How Does Hedge Fund Replication Work?
Hedge fund replication comes in three flavors: mechanical,2 distributional3 and factor-based. Each method has proponents, but the commercial applications currently available to investors rely primarily on factor-based replication, with a smaller number using the mechanical approach. Each method springs from a belief that one can mimic the behavior of groups of hedge fund managers with incomplete knowledge of their true behavior. The mechanical approach copies actual positions held by hedge funds. The distributional approach attempts to infer the exposures of hedge fund portfolios from the statistical properties of time series of their returns. The factor-based approach identifies correlations between hedge fund indexes and conventional investment indexes (Figure 1).
In the mechanical approach, managers populate portfolios with positions characteristic of particular hedge fund strategies to attempt to reproduce such strategies' returns. Because of its construction, some call it "trade-related" replication.4 Managers have applied mechanical replication primarily to two hedge fund strategies: merger arbitrage and event-driven activism. The mechanical approach works in both instances because the information required for each is publicly available. For merger arbitrage, replicators take positions in announced mergers, especially those to which both parties have agreed to the terms of the merger. In the activist case, replicators review public records; e.g., 13F filings of large investors, to help identify strategic positions. In both of these applications, the copying of the positions most widely held by managers tends to reproduce the returns individual managers have in common. Only a small but notable segment of the participants in this market take this approach.
The distributional method uses portfolios of futures contracts to attempt to reproduce the statistical properties of the targeted hedge fund strategy. Amin and Kat  presented a model that used only combinations of the S&P 500 Index futures contract and cash over time to create distributions of returns whose first four statistical moments5 resemble those of individual hedge funds. While mathematically satisfying, this approach generally does not provide investors with an ex ante alternative superior to a direct investment in a portfolio of hedge funds. That may account for its lack of commercial success.
Most purveyors of hedge fund replication use linear factor replication to create their indexes and products. In this approach, a multivariate linear regression identifies financial risk factors that explain as much of the returns of a hedge fund index as possible. Regression breaks hedge fund index returns down into random and nonrandom components by computing the correlations between the latter and some explanatory variables that correspond either to financial risk factors or, in one special case, to an undefined factor. Regressions of hedge fund returns usually help identify correlations with financial risk factors such as broad equity indexes, sector equity indexes, interest rates, commodity prices and foreign exchange. In the language of statistics, each such correlation constitutes a regression "beta."