Statistical Properties
Hedge fund indexes generally comprise hedge funds that report their returns on a voluntary basis. As such, these indexes are susceptible to biases that can arise from managers deciding not to report their returns once the returns are no longer attractive or from managers choosing to begin reporting returns only when they have a successful track record that they can add to the database. Numerous articles have been written about survivorship and back-fill biases in hedge fund returns. Fung and Hsieh [2009]11 found that “[i]n general, return measurement biases can be traced to two key events: when a hedge fund elects to enter one or more databases and when a hedge fund exits a database.” Estimates of the effect of these biases on reported returns range from 4-6 percent per annum.12 Surprisingly, this bias is often used as a counterargument against hedge fund replication. The bias is actually supportive of replication. Replication is often attacked for targeting the “average” manager. Most investors would prefer to have the returns of an “above average” manager. If the performance as reported by the hedge fund indexes is overstated by at least 4 percent per year, then a replication product that can deliver these returns must be “above average.”
When working with data sets that contain performance information, it is important to review the data with an eye toward quality control. Extreme data points can cause a process to produce undesirable outcomes if the data quality is not verified. An example of this issue occurred in November 2008 in the Dow Jones Credit Suisse Equity Market Neutral Hedge Fund Index. Typically, a market-neutral hedge fund will have very low volatility. Indeed, this index had an annualized standard deviation of 2.92 percent from its inception in January 1994 through October 2008. However, in November 2008, a single manager comprising over 40 percent of the index had a return of -100 percent, as its assets were written down to zero due to its exposure to a Madoff Investments fund. As a consequence, the index was down 40.45 percent in November 2008. This return is an almost 14-standard-deviation event. Clearly, using this return in a replication process would cause an undesirable result.
One solution is to identify returns that are extreme relative to the environment and the strategy being evaluated. If an extreme value is detected, an algorithm can be used to estimate a more suitable value to be used in the replication process. This ensures that extreme data values do not corrupt the replication process.
An oft-cited characteristic of hedge funds is the sometimes-illiquid nature of their underlying holdings. This illiquidity can perhaps lead to superior returns over the longer run but can cause difficulties in valuing an asset in the shorter run. If assets are not marked-to-market accurately at the end of each reporting period, the volatility of the reported returns can be muted and the fund returns can appear to be less correlated to exchange-listed assets than they actually are. Low volatility and low correlation to exchange-listed assets are obviously desirable attributes of an investment vehicle. However, misestimation of the true volatility and correlation can introduce errors in the replication process. IndexIQ chooses to employ a process that measures the degree of misestimation of the volatility and correlation, and applies a correction factor designed to yield a better estimate of the true returns as opposed to the reported returns.
Estimation Methods
One of the key decisions one needs to make when designing a replication product is which estimation method to employ. The choices can range from a simple ordinary least squares (OLS) regression method to a more complicated Kalman filter. OLS is best suited for estimating stable, linear relationships, such as factor exposures. Given that many hedge fund returns exhibit time-varying and nonlinear properties, more sophisticated methodologies may be better suited. Amenc et al. researched the impact of using conditional and nonlinear models to create hedge fund clones. They wrote, “… it appears that conditional and non-linear models, which are less parsimonious than their linear counterparts, do not necessarily lead to improved out-of-sample replication.” Thus it appears that despite the intuitive appeal of more complex models, the out-of-sample efficacy of OLS is supported by the evidence.
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