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Alternative Beta Strategies and Hedge Fund Replication by Lars Jaeger

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7

The Distributional Approach

7.1 BEING LESS AMBITIOUS

Next to the linear factor model approach to hedge fund replication which aims at mimicking the month-to-month (or at whatever frequency) returns of a chosen hedge fund return time series we can try to be less ambitious. What if the end investor was actually interested in having a replica that only matches the statistical properties of the long-term distribution of hedge fund returns instead of the month-to-month performance? This is much less than what we originally aimed at. In other words, we could try to reproduce only the desirable distributional characteristics of hedge funds their as described by volatility, skewness, kurtosis (i.e. the higher moments of the distribution) – and of course their mean return. The obtained replica return series would not match the exact time series of the original hedge fund index; in particular it will not match the correlation profile. But over time, the distribution of the replica time series would converge to the desired original hedge fund distribution. Evidently, this seems to be a less ambitious task as we give up on the point-to-point matching of the hedge fund return time series. We shall refer to this approach as the ‘distributional replication’ method. It finds its roots in the seminal work by P. Dybvig (who developed it, however, in a quite different context)1 and has more recently been popularized by Harry Kat from the Cass Business School in numerous public appearances as well ...

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