superior to the benchmark of buy-and-hold, then the null is rejected for most data series at the 10% significance level for all cost cases. If a correction is made for data snooping, then it is found for the no transaction costs case that for 10 data series the null hypothesis that the best strategy is not superior to the benchmark after correcting for data snooping is rejected by the RC. However for 30 data series the null hypothesis that none of the alternative strategies is superior to the buy-and-hold benchmark after correcting for data snooping is rejected by the SPA-test. The two data snooping tests thus give contradictory results for 20 data series. Even if costs are charged it is found that in a large number of cases the SPA-test rejects the null, while the RC does not. If costs are increased to 0.10 and 1%, then for respectively 17 and 15 data series the null of no superior predictive ability is rejected by the SPA-test. Note that these results differ substantially from the mean return selection criterion where in the cases of 0.10 and 1% transaction costs the null was rejected for respectively 2 and 1 data series. Hence, we conclude that the best strategy selected by the Sharpe ratio criterion is capable of beating the benchmark of a buy-and-hold strategy for approximately 30% of the stocks analyzed, after a correction is made for transaction costs and data snooping.
costs pn pW pH 0% 50 10 30 0.10% 51 4 17 0.25% 51 4 13 0.50% 51 4 15 0.75% 51 2 15 1% 51 2 15
Table 4.13: Summary: Testing for predictive ability, Sharpe ratio criterion. For each transaction cost case, the table shows the number of data series for which the nominal (pn), White's (2000) Reality Check (pW) or Hansen's (2001) Superior Predictive Ability test (pH) p-value is smaller than 0.10. Note that the number of data series analyzed is equal to 51 (50 stocks and the AEX-index).