In this paper we extend Hasanhodzic and Lo (2007) by assessing the out-ofsample performance of various non-linear and conditional hedge fund replication models. We find that going beyond the linear case does not necessarily enhance the replication power. On the other hand, we find that selecting factors on the basis on an economic analysis allows for a substantial improvement in out-of-sample replication quality, whatever the underlying form of the factor model. Overall, we confirm the findings in Hasanhodzic and Lo (2007) that the performance of the replicating strategies is systematically inferior to that of the actual hedge funds.

This paper attempts to evaluate the out-of-sample performance of an improved estimator of the covariance structure of hedge fund index returns, focusing on its use for optimal portfolio selection. Using data from CSFB-Tremont hedge fund indices, we …nd that ex-post volatility of minimum variance portfolios generated using implicit factor based estimation techniques is between 1.5 and 6 times lower than that of a value-weighted benchmark, such di¤erences being both economically and statistically signi…cant. This strongly indicates that optimal inclusion of hedge funds in an investor portfolio can potentially generate a dramatic decrease in the portfolio volatility on an out-of-sample basis. Di¤erences in mean returns, on the other hand, are not statistically signi…cant, suggesting that the improvement in terms of risk control does not necessarily come at the cost of lower expected returns.

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