Diversifying the Diversifiers
Ever since the cap weighting has been proved to be inefficient (in terms of mean variance efficiency), several alternative weighting schemes have been proposed. These strategies differ from each other in the assumptions they make and the objectives they aim to achieve. For example, a Minimum Volatility (GMV) strategy aims to minimize the variance of the portfolio with no regard to the returns. In contrast, the Maximum Sharpe Ratio (MSR) aims to maximize the return per unit of volatility (the Sharpe Ratio) of the portfolio. Both approaches have the objective to improve portfolio diversification in order to provide proxies for portfolios on the efficient frontier.
Although these two alternative strategies rely on portfolio selection models that are based on sound methods (both in terms of statistical estimation procedures and financial economic theory), none of these weighting schemes can be expected to be truly optimal. In addition, none of these approaches can be expected to be consistently superior across different market conditions. This is true more generally for any index weighting scheme. Table 1 shows that some strategies are favored more than others in a given market condition (Amenc et al, 2012). Also, the difference in performance (returns) of the best and worst performing strategies in a given period can be large. The reason for this erratic behavior is that the implicit assumptions associated with each strategy hold only in certain market conditions.
Table 1: Relative Return of Different Alternative Weighting Schemes on a biyearly basis from 2003 to 2011:
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By choosing a particular weighting scheme, the investor exposes himself to a model selection risk. Kan and Zhou (2007) argue that in the presence of parameter uncertainty, an investor should hold a combination of GMV and MSR strategy, along with a risk free asset. The idea of diversifying across the two different strategies stems from the fact that the parameter estimation errors are not perfectly correlated and hence can be diversified away.
In a recent paper, Amenc et al (2012) show that individually the GMV portfolio provides defensive exposure to the equity premium that does well in adverse market conditions, whereas the MSR portfolios provide a higher access to the upside of equity markets. They also show that a 50/50 combination of GMV and MSR (or the Diversified portfolio) results in smoother outperformance across market regimes hence reducing the tracking error. In the absence of having knowledge about the true best weighting strategy, perhaps it’s time for investors to consider diversifying across different optimized weighting schemes.
References:
- Amenc, N., F, Goltz., A, Lodh., and L,Martellini. ”Diversifying the Diversifiers and Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of Underperformance.” The Journal of Portfolio Management, Vol. 38, No. 3 (Spring 2012), pp. 72-88.
- Kan, R., and G. Zhou. “Optimal Portfolio Choice with Parameter Uncertainty.” Journal of Financial and Quantitative Analysis, Vol. 42, No. 3 (2007), pp. 621-656.