Data snooping
In the case of 0 and 0.25% transaction costs table 5.8B shows for trading case 3 the nominal, White's RC and Hansen's SPA-test p-values, if the best strategy is selected by the Sharpe ratio criterion. For trading case 3 table 5.12 summarizes the results for all transaction cost cases by showing the number of indices for which the corresponding p-value is smaller than 0.10.
The results for the Sharpe ratio selection criterion differ from the results for the mean return selection criterion. If the nominal p-value is used to test the null hypothesis that the best strategy is not superior to the benchmark of buy-and-hold, then the null is rejected for all indices at the 10% significance level for all cost cases. If a correction is made for data snooping, then it is found in the case of zero transaction costs that for 24 indices the null hypothesis that the best strategy is not superior to the buy-and-hold benchmark is rejected by the RC. However, for 35 indices 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. Thus for half of the indices we find that the best technical trading rule has forecasting power even when correcting for the specification search. These numbers are higher than for the mean return selection criterion. In total we find for 11 indices contradictory results, which is less than for the mean return selection criterion. Even in the case of 0.10% costs per trade, the number of indices for which the RC and the SPA-test reject the null is high, namely for 17 and 28 indices respectively. However, if transaction costs are increased any further, then the number of indices for which the RC rejects its null declines sharply: to 7, 3, 3, 1 in the 0.25, 0.50, 0.75 and 1% transaction costs cases. In contrast, the SPA-test rejects its null for 23, 16, 15 and 13 indices in the 0.25, 0.50, 0.75 and 1% transaction costs cases. Note that these results differ substantially from the mean return selection criterion in which case under 0.25, 0.50, 0.75 and 1% costs per trade the null of no superior predictive ability was rejected for
Trading case 3 costs pn pW pH 0% 51 24 35 0.10% 51 17 28 0.25% 51 7 23 0.50% 51 3 16 0.75% 51 3 15 1% 51 1 13
Table 5.12: Summary: Testing for predictive ability, Sharpe ratio criterion. For each transaction cost case, the table shows the number of indices 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 indices analyzed is equal to 51.
201