Reducing Risk Rather than Trying to Beat the Market: A New Look at Optimal Portfolios under the Mean-Variance Model

Abstract

While much of the equity investment management industry is focused on achieving returns superior to that of the overall market, widespread studies have shown that this is both difficult to do consistently and that the achievable gains have low economic significance (fund returns show low dispersion about the mean). In this investigation, we look at another aspect of “beating the market” – whether or not it is possible to achieve the same market gains, but with lower volatility. We first investigate the performance of portfolios formed from a number of weighting schemes, including commonly used weights as well as weights suggested by a risk-parity approach (as suggested by Asness, Frazzini, and Pedersen (2012)). We then look at the empirical performance of both unconstrained and long-only Global Minimum Variance Portfolios. Further, we develop an optimization algorithm to calculate low-volatility portfolios in an iterative fashion. Finally, as an extension, for a selection of portfolios that empirically dominate the market portfolio in a mean-variance sense (in a theoretical environment), we investigate their real-world performance taking into account various real-world frictions.We find that, in a frictionless environment, there are a number of portfolios formed from simple weighting schemes that show both higher mean return and lower volatility than the market portfolio in the test period (1930 to 2010). The optimization algorithm that is proposed is successful (empirically) in generating portfolios with much lower volatility than the initial portfolios it is given (with only a lesser decline in mean return). The real-world performance analysis accounting for market frictions suggests that, prior to 2002, high transaction costs prevent desirable properties of portfolios that dominate the market portfolio from being realized. However, lower trading costs (due to decimalization, etc.) since then allows the practical implementation of portfolios that achieve market returns with lower volatility.