2011-01: Minimizing Shortfall


Despite the increasing sophistication of Finance in the past 30 years, quantitative tools for building portfolios remain entrenched in the paradigm proposed by Markowitz in 1952; these tools offer investors a trade‐off between mean return and variance. However, Markowitz himself was not satisfied with variance, which penalizes gains and losses equally. Instead, he preferred semi‐deviation that only penalizes losses.

Recent work has made downside risk optimization practical, but there has been no reliable non‐ Gaussian risk model. This void is filled with Barra Extreme Risk (BxR), an empirical, fundamental factor‐ based model that captures features of return beyond variance. BxR reflects persistent characteristics, such as the higher asymmetry and downside risk of high‐yield bonds compared to government bonds, or Growth stocks compared to Value stocks.

This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing shortfall generally improves performance over minimizing variance, especially during down‐markets, over the period 1985‐ 2010. The outperformance of shortfall is due to intuitive tilts towards protective factors like Value, and away from aggressive factors like Growth and Momentum. The outperformance is largest for the shortfall that measures overall asymmetry rather than the extreme losses.

Michael Y. Hayes
Publication date: 
January 1, 2011
Publication type: 
2011 Working Papers
(revised July 2012, working paper #2012-05)