example, still for respectively 45, 44, 37, 32 and 27 indices out of 51 the estimate of α is significantly positive at the 10% significance level. The estimate of β is significantly smaller than one for 28, 28, 28, 33 and 34 indices, in the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade cases, indicating that even in the presence of high costs, the best selected technical trading strategies are less risky than the buy-and-hold strategy. The number of data series for which the estimate of β is significantly smaller than one increases as transaction costs increase. This is mainly caused because as transaction costs increase, by the selection criteria strategies are selected which trade less frequently and are thus less risky. Notice that for a large number of cases it is found that the estimate of α is significantly positive while simultaneously the estimate of β is significantly smaller than one. This means that the best-selected strategy did not only generate a statistically significant excess return over the buy-and-hold benchmark, but is also significantly less risky than the buy-and-hold benchmark. The results for the two other trading cases are similar.
If the MSCI World Index is used as market portfolio in the CAPM estimations, then the results for α become less strong4. In the case of zero transaction costs for 46 stock market indices it is found that the estimate of α is significantly different from zero. In the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade cases, for respectively 40, 34, 24, 24 and 19 indices out of 51 the estimate of α is significantly positive at the 10% significance level. However still the estimate of β is significantly smaller than one for 41, 41, 40, 40 and 42 indices in the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade case.
From these findings we conclude that there are trend-following technical trading techniques which can profitably be exploited, even after correction for transaction costs, when applied to local main stock market indices. As transaction costs increase, the best strategies selected are those which trade less frequently. Furthermore, if a correction is made for risk by estimating Sharpe-Lintner CAPMs, then it is found for many local main stock market indices that the best strategy has forecasting power, i.e. α>0. It is also found that in general the best strategy is less risky, i.e. β<1, than buying and holding the market portfolio. Hence, for most stock market indices, we can reject the null hypothesis that the profits of technical trading are just the reward for bearing risk.