Computing equal risk contribution portfolios

For institutional investors, optimizing the trade-off between risk and reward poses significant modeling and computational challenges. Notably, small errors in the estimated returns of financial assets can lead to optimized portfolios that incur far too much risk for the returns they actually deliver. Given these adverse effects, portfolio construction techniques that are based exclusively on risk have grown in popularity. For instance, equal risk contribution (ERC) portfolios seek to equalize the risk contributions of all assets, so that the portfolio is fully diversified from a risk perspective. This paper reviews the nonlinear optimization models that underlie the ERC approach and, in response to the reported difficulty of solving such optimization problems, compares the performance of several nonlinear programming algorithms when constructing ERC portfolios. Our results suggest that performance worsens with a poor choice of algorithm or a bad problem formulation. We provide alternative formulations and also develop heuristic procedures that construct an approximation to the ERC portfolio in an efficient manner.