Managing Portfolio Diversity within the Mean Variance Theory

Abstract

It is well documented that the classical mean variance theory (MVT) may yield portfolios (MVTP) that are highly concentrated and/or are outperformed by equal weight portfolios (EWP). In this work, it is proposed to expand the MVT minimizing utility function with diversity booster DB = δ∑_(i=1)^N=w_i^2 where wi are portfolio weights; ∑_(i=1)^N=w_i = 1. DB decreases with growing number of non-zero weights and has a minimum when all weights are equal (wi = 1/N). At high δ, DB becomes the dominant term in the utility function and yields EWP. For performance analysis, portfolio constructed with 12 major US equity ETFs is considered. Out-of-sample performance of maximum Sharpe portfolios is tested using statistics of bootstrapped Sharpe ratios for monthly rebalancing periods. It is found that for the three-year calibrating window the diversified MVT portfolio (DMVTP) outperformed both MVTP and EWP in 2012 - 2015. While the MVTP weights were highly concentrated and had sharp jumps between rebalancing periods, the DMVTP weights slowly changed with time.