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.