Every year around this time, the media turns its attention towards last year’s hedge fund performance results (e.g. here). It turned out that a late-game rally by hedge funds led to a double digit return last year. And, as usual, returns differed across strategy. Unfortunately, more than a few investors will place their 2011 bets based on 2010’s winners. After all, return chasing is a cherished tradition in both the long-only and the hedge fund sectors.

Informed investors will, of course, look beyond just returns and examine the volatility of each strategy before investing. They’ll likely use some kind of Sharpe-like ratio.

Even more informed investors may go beyond returns and volatility, and take a look at the skew of each strategy. After all, two strategies can have the same standard deviation and Sharpe, but one could save up its “deviant” behaviour, and then unleash it in one massive drawdown while the other one simply goes up and down a little every month. While the Sharpe ratio doesn’t capture those “higher moments”, the “Omega ratio” does. Regular readers may recall that the Omega ratio is based on the cumulative return distribution, not just the standard deviation. As a result, it counts the skew and other higher moments of the return distribution.

But the Sharpe ratio and the Omega ratio assume that the investment in question is being made in isolation. Invariably, a hedge fund investment is added to a pre-existing portfolio, usually a “traditional” one (e.g. a “60/40” stock/bond portfolio). So the correlation between the hedge fund and the existing portfolio is actually a critical factor. A fund with a 2% annual return might be a dog if it has a 100% correlation to your existing portfolio, but a total rock star if it has a perfectly *negative* correlation to your portfolio.

If only there was a way to rank hedge funds based on their performance *and* their correlation to a traditional portfolio? Well, there is. A little over a year ago, Alexandre Hocquard, Nicolas Papageorgiou and Bruno Remillard at Montreal business school HEC Montreal proposed an “Alternative Performance Measure” that actually integrates performance *and *correlation.

Their technique is based on the complex options pricing theory that is also the foundation of so-called “distributional hedge fund replication”. Their basic idea is to price the option that would essentially warp a passive hedge fund portfolio into the hedge fund in question. If that option was worth nothing, then the hedge fund can be thought of as basically being the same as the passive index, for example the HFRI Composite. If that option was worth a lot, you would think highly of the hedge fund in question and if the option had a negative value, you’d be better off buying the HFRI index.

The trio begins by illustrating the deficiencies they see in the Sharpe and Omega ratios. They do this by tweaking the return, standard deviation, skew and correlation (to a 60/40 portfolio) of a hypothetical hedge fund to crate 36 variants of that fund. As you can see from the chart below, changing the skew and correlation (correlation to a to 60/40 portfolio) likely won’t change your opinion of a fund if you’re using *only a Sharpe ratio*. In this case, only a change to the mean and standard deviation impacts your view of the fund…

Since the Omega ratio captures higher moments such as skew, your opinion (ranking) of the fund would change if the skew was different. But still, the Omega ratio would not be affected by a change in the correlation of that fund to your 60/40 portfolio….

Enter the “Alternative Performance Measure (APM)”. Since the APM capture return, volatility, higher moments *and *correlation to an investor’s portfolio (in this case a 60/40 portfolio), different correlations lead to different rankings…

Okay, so much for the theoretical explanation. But Hocquard, Papageorgiou and Remillard also put the idea into practice by applying it to the full suite of HFRI sub-indexes. We created a series of charts below based on the data presented in Tables 8 and 10 of their paper. The results are intriguing and certainly highlight why a losing year – even a lacklustre Sharpe ratio – shouldn’t remove a fund (or strategy) from consideration.

In order to see how the approach changes things, we followed certain sub-indexes through a series of charts

**Light purple:**Emerging Markets**Brown:**Merger Arb**Green**: Equity Market Neutral**Red:**Short Bias

First, we took a tradition mean-variance view of the world:

Then we put the strategies in order of raw returns and showed their Sharpe ratios…

Poor old short bias managers, right? Awful returns and an even worse Sharpe ratio.

But wait! As we can see below, the short bias index has a negative correlation to long-only equities (a major chunk of our 60/40 portfolio).

So maybe holding the short bias index isn’t so bad after all. Apparently, it should hold some diversification benefits and as long as it doesn’t move like a mirror image of the 60/40 portfolio, it could even produce some alpha.

The chart below shows this intuition is, of course, true. The short bias index does indeed produce a modest amount alpha.

It turns out that the relationship between Alpha and correlation is, of course, roughly linear (although not that tight as you can see from the chart below).

While alpha loosely captures the relationship of the fund to the systematic risk factors in the 60/40 portfolio, it has the drawback that it’s “path dependent” in that the arrangements of the returns across time can impact it. Ideally, as Hocquard, Papageorgiou and Remillard argue, a performance measure should capture the inherent dynamics of a fund regardless of *which *monthly return happened *when*.

The Alternative Performance Measure (APM) aims to do just that. Below are APMs of the HFRI sub-indexes assuming the investor’s “other” portfolio is a 60/40 portfolio.

Hold the phone!? Check out the APM for the Short bias index. It’s back from the dead – largely because it’s extreme negative correlation and only modest (i.e. not mirror image) losses when the HFRI Composite rises. Therefore, the price of the option required to warp the HFRI Composite into the Short Bias index is actually pretty significant.

Notice that Equity Market Neutral – which you may recall from above had a pretty solid Sharpe ratio – kind of crashes and burns when you rank the indexes based on APM.

So as the 2010 returns flood in, investor might want to take returns – even Sharpe and Omega ratios – with a grain of salt. After all, “diversification” is the reason why a lot of investors were drawn to hedge funds in the first place.

## 3 Comments

February 2, 2011 at 3:39 pm## Charles T. Hage

February 2, 2011 at 5:45 pm## herman

June 10, 2011 at 8:34 am## Sim Con