Based on the restrictions for an official institution, with a low risk tolerance and a goal of capital preservation, this document seeks to evaluate alternative ways for benchmark construction. Specifically, it seeks to integrate into the optimization problem a diversification measure in order to find portfolios with a higher return which are in line with the risk restrictions. Rao's quadratic entropy will be used as a measure of diversification, as explained by Carmichael, B., Koumou, G. B., & Moran, K. (2015). The concept of dissimilarity matrix is introduced and two specification approaches are explored in order to compare their results against other portfolios. It was found that, using the mentioned methodology, the Sharpe ratio of these portfolios are similar to each other and to the portfolios of maximum Sharpe and minimum variance. The results are sensitive to the use of constraints, but do not alter the conclusions. The extent of the exercise will depend on the different objectives of the institutional investor.
