Construction of Risk-Averse Enhanced Index Funds

We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is required to be below a low-risk threshold with a large probability, thereby limiting the market risk exposure of the investors. The resulting stochastic integer problem is reformulated through the derivation of a deterministic equivalent for the risk constraint and the use of a block decomposition technique. We develop an exact outer approximation method based on the relaxation of some binary restrictions and the reformulation of the cardinality constraint. The method provides a hierarchical organization of the computations with expanding sets of integer-restricted variables and outperforms the Bonmin and the CPLEX solvers. The method can solve large instances (up to 1,000 securities), converges fast, scales well, and is general enough to be applicable to problems with buy-in-threshold constraints.