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 talk compares the performance of several nonlinear optimization algorithms when constructing ERC portfolios. Our results suggest that performance worsens with a poor choice of algorithm or a bad problem formulation. We develop second order conic optimization formulations that construct ERC portfolios in an efficient manner.