Regular(ized) hedge funds

This article addresses the problem of portfolio construction in the context of efficient hedge fund investmentsreplication. We propose a modification to the standard à la Sharpe ‘style analysis’ where we augment the objectivefunction with a penalty proportional to the sum of the absolute values of the replicating asset weights, i.e. the normof the asset weights vector. This penalty regularizes the optimization problem, with significant impacts on thestability of the resulting asset mix and the risk and return characteristics of the replicating portfolio. Our resultssuggest that the norm-constrained replicating portfolios exhibit significant correlations with their benchmarks, oftenhigher than 0.9, have a fraction, i.e. about 1/2 to 2/3, of active positions relative to those determined through thestandard method, and are obtained with turnover which is in some instances about 1/4 of that for the standardmethod. Moreover, the extreme risk of the replicating portfolios obtained through the regularization method isalways lower than that exhibited by currently available commercial hedge fund investment replication products.