to 3.16 basis points per day, 8% per year, but is still significantly positive. However the estimate of β is not significantly smaller than one anymore if as little as 0.10% costs per trade are charged.
costs α<0 α>0 β<1 β>1 α>0 ∧ α>0 ∧ β<1 β>1 0% 2 37 39 2 29 2 0.10% 2 37 38 2 29 1 0.25% 3 32 39 3 27 0 0.50% 3 31 38 3 25 0 0.75% 3 26 35 3 19 0 1% 3 24 35 3 17 0
Table 4.10: Summary: significance CAPM estimates, mean return criterion. For each transaction cost case, the table shows the number of data series for which significant estimates are found at the 10% significance level for the coefficients in the Sharpe-Lintner CAPM (4.1). Columns 1 and 2 show the number of data series for which the estimate of α is significantly negative and positive. Columns 3 and 4 show the number of data series for which the estimate of β is significantly smaller and larger than one. Column 5 shows the number of data series 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 data series 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 data series analyzed is equal to 51 (50 stocks and the AEX-index).
As further can be seen in the tables, if no transaction costs are implemented, then for most of the stocks the estimate of α is also significantly positive at the 10% significance level. Only for 2 stocks the estimate of α is significantly smaller than zero, while it is significantly positive for 36 stocks. Further the estimate of β is significantly smaller than one for 36 stocks (Fokker and UPC excluded). Only for two stocks β is significantly larger than one. The estimate of α decreases as costs increase and becomes less significant in more cases. However in the 0.50% and 1% costs per trade cases for example, still for respectively 31 and 24 data series out of 51 the estimate of α is significantly positive at the 10% significance level. 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.
From the findings until now we conclude that there are trend-following technical trading techniques which can profitably be exploited, also after correction for transaction costs, when applied to the AEX-index and to stocks listed in the AEX-index in the period January 1983 through May 2002. 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 that in many cases the best strategy has significant forecasting power, i.e. α>0. It is also even found that in general