the best strategy applied to a stock is less risky, i.e. β<1, than buying and holding the market portfolio. Hence we can reject the null hypothesis that the profits of technical trading are just the reward for bearing risk.

Data snooping

The question remains open whether the findings in favour of technical trading for particular stocks are the result of chance or of real superior forecasting power. Therefore we apply White's (2000) Reality Check (RC) and Hansen's (2001) Superior Predictive Ability (SPA) test. Because Hansen (2001) showed that White's RC is biased in the direction of one, p-values are computed for both tests to investigate whether these tests lead in some cases to different inferences.

In the case of 0 and 0.10% transaction costs table 4.9A shows the nominal, White's (2000) RC and Hansen's (2001) SPA-test p-values, if the best strategy is selected by the mean return criterion. Calculations are also done for the 0.25, 0.50, 0.75 and 1% costs per trade cases, but these yield no remarkably different results compared with the 0.10% costs per trade case. Table 4.11 summarizes the results for all transaction cost cases by showing the number of data series for which the corresponding p-value is smaller than 0.10. That is, the number of data series for which the null hypothesis is rejected at the 10% significance level.

costs pn pW pH
0% 50 2 14
0.10% 51 0 2
0.25% 51 0 2
0.50% 51 0 2
0.75% 51 0 1
1% 51 0 1

Table 4.11: Summary: Testing for predictive ability, mean return 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).

The nominal p-value, also called data mined p-value, tests the null hypothesis that the best strategy is not superior to the buy-and-hold benchmark, but does not correct for data snooping. From the tables it can be seen that this null hypothesis is rejected for most data series in all cost cases at the 10% significance level. Only for the postal company Koninklijke PTT Nederland the null hypothesis is not rejected if no transaction costs are implemented. However, if we correct for data snooping, then we find, in the case of zero transaction costs, that for only two of the data series the null hypothesis that the best
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