy to buy the S&P via ETFs and index mutual funds. The objective, however, was to illustrate the process via R code that I wrote.

Let’s try something more ambitious this time by attempting to replicate the Barclay Global Macro Index (BGMI), which aggregates the performances of dozens of funds in the niche. The index’s monthly returns are freely available so in theory we can decompose the weights by performing regression analysis on the benchmark in context with a relevant set of securities that, overall, represent guesstimates for BGMI’s portfolio.

The challenge is that we don’t know what’s inside BGMI. Yes, we could subscribe to the database and see the funds, but that wouldn’t help since it’s unlikely that the underlying portfolios would be listed. The fact that the index is comprised of many individual global macro products makes our task especially difficult. Indeed, the global macro space covers a wide array of strategies across stocks, bonds, futures and options and employs varying amounts of leverage while taking long and short positions. A professional-grade effort to replicate a benchmark that proxies for dozens of funds in this corner would require considerable effort beyond what’s attempted here. But let’s take a stab at a first approximation by making some general assumptions.

The critical first step is choosing the opportunity set. The success (or failure) of the replication is highly dependent on this aspect of the analysis. In a serious consulting project I’d spend quite a bit of time researching the possibilities and running several statistical tests to determine which securities to use. For this toy example, however, I’ll forgo the usual routine and make a quick guesstimate by selecting 14 funds to replicate BGMI (see table below). No one should confuse this list as optimal, although the funds cover a wide spectrum of assets, including several short strategies. As such, these ETFs (and one mutual fund) should provide a rough if incomplete approximation of the betas that comprise most of what goes on the global macro space.

Although BGMI’s history begins in 1997, our analysis is restricted to the shortest history for the fund list above, which begins in 2009. Because of this short historical sample, I’ll use a relatively short window for the regression analysis: 14 months, which is the shortest run available to generate quasi-robust data. The procedure is to re-run the regression every nine months on BGMI and the funds and rebalance the portfolio. Why every 14 months? A bit of testing shows that this window comes close to matching BGMI’s results. Keep in mind that the possibilities for rolling windows are restricted in this test due to the relatively short dataset. It doesn’t help that we’re using monthly numbers, which further limits the analytical options.

In any case, here’s what the cat dragged in. As the chart below shows, the replication results echo BGMI’s returns, albeit with some obvious limitations. In the first several years the returns line up fairly closely, but the replication begins to degrade in the second half of the test. If this was a serious project I’d spend time analyzing the deterioration in the last several years in search of possible fixes.

Although the replication index’s performance trails BGMI’s results by a wide margin, it’s still clear that we’re on the right track. The correlation of monthly returns between the two series is a relatively high 0.88, which suggests that the first attempt at replication is picking up a fair amount of BGMI’s beta profile.

Here’s how the two return series compare via some basic risk metrics:

The results obviously fall short of what most investors would define as a successful replication. But the fact that I was able to generate a rough approximation with minimal effort implies that a deeper level of analysis could deliver superior results. Using daily returns would help, too. Expanding the opportunity set to more ETFs, and perhaps individual securities – stocks, bonds, futures, etc. – would also be productive.

The larger point is that this toy example shows that there are intriguing opportunities for replicating indexes. One of the more popular applications is replicating, say, the S&P 500 Index with a set of stocks that adhere to some definition of environmental, social and governance (ESG) criteria. For instance, let’s say that you want to own the S&P’s beta but without the influence of tobacco, alcohol and gaming companies. The solution: replicate the index by excluding those stocks while simultaneously minimizing tracking error.

In part III of this series I’ll provide an example on this front – a technique that effectively uses style analysis to customize indexing on your terms, using just about any criteria you deem relevant.

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