Risk-only investment strategies have been growing in popularity as traditional investment strategies have fallen short of return targets over the last decade. However, risk-based investors should be aware of four things. First, theoretical considerations and empirical studies show that apparently distinct risk-based investment strategies are manifestations of a single eect. Second, turnover and associated transaction costs can be a substantial drag on return. Third, capital diversication benefits may

be reduced. Fourth, there is an apparent connection between performance and risk

diversication. To analyze risk diversification benets in a consistent way, we introduce the Risk Diversification index (RDI) which measures risk concentrations and complements the Herndahl-Hirschman index (HHI) for capital concentrations.

(from the introduction...)

In this paper, we combine the innovations described above in an empirical study of expected shortfall optimization with Factor-Based Extreme Risk. We avoid the issue of forecasting mean return by comparing minimum expected shortfall to minimum variance portfolios. Our study is carried out for the US, UK, and Japanese equity markets and it uses Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing expected shortfall generally improves performance over minimizing variance, especially during down-markets, over the period 1985-2010. The outperformance of expected shortfall is due to intuitive tilts towards protective factors like Value, and away from aggressive factorslike Growth and Momentum. The outperformance is largest for the expected shortfall at relatively low confidence levels, which measures distributional asymmetry rather than the extreme losses.

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, which only penalizes losses.