to predict future price changes. The good performance of the technical trading rules could therefore be the reward for holding a risky asset needed to attract investors to bear the risk. Since the technical trading rule forecasts only depend on past price history, it seems unlikely that they should result in unusual risk-adjusted profits. To test this hypothesis we regress Sharpe-Lintner capital asset pricing models (CAPMs)

rti-rtf=α + β (rtM-rtf) + εt.     (1)
Here rti is the return on day t of the best strategy applied to index i, rtM is the return on day t of a (preferably broad) market portfolio M and rtf is the risk-free interest rate. As proxy for the market portfolio M we use the local index itself or the MSCI World Index, both expressed in the same currency according to which the return of the best strategy is computed. Because we considered three different trading cases for computing rti, and combine these with two different choices for the market portfolio M, we estimated in total six different CAPMs for each index. The coefficient β measures the riskiness of the active technical trading strategy relatively to the passive strategy of buying and holding the market portfolio. If β is not significantly different from one, then it is said that the strategy has equal risk as a buying and holding the market portfolio. If β>1 (β<1), then it is said that the strategy is more risky (less risky) than buying and holding the market portfolio and that it therefore should yield larger (smaller) returns. The coefficient α measures the excess return of the best strategy applied to stock i after correction of bearing risk. If it is not possible to beat a broad market portfolio after correction for risk and hence technical trading rule profits are just the reward for bearing risk, then α should not be significantly different from zero.

We estimated the Sharpe-Lintner CAPMs in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade. For trading case 3 table 5.7 shows in the cases of 0 and 0.50% transaction costs the estimation results if for each index the best strategy is selected by the mean return criterion and if the market portfolio is chosen to be the local main stock market index. Estimation is done with Newey-West (1987) heteroskedasticity and autocorrelation consistent (HAC) standard errors. Table 5.9 summarizes the CAPM estimation results for all trading cases and for all transaction cost cases by showing the number of indices for which significant estimates of α or β are found at the 10% significance level.

For example, for the best strategy applied to the MSCI World Index in the case of zero transaction costs, the estimate of α is significantly positive at the 1% significance level and equal to 13.42 basis points per day, that is approximately 33.8% on a yearly basis. The estimate of β is significantly smaller than one at the 10% significance level, which indicates that although the strategy generates a higher reward than simply buying

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