Optimal Portfolios Under a Correlation Constraint

Pourbabaee, Kwak, and Pirvu (2016) determine the constant-mix strategy that minimizes Capital at Risk (CaR) under a negative correlation constraint with a benchmark. We extend their result to any increasing law invariant objective function without condition on the sign of the correlation. In doing so we use characterization results of optimal portfolios that were recently established in Bernard, Boyle, and Vanduffel (2014a). We illustrate the theoretical results by establishing the portfolio that has maximum Sharpe ratio under a correlation constraint