We define the training period on day t to last from t-Tr until and including t-1, where Tr is the length of the training period. The testing period lasts from t until and including t+Te-1, where Te is the length of the testing period. At the end of the training period the best strategy is selected by the mean return or Sharpe ratio criterion. Next, the selected technical trading strategy is applied in the testing period to generate trading signals. After the end of the testing period this procedure is repeated again until the end of the data series is reached. For the training and testing periods we use 28 different parameterizations of [Tr, Te] which can be found in Appendix B.
Table 4.14A, B shows the results for both selection criteria in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% transaction costs. Because the longest training period is one year, the results are computed for the period 1984:12-2002:5. In the second to last row of table 4.14A it can be seen that, if in the training period the best strategy is selected by the mean return criterion, then the excess return over the buy-and-hold of the best recursive optimizing and testing procedure is, on average, 32.23, 26.45, 20.85, 15.05, 10.43 and 8.02% yearly in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade. If transaction costs increase, the best recursive optimizing and testing procedure becomes less profitable. However, the excess returns are considerable large. If the Sharpe ratio criterion is used for selecting the best strategy during the training period, then the Sharpe ratio of the best recursive optimizing and testing procedure in excess of the Sharpe ratio of the buy-and-hold benchmark is on average 0.0377, 0.0306, 0.0213, 0.0128, 0.0082 and 0.0044 in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade, also declining if transaction costs increase (see second to last row of table 4.14B).
For comparison, the last row in table 4.14A, B shows the average over the results of the best strategies selected by the mean return or Sharpe ratio criterion in sample for each data series tabulated. As can be seen, clearly the results of the best strategies selected in sample are much better than the results of the best recursive out-of-sample forecasting procedure. Mainly for the network and telecommunications related companies the out-of-sample forecasting procedure performs much worse than the in-sample results.
If the mean return selection criterion is used, then table 4.15A shows for the 0 and 0.50% transaction cost cases for each data series the estimation results of the Sharpe-Lintner CAPM (see equation 4.1) where the return of the best recursive optimizing and testing procedure in excess of the risk-free interest rate is regressed against a constant α and the return of the AEX-index in excess of the risk-free interest rate. Estimation is done with Newey-West (1987) heteroskedasticity and autocorrelation consistent (HAC) standard errors. Table 4.16 summarizes the CAPM estimation results for all transaction cost cases by showing the number of data series for which significant estimates of α and