positive at the 10% significance level. This number decreases from 37 to 28 if transaction costs increase from 0.50 to 1% per trade. As for the mean return selection criterion, for many indices it is found that the estimate of α is significantly positive and that simultaneously the estimate of β is significantly smaller than one. Thus, after correction for transaction costs and risk, for more than half of the indices it is found that the best technical trading strategy selected by the Sharpe ratio criterion significantly outperforms the buy-and-hold benchmark strategy and is even significantly less risky.
If the MSCI World Index is taken to be the market portfolio, then the results for α become less strong, as in the mean return selection criterion case. If transaction costs increase from 0% to 0.50 and 1%, then the number of indices for which a significant estimate of α is found declines from 46 to 25 and 18.
Trading case 1 α<0 α>0 β<1 β>1 α>0 ∧ α>0 ∧ β<1 β>1 0% 0 50 26 0 25 0 0.10% 0 46 34 0 29 0 0.25% 0 46 37 0 32 0 0.50% 0 39 43 0 32 0 0.75% 0 33 43 1 28 1 1% 1 27 42 1 22 1 Trading case 2 0% 0 50 21 0 20 0 0.10% 0 46 30 1 26 0 0.25% 0 43 36 1 30 0 0.50% 0 38 39 1 30 0 0.75% 0 33 37 1 26 0 1% 0 31 36 3 23 1 Trading case 3 0% 0 51 28 0 28 0 0.10% 0 45 37 0 31 0 0.25% 0 42 41 0 33 0 0.50% 0 37 43 1 33 0 0.75% 1 33 47 1 32 0 1% 2 28 47 1 26 0
Table 5.11: Summary: significance CAPM estimates, Sharpe ratio criterion. For each transaction cost case, the table shows the number of indices for which significant estimates are found at the 10% significance level for the coefficients in the Sharpe-Lintner CAPM. The local main stock market index is taken to be the market portfolio in the CAPM estimations. Columns 1 and 2 show the number of indices for which the estimate of α is significantly negative and positive. Columns 3 and 4 show the number of indices for which the estimate of β is significantly smaller and larger than one. Column 5 shows the number of indices for which the estimate of α is significantly positive as well as the estimate of β is significantly smaller than one. Column 6 shows the number of indices for which the estimate of α is significantly positive as well as the estimate of β is significantly larger than one. Note that the number of indices analyzed is equal to 51.