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Abstract
Country indices as represented by iShares exhibit non-normal return distributions with both skewness and kurtosis. Earlier studies provide procedures for determining the statistical significance of stochastic dominance measures and the Sharpe Ratio. This present study uses these refinements to compare the performance of 18 country market indices. The iShares are indistinguishable when using the Sharpe Ratio as no significant differences are found. In contrast, stochastic dominance procedures identify dominant iShares. Although the results vary over time, stochastic dominance appears to be both more robust and discriminating than the CAPM in the ranking of the iShares.
Acknowledgements
We would like to acknowledge Hooi Hooi Lean and Jun Du for their assistance in the SD computations.
Notes
1Recently Kaur et al. Citation(1994), Barrett and Donald Citation(2003), and Anderson (Citation1996, Citation2004) developed alternative SD tests. However, the DD test developed by Davidson and Duclos Citation(2000) is found by Tse and Zhang Citation(2004) and Lean et al. Citation(2006) to be one of the least conservative but most powerful SD tests.
2Prior to the introduction of the SPDRs, investors could only trade the S&P 500 through the Vanguard 500 Trust mutual fund. Purchases and sales were only made at the net asset value at the closing price once each day.
3Since we are using daily return data and the DD test assumes that each pair of variables is independent and identically distributed (iid) we need to ensure that the DD inference is not problematic. To examine the robustness of our results we use Linton et al. Citation(2002) test, which relaxes the iid assumption, and in addition also examine the Barrett and Donald Citation(2003) stochastic dominance test. As the conclusion from these stochastic dominance tests is similar we report only the DD results.
4Davidson and Duclos Citation(2000) state that the null hypothesis can be rejected if any of the t statistics is significant with the wrong sign. To minimize type II error of finding dominance when there is none and to avoid ‘almost stochastic dominance’ (Leshno and Levy, Citation2002), we use a conservative 10% cutoff point for the proportion of t statistics.
5Refer to Fong et al. Citation(2005) and Lean et al. Citation(2006) for the reasoning. Critical values are: 3.691, 3.25 and 3.043 for 1%, 5% and 10% level of significance tabulated in Stoline and Ury Citation(1979).
6See Jobson and Korkie Citation(1981) and Memmel Citation(2003) for the development of the ratio test. The results of the test are available from the authors.
7We note that the comparison of any other pairs of funds (except EWP-EWJ) results in similar conclusions as the SPY–EWM comparison. Hence we only report the SPY–EWM and EWP–EWJ comparisons. Results of the other comparisons are available upon request.
8Refer to Equationequation (1) for the formula of Tk for k=1, 2 and 3.
9The subperiod results are not reported here, but are available from the authors.