Investment in Value: A Copula Approach

Abstract: We evaluate how factor equity strategies are optimally combined, focusing on the role of the value factor (HML) against the background of a recent academic discussion about its potential redundancy, and the discovery of the investment (CMA) and profitability (RMW) factors. The analysis is centered around a conditional joint return distribution from a dynamic copula model, which allows for simulation with a time-varying and non-normal dependence structure. We study portfolios of six of the most common equity factors (market (Mkt.RF), size (SMB), value (HML), investment (CMA), profitability (RMW) and momentum (Mom)) on weekly US data 1963--2016, applying two different optimization strategies: mean-variance and conditional diversification benefit, where the latter is based on expected shortfall. Our results show that HML remains an important factor that increases the Sharpe Ratio and also decreases the tail risk of portfolios. However, HML should only be combined carefully with CMA, as they overlap to some extent. In parallel, we find that RMW is fundamentally different from HML and CMA, and that the factor is significantly more impactful on the risk-reward profile of portfolios.