Measuring the economic significance of mean-variance spanning

This paper investigates the economic significance of mean-variance spanning tests using three classical statistical tests in a unified framework. I show how to compute confidence intervals about the Sharpe ratios of tangent portfolios, the variance of return of minimum variance portfolios, as well as the certainty equivalent utility gains. I apply this statistical framework to the question of whether US investors should diversify internationally. The analysis suggests that a strong statistical rejection of the hypothesis that there is no improvement in the minimum variance portfolio’s standard deviation of return does not imply that there are no significant economic benefits to be made in terms of a substantial risk reduction. These results have important implications for empirical tests of mean-variance spanning as well as empirical assets pricing tests and minimum variance bounds on stochastic discount factors.     

An Exact Test of the Improvement of the Minimum Variance Portfolio

I propose an exact finite sample test of the risk reduction of the global minimum variance (GMV) portfolio. The GMV test statistic is proportional to the reduction in the variance of the GMV portfolio and has a straightforward geometric and portfolio interpretation and complements the celebrated GRS test in Gibbons et al. (1989). In practical applications, the GMV test leads to a rejection of the null hypothesis of no improvement in the GMV portfolio more often than the GRS test rejects the null hypothesis of no improvement in the risk‐return profile of the tangent portfolio. The power of the GMV test increases with the variance reduction of the GMV portfolio. Using test asset returns scaled by predetermined predictive variables is equivalent to increasing the overall number of test assets and leads to substantial power gains.     

Market Timing With Moving Averages

I present evidence that a moving average (MA) trading strategy has a greater average return and skewness as well as a lower variance compared to buying and holding the underlying asset using monthly returns of value‐weighted US decile portfolios sorted by market size, book‐to‐market, and momentum, and seven international markets as well as 18,000 individual US stocks. The MA strategy generates risk‐adjusted returns of 3–7% per year after transaction costs. The performance of the MA strategy is driven largely by the volatility of stock returns and resembles the payoffs of an at‐the‐money protective put on the underlying buy‐and‐hold return. Conditional factor models with macroeconomic variables, especially the default premium, can explain some of the abnormal returns. Standard market timing tests reveal ample evidence regarding the timing ability of the MA strategy.     

The Market Timing Power of Moving Averages: Evidence from US REITs and REIT Indexes

I present evidence that a moving average (MA) trading strategy dominates buying and holding the underlying asset in a mean‐variance sense using monthly returns of value‐weighted and equal‐weighted US REIT indexes over the period January 1980 until December 2010. The abnormal returns are largely insensitive to the four Carhart factors and produce economically and statistically significant alphas of between 10 and 15% per year after transaction costs. This performance is robust to different lags of the MA and in subperiods while investor sentiment, liquidity risks, business cycles, up and down markets, and the default spread cannot fully account for its performance. The MA strategy works just as well with randomly generated returns and bootstrapped returns. The substantial market timing ability of the MA strategy appears to be the main driver of the abnormal returns. The returns to the MA strategy resemble the returns of an imperfect at‐the‐money protective put strategy relative to the underlying portfolio. The lagged signal to switch has substantial predictive power over the subsequent return of the REIT index. The MA strategy avoids the sharp downturn at the beginning of 2008 and substantially outperforms the cumulative returns of the buy‐and‐hold strategy using all of the 20 REIT indexes. The results from applying the MA strategy with 274 individual REITs largely corroborate the findings for the REIT indexes.