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CAIA Level II: Advanced Core Topics in Alternative Investments, 2nd Edition by CAIA Association

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33.7 PAYOFF-DISTRIBUTION APPROACH

The payoff-distribution approach was developed by Amin and Kat (2003), based on initial theoretical work done by Dybvig (1988) that was later applied by Robinson (1998). The objective of this methodology is far less ambitious than the one pursued in the factor-based approach to hedge fund replication. While the factor-based approach aims to produce a portfolio whose per-period returns match those of the underlying benchmark, the payoff-distribution approach aims to produce a return distribution that matches that of the benchmark. The following simple numerical example can highlight the difference.

Exhibit 33.3 displays the monthly returns on a hypothetical hedge fund and the returns on two replicators: a factor-based replicator and a payoff-distribution replicator. Exhibit 33.4 displays some basic statistics related to the performance of these three investment products. The factor-based replicator does a reasonable job of tracking the performance of the hedge fund on a monthly basis. In fact, the correlation between the two is about 80%. However, this replicator cannot produce the same mean return, standard deviation, skewness, and kurtosis as the hedge fund. On the other hand, the payoff-distribution replicator exactly matches the higher moments of the distribution of the hedge fund's return, but does a poor job of tracking the monthly returns on the hedge fund. It can be seen that its monthly return has almost no correlation to the monthly return ...

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