A novel approach to monitoring daily HF returns when they don’t actually exist

In just about every action movie and TV show these days there is at least one scene where the hero asks one of his or her techies to “sharpen” a satellite image.  Suddenly, what looked like a fuzzy bunch of pixelated squares takes on the form of someone’s face, a car, or some kind of mobile rocket launcher.   We’re not graphic imaging specialists.  But to us, it looks kind of outlandish that someone could take a very small amount of information (a few pixels) and divine the underlying image in fantastic detail.

But in a way, that’s exactly what Daniel Li & Michael Markov (of quantitative investment software vendor Markov Processes) and Russ Wermers of the University of Maryland have done in a paper released last month called “Monitoring Daily Hedge Fund Performance When Only Monthly Data is Available.”  Their trick is to leverage another kind of technology: hedge fund replication.

As we have reported extensively, “linear factor replication” aims to predict the performance of hedge funds based on a multiple regression of their historical returns on a number of variables such as equities, Fama/French factors, and several more “exotic” risk factors.

But while hedge fund replication has sought to mimic hedge fund returns in a vacuum, the application of the concept to daily returns means that theory and reality can be brought into alignment on a regular basis.  In other words, the model is calibrated to match the empirical data on a regular basis.  The result is that tracking error is reduced.

To prove the concept, the researchers ran their model using the monthly returns of the (daily) HFRX Equity Hedge Index (red line).  Then they compared them to the actual daily returns of the HFRX Equity Hedge (green line).  They ran the analysis using a traditional linear regression and “dynamic filtering technique” called Dynamic Style Analysis (DSA).

So in essence, this approach amounts to “assisted” hedge fund replication, where the linear replication model is helped along by regular infusions of real data as a reference point.

While this concept won’t provide better hedge fund replication per se, it does suggest a novel way for hedge fund investors to track monthly-reported funds on a daily basis.  To see if the model could actually be used for individual funds, researchers also tested the model on 17 long/short funds.

Average tracking error was slightly higher than for the HFRX, reflecting the idiosyncratic nature of individual hedge funds.  But the model stood its own.

If a hedge fund investor can approximate daily returns, then it follows that they also might be able to hedge out unwanted risk on a daily basis.  As the researchers point out, this can be particularly useful when an investor is locked in to a hedge fund due to a redemption gate, but still wants to reduce their economic exposure to the fund. The green line below shows the results of buying the HFRX Equity Hedge Index and taking an off-setting position in a replica based solely on the monthly returns.

Other applications such as “Estimating Daily VaR” are mentioned in the research paper.

In what has become a somewhat over-analyzed field of hedge fund replication, this approach to divining detail where none is provided is a refreshingly straightforward and novel idea.

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One Comment

  1. Peter Urbani
    April 13, 2009 at 5:31 pm

    The Markov Process software is one of the best style analysis packages on the market. The statistical backfill engine in our own Infinti Analytics Suite also allows the forward filling of one or more data points using potentially relevant benchmarks or factors. However the problem with all such ‘linear regression’ or Ordinary Least Squares methods is that they may not accurately capture some of the embedded ‘non-linearities’ common to hedge funds. In essence such returns based style analysis based on the method by Sharpe are essentially a form of reverse optimisation. Like all mean variance optimisation the fact the you are attempting to explain the variance of the original return series in terms of the possibly explanatory variables or factors is subject to all of the same sort of problems as traditional mean variance optimisation most notably sensitivity to change. This manifests itself as weights which change too frequently through time when you use a rolling window period rather than a single period. More significantly it is the inappropriate use of variance as the ‘risk measure’ that causes the biggest problem because it is a symmetrical measure that is incapable of capturing non-linear properties that make hedge funds desirable in the first place. Only more sophisticated methods such as those using kalman filters or better yet distributional modeling are able to capture this embedded optionality that represents the ‘hedge’ in a decent hedge fund.

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