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Technical Trading Rule Performance in Amsterdam Stock Exchange Listed Stocks
4.1 Introduction
In Chapter 3 we have shown that objective computerized trend-following technical trading techniques applied to the Dow-Jones Industrial Average (DJIA) and to stocks listed in the DJIA in the period 1973-2001 are not statistically significantly superior to a buy-and-hold benchmark strategy after correction for data snooping and transaction costs. In this chapter we use a similar approach to test whether technical trading shows statistically significant forecasting power when applied to the Amsterdam Stock Exchange Index (AEX-index) and to stocks listed in the AEX-index in the period 1983-2002.
In section 4.2 we list the stock price data examined in this chapter and we present and discuss the summary statistics. We refer to the sections 3.3, 3.4 and 3.5 of Chapter 3 for the discussions on the set of technical trading rules applied, the computation of the performance measures and finally the problem of data snooping. Section 4.3 presents the empirical results of our study. In section 4.4 we test whether recursively optimizing and updating our technical trading rule set shows genuine out-of-sample forecasting ability. Finally, section 4.5 summarizes and concludes.
4.2 Data and summary statistics
The data series examined in this chapter are the daily closing levels of the Amsterdam Stock Exchange Index (AEX-index) and the daily closing prices of all stocks listed in this index in the period January 3, 1983 through May 31, 2002. The AEX-index is a market-weighted average of the 25 most important stocks traded at the Amsterdam Stock Exchange. These stocks are chosen once a year and their selection is based on the value of trading turnover during the preceding year. At the moment of composition of the index the weights are restricted to be at maximum 10%. Table 4.1 shows an historical overview when and which stocks entered or left the index and in some cases the reason why. For example, Algemene Bank Nederland (ABN) merged with AMRO Bank at August 27, 1990 and the new combination was listed under the new name ABN AMRO Bank. In total we evaluate a set of 50 stocks. All data series are corrected for dividends, capital changes and stock splits. As a proxy for the risk-free interest rate we use daily data on Dutch monthly interbank rates. Table 4.2 shows for each data series the sample period and the largest cumulative loss, that is the largest decline from a peak to a through. Next, table 4.3 shows the summary statistics. Because the first 260 data points are used for initializing the technical trading strategies, the summary statistics are shown from January 1, 1984. The first and second column show the names of the data series examined and the number of available data points. The third column shows the mean yearly effective return in percentage/100 terms. The fourth through seventh column show the mean, standard deviation, skewness and kurtosis of the logarithmic daily return. The eight column shows the t-ratio to test whether the mean logarithmic daily return is significantly different from zero. The ninth column shows the Sharpe ratio, that is the extra return over the risk-free interest rate per extra point of risk, as measured by the standard deviation. The tenth column shows the largest cumulative loss of the stocks in percentage/100 terms. The eleventh column shows the Ljung-Box (1978) Q-statistic testing whether the first 20 autocorrelations of the return series as a whole are significantly different from zero. The twelfth column shows the heteroskedasticity adjusted Box-Pierce (1970) Q-statistic, as derived by Diebold (1986). The final column shows the Ljung-Box (1978) Q-statistic testing for autocorrelations in the squared returns.
The mean yearly effective return of the AEX-index during the 1983-2002 period is equal to 10.4% and the yearly standard deviation is approximately equal to 19%. For the AEX-index and 21 stocks the mean logarithmic return is significantly positive, as tested with the simple t-ratios, while for 5 stocks the mean yearly effective return is severely and significantly negative. For example, the business firm Ceteco and truck builder Daf went broke, while the communications and cable networks related companies KPNQWest, UPC and Versatel stopped recently all payments due to their creditors. For the other 4 stocks which show negative returns, plane builder Fokker went broke, software builder Baan was taken over by the British Invensys, while telecommunications firm KPN and temporary employment agency Vedior are nowadays struggling for survival. The return distribution is strongly leptokurtic for all data series, especially for Ceteco, Fokker, Getronics and Nedlloyd, and is negatively skewed for the AEX-index and 32 stocks. On individual basis the stocks are more risky than the market-weighted AEX-index, as can be seen by the standard deviations and the largest cumulative loss numbers. Thus it is clear that firm specific risks are reduced by a diversified index. The Sharpe ratio is negative for 12 stocks, which means that these stocks were not able to beat a risk free investment. Among them are ABN, KLM and the earlier mentioned stocks. The largest cumulative loss of the AEX-index is equal to 47% and took place in the period August 12, 1987 through November 10, 1987. October 19, 1987 showed the biggest one-day percentage loss in history of the AEX-index and brought the index down by 12%. November 11, 1987 on its turn showed the largest one-day gain and brought the index up by 11.8%. For 30 stocks, for which we have data starting before the crash of 1987, only half showed a largest cumulative loss during the year 1987, and their deterioration started well before October 1987, indicating that stock prices were already decaying for a while before the crash actually happened. The financials, for example, lost approximately half of their value during the 1987 period. For the other stocks, for which we have data after the crash of 1987, the periods of largest decline started ten years later in 1997. Baan, Ceteco, Getronics, KPN, KPNQWest, OCE, UPC and Versatel lost almost their total value within two years during the burst of the internet and telecommunications bubble. The summary statistics show no largest declines after the terrorist attack against the US on September 11, 20011. With hindsight, the overall picture is that financials, chemicals and foods produced the best results.
We computed autocorrelation functions (ACFs) of the returns and significance is tested with Bartlett (1946) standard errors and Diebold's (1986) heteroskedasticity-consistent standard errors2. Typically autocorrelations of the returns are small with only few lags being significant. Without correcting for heteroskedasticity we find for 36 of the 50 stocks a significant first order autocorrelation, while when corrected for heteroskedasticity we find for 24 stocks a significant first order autocorrelation at the 10% significance level. No severe autocorrelation is found in the AEX-index. It is noteworthy that for most data series the second order autocorrelation is negative, while only in 8 out of 51 cases it is positive. The first order autocorrelation is negative in 10 cases. The Ljung-Box (1978) Q-statistics in the second to last column of table 4.3 reject for almost all data series the null hypothesis that the first 20 autocorrelations of the returns as a whole are equal to zero. For only 10 data series the null is not rejected. When looking at the first to last column with Diebold's (1986) heteroskedasticity-consistent Box-Pierce (1970) Q-statistics it appears that heteroskedasticity indeed seriously affects the inferences about serial correlation in the returns. When a correction is made for heteroskedasticity, then for the AEX-index and 41 stocks the null of no autocorrelation is not rejected. The autocorrelation functions of the squared returns show that for all data series the autocorrelations are high and significant up to order 20. The Ljung-Box (1978) Q-statistics reject the null of no autocorrelation in the squared returns firmly, except for steel manufacturer Corus. Hence, almost all data series exhibit significant volatility clustering, that is large (small) shocks are likely to be followed by large (small) shocks.
4.3 Empirical results
4.3.1 Results for the mean return criterion
Technical trading rule performance
In section 4.2 we have shown that almost no significant autocorrelation in the daily returns can be found after correction for heteroskedasticity. This implies that there is no linear dependence present in the data. One may thus question whether technical trading strategies can persistently beat the buy-and-hold benchmark. However, as noted by Alexander (1961), the dependence in price changes can be of such a complicated nonlinear form that standard linear statistical tools, such as serial correlations, may provide misleading measures of the degree of dependence in the data. Therefore he proposed to use nonlinear technical trading rules to test for dependence. In total we apply 787 objective computerized trend-following technical trading techniques with and without transaction costs to the AEX-index and to 50 stocks listed in the AEX-index (see sections 2.3 and 3.3 and
Appendix B of Chapter 3 for the technical trading rule parameterizations). Tables 4.4 and 4.5 show for each data series some statistics of the best strategy selected by the mean return criterion, if 0% and 0.25% costs per trade are implemented. Column 2 shows the parameters of the best strategy. In the case of a moving-average (MA) strategy these parameters are ``[short run MA, long run MA]'' plus the refinement parameters ``[%-band filter, time delay filter, fixed holding period, stop-loss]''. In the case of a trading range break, also called support-and-resistance (SR), strategy, the parameters are ``[the number of days over which the local maximum and minimum is computed]'' plus the refinement parameters as with the moving averages. In the case of a filter (FR) strategy the parameters are ``[the %-filter, time delay filter, fixed holding period]''. Columns 3 and 4 show the mean yearly return and excess mean yearly return of the best-selected strategy over the buy-and-hold benchmark, while columns 5 and 6 show the Sharpe ratio and excess Sharpe ratio of the best-selected strategy over the buy-and-hold benchmark. Column 7 shows the maximum loss the best strategy generates. Columns 8, 9 and 10 show the number of trades, the percentage of profitable trades and the percentage of days profitable trades last. Finally, the last column shows the standard deviation of the returns of the data series during profitable trades divided by the standard deviation of the returns of the data series during non-profitable trades.
To summarize, for each data series examined table 4.7A (i.e. table 4.7 panel A) shows the mean yearly excess return over the buy-and-hold benchmark of the best strategy selected by the mean return criterion, after implementing 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade. This wide range of costs captures a range of different trader types. For example, floor traders and large investors, such as mutual funds, can trade against relatively low transaction costs in the range of 0.10 to 0.25%. Home investors face higher costs in the range of 0.25 to 0.75%, depending whether they trade through the internet, by telephone or through their personal account manager. Next, because of the bid-ask spread, extra costs over the transaction costs are faced. By examining a wide range of 0 to 1% costs per trade, we belief that we can capture most of the cost possibilities faced in reality by most of the traders.
The results in table 4.7A are astonishing. As can be seen in the last row of the table, on average, the mean yearly excess return of the best strategy over the buy-and-hold benchmark is equal to 152% in the case of zero transaction costs, and it still is 124% in the case of 1% transaction costs. These incredibly good results are mainly caused by the communications and cable network firms KPNQWest, UPC and Versatel. However, subtracting all stocks for which the best strategy generates a return of more than 100% yearly in excess of the buy-and-hold, then, on average, the yearly excess return of the best strategy is equal to 32% in the case of no transaction costs, declining to 15%, if transaction costs increase to 1% per trade. Thus from these results we conclude that technical trading rules are capable of beating a buy-and-hold benchmark even after correction for transaction costs. These results are substantially better than when the same strategy set is applied to the DJIA and to stocks listed in the DJIA. In that case in the period 1987-2001, on average, the mean yearly excess return over the buy-and-hold benchmark declines from 17% to 7%, if transaction costs are increased from 0% to 1% per trade (see section 3.6.1, page ??, and table 3.7, page ??). It is interesting to compare our results to Fama (1965) and Theil and Leenders (1965). It was found by Theil and Leenders (1965) that the proportions of securities advancing and declining today on the Amsterdam Stock Exchange can help in predicting the proportions of securities advancing and declining tomorrow. However, Fama (1965) in contrast found that this is not true for the New York Stock Exchange. In our study we find that this difference in forecastability of both stock markets tends to persists into the 1980s and 1990s.
From table 4.4 it can be seen that in the case of zero transaction costs the best-selected strategies are mainly strategies which generate a lot of signals. Trading positions are held for only a few days. With hindsight, the best strategy for the Fokker and UPC stocks was to never have bought them, earning a risk-free interest rate during the investment period. For the AEX-index, in contrast, the best strategy is a single crossover moving-average rule which generates a signal if the price series crosses a 25-day moving average and where the single refinement is a 10% stop-loss. The mean yearly return is equal to 25%, which corresponds with a mean yearly excess return of 13.2%. The Sharpe ratio is equal to 0.0454 and the excess Sharpe ratio is equal to 0.0307. These excess performance measures are considerably large. The maximum loss of the strategy is 43.9%, slightly less than the maximum loss of buying and holding the AEX-index, which is equal to 46.7% (table 4.2). Once every 12 days the strategy generates a trade and in 65.9% of the trades is profitable. These profitable trades span 85% of the total number of trading days. Although the technical trading rules show economic significance, they all go through periods of heavy losses, well above the 50% for most stocks.
If transaction costs are increased to 0.25%, then table 4.5 shows that the best-selected strategies are strategies which generate substantially fewer signals in comparison with the zero transaction costs case. Trading positions are now held for a longer time. For example, for the AEX-index the best-selected strategy generates a trade every one-and-a-half year. Also the percentage of profitable trades and the percentage of days profitable trades last increases for most data series. Most extremely this is the case for the AEX-index; the 13 trading signals of the best-selected strategy were all profitable.
CAPM
If no transaction costs are implemented, then from the last column in table 4.4 it can be seen that the standard deviations of the returns of the data series themselves during profitable trades are higher than the standard deviations of the returns during non-profitable trades for the AEX-index and almost all stocks, except for Gist Brocades, Stork, TPG and Unilever. However, if 0.25% costs per trade are calculated, then for 22 data series out of 51 the standard deviation ratio is larger than one. According to the efficient markets hypothesis it is not possible to exploit a data set with past information to predict future price changes. The excellent 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=a + b (rtAEX-rtf) + et.
(1)
Here rti is the return on day t of the best strategy applied to stock i, rtAEX is the return on day t of the market-weighted AEX-index, which represents the market portfolio, and rtf is the risk-free interest rate. The coefficient b measures the riskiness of the active technical trading strategy relatively to the passive strategy of buying and holding the market portfolio. If b 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 b>1 (b<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 a 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 a should not be significantly different from zero. Table 4.8A shows for the 0 and 0.50% transaction costs cases3 the estimation results if for each data series the best strategy is selected by the mean return criterion. Estimation is done with Newey-West (1987) heteroskedasticity and autocorrelation consistent (HAC) standard errors. Table 4.10 summarizes the CAPM estimation results for all transaction cost cases by showing the number of data series for which significant estimates of a or b are found at the 10% significance level.
| costs |
a<0 |
a>0 |
b<1 |
b>1 |
a>0 Ù |
a>0 Ù |
| |
|
|
|
|
b<1 |
b>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 a is significantly negative and positive. Columns 3 and 4 show the number of data series for which the estimate of b is significantly smaller and larger than one. Column 5 shows the number of data series for which the estimate of a is significantly positive as well as the estimate of b is significantly smaller than one. Column 6 shows the number of data series for which the estimate of a is significantly positive as well as the estimate of b is significantly larger than one. Note that the number of data series analyzed is equal to 51 (50 stocks and the AEX-index).
For example, for the best strategy applied to the AEX-index in the case of zero transaction costs, the estimate of a is significantly positive at the 1% significance level and is equal to 5.27 basis points per day, that is approximately 13.3% per year. The estimate of b is significantly smaller than one at the 5% significance level, which indicates that although the strategy generates a higher reward than simply buying and holding the index, it is less risky. If transaction costs increase to 1%, then the estimate of a decreases to 3.16 basis points per day, 8% per year, but is still significantly positive. However the estimate of b is not significantly smaller than one anymore if as little as 0.10% costs per trade are charged.
As further can be seen in the tables, if no transaction costs are implemented, then for most of the stocks the estimate of a is also significantly positive at the 10% significance level. Only for 2 stocks the estimate of a is significantly smaller than zero, while it is significantly positive for 36 stocks. Further the estimate of b is significantly smaller than one for 36 stocks (Fokker and UPC excluded). Only for two stocks b is significantly larger than one. The estimate of a 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 a is significantly positive at the 10% significance level. Notice that for a large number of cases it is found that the estimate of a is significantly positive while simultaneously the estimate of b 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. a>0. It is also even found that in general the best strategy applied to a stock is less risky, i.e. b<1, than buying and holding the market portfolio. Hence we can reject the null hypothesis that the profits of technical trading are just the reward for bearing risk.
Data snooping
The question remains open whether the findings in favour of technical trading for particular stocks are the result of chance or of real superior forecasting power. Therefore we apply White's (2000) Reality Check (RC) and Hansen's (2001) Superior Predictive Ability (SPA) test. Because Hansen (2001) showed that White's RC is biased in the direction of one, p-values are computed for both tests to investigate whether these tests lead in some cases to different inferences.
In the case of 0 and 0.10% transaction costs table 4.9A shows the nominal, White's (2000) RC and Hansen's (2001) SPA-test p-values, if the best strategy is selected by the mean return criterion. Calculations are also done for the 0.25, 0.50, 0.75 and 1% costs per trade cases, but these yield no remarkably different results compared with the 0.10% costs per trade case. Table 4.11 summarizes the results for all transaction cost cases by showing the number of data series for which the corresponding p-value is smaller than 0.10. That is, the number of data series for which the null hypothesis is rejected at the 10% significance level.
| costs |
pn |
pW |
pH |
| 0% |
50 |
2 |
14 |
| 0.10% |
51 |
0 |
2 |
| 0.25% |
51 |
0 |
2 |
| 0.50% |
51 |
0 |
2 |
| 0.75% |
51 |
0 |
1 |
| 1% |
51 |
0 |
1 |
Table 4.11: Summary: Testing for predictive ability, mean return criterion. For each transaction cost case, the table shows the number of data series for which the nominal (pn), White's (2000) Reality Check (pW) or Hansen's (2001) Superior Predictive Ability test (pH) p-value is smaller than 0.10. Note that the number of data series analyzed is equal to 51 (50 stocks and the AEX-index).
The nominal p-value, also called data mined p-value, tests the null hypothesis that the best strategy is not superior to the buy-and-hold benchmark, but does not correct for data snooping. From the tables it can be seen that this null hypothesis is rejected for most data series in all cost cases at the 10% significance level. Only for the postal company Koninklijke PTT Nederland the null hypothesis is not rejected if no transaction costs are implemented. However, if we correct for data snooping, then we find, in the case of zero transaction costs, that for only two of the data series the null hypothesis that the best strategy is not superior to the benchmark after correcting for data snooping is rejected by the RC, while for 14 data series the null hypothesis that none of the alternative strategies is superior to the buy-and-hold benchmark after correcting for data snooping is rejected by the SPA-test. The two data snooping tests thus give contradictory results for 12 data series. However, if we implement as little as 0.10% costs, then both tests do not reject the null anymore for almost all data series. Only for Robeco and UPC the null is still rejected by the SPA-test. Remarkably, for Robeco and UPC the null is rejected even if costs are increased to 0.50%, and for UPC only if costs per trade are even higher. Hence, we conclude that the best strategy, selected by the mean return criterion, is not capable of beating the buy-and-hold benchmark strategy, after a correction is made for transaction costs and data snooping.
4.3.2 Results for the Sharpe ratio criterion
Technical trading rule performance
Similar to tables 4.4 and 4.5, table 4.6 shows for some data series some statistics of the best strategy selected by the Sharpe ratio criterion, if 0 or 0.25% costs per trade are implemented. Only the results for those data series are presented for which the best strategy selected by the Sharpe ratio criterion differs from the best strategy selected by the mean return criterion. Further table 4.7B shows for each data series the Sharpe ratio of the best strategy selected by the Sharpe ratio criterion, after implementing 0, 0.10, 0.25, 0.50, 0.75 and 1% transaction costs, in excess of the Sharpe ratio of the buy-and-hold benchmark. It is found that the Sharpe ratio of the best-selected strategy in excess of the Sharpe ratio of the buy-and-hold benchmark is positive in all cases. In the last row of table 4.7B it can be seen that the average excess Sharpe ratio declines from 0.0477 to 0.0311 if transaction costs increase from 0 to 1%. For the full sample period table 4.6 shows that the best strategies selected in the case of zero transaction costs are mainly strategies that generate a lot of signals. Trading positions are held for only a short period. Moreover, for most data series, except 13, these best-selected strategies are the same as in the case that the best strategies are selected by the mean return criterion. If transaction costs are increased to 0.25% per trade, then the best strategies generate fewer signals and trading positions are held for longer periods. In that case for the AEX-index and 18 stocks the best-selected strategy differs from the case where strategies are selected by the mean return criterion.
As for the mean return criterion it is found that for each data series the best technical trading strategy, selected by the Sharpe ratio criterion, beats the buy-and-hold benchmark and that this strategy can profitably be exploited, even after correction for transaction costs.
CAPM
The estimation results of the Sharpe-Lintner CAPM in tables 4.8B and 4.12 for the Sharpe ratio criterion are similar to the estimation results in tables 4.8A and 4.10 for the mean return criterion. If zero transaction costs are implemented, then it is found for 39 out of 51 data series that the estimate of a is significantly positive at the 10% significance level. This number decreases to 32 and 25 data series if transaction costs increase to 0.50 and 1% per trade. The estimates of b are in general significantly smaller than one. Thus, after correction for transaction costs and risk, for approximately half of the data series examined it is found that the best technical trading strategy selected by the Sharpe ratio criterion outperforms the strategy of buying and holding the market portfolio and is even less risky.
| costs |
a<0 |
a>0 |
b<1 |
b>1 |
a>0 Ù |
a>0 Ù |
| |
|
|
|
|
b<1 |
b>1 |
| 0% |
2 |
39 |
41 |
2 |
32 |
2 |
| 0.10% |
2 |
38 |
42 |
1 |
32 |
1 |
| 0.25% |
2 |
35 |
42 |
1 |
30 |
0 |
| 0.50% |
2 |
32 |
41 |
0 |
26 |
0 |
| 0.75% |
2 |
29 |
40 |
0 |
23 |
0 |
| 1% |
3 |
25 |
40 |
0 |
19 |
0 |
Table 4.12: Summary: significance CAPM estimates, Sharpe ratio 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 a is significantly negative and positive. Columns 3 and 4 show the number of data series for which the estimate of b is significantly smaller and larger than one. Column 5 shows the number of data series for which the estimate of a is significantly positive as well as the estimate of b is significantly smaller than one. Column 6 shows the number of data series for which the estimate of a is significantly positive as well as the estimate of b is significantly larger than one. Note that the number of data series analyzed is equal to 51 (50 stocks and the AEX-index).
Data snooping
In the case of 0 and 0.10% transaction costs table 4.9B shows the nominal, White's RC and Hansen's SPA-test p-values, if the best strategy is selected by the Sharpe ratio criterion. Table 4.13 summarizes the results for all transaction cost cases by showing the number of data series for which the corresponding p-value is smaller than 0.10.
The results for the Sharpe ratio selection criterion differ from the mean return selection criterion. If the nominal p-value is used to test the null that the best strategy is not superior to the benchmark of buy-and-hold, then the null is rejected for most data series at the 10% significance level for all cost cases. If a correction is made for data snooping, then it is found for the no transaction costs case that for 10 data series the null hypothesis that the best strategy is not superior to the benchmark after correcting for data snooping is rejected by the RC. However for 30 data series the null hypothesis that none of the alternative strategies is superior to the buy-and-hold benchmark after correcting for data snooping is rejected by the SPA-test. The two data snooping tests thus give contradictory results for 20 data series. Even if costs are charged it is found that in a large number of cases the SPA-test rejects the null, while the RC does not. If costs are increased to 0.10 and 1%, then for respectively 17 and 15 data series the null of no superior predictive ability is rejected by the SPA-test. Note that these results differ substantially from the mean return selection criterion where in the cases of 0.10 and 1% transaction costs the null was rejected for respectively 2 and 1 data series. Hence, we conclude that the best strategy selected by the Sharpe ratio criterion is capable of beating the benchmark of a buy-and-hold strategy for approximately 30% of the stocks analyzed, after a correction is made for transaction costs and data snooping.
| costs |
pn |
pW |
pH |
| 0% |
50 |
10 |
30 |
| 0.10% |
51 |
4 |
17 |
| 0.25% |
51 |
4 |
13 |
| 0.50% |
51 |
4 |
15 |
| 0.75% |
51 |
2 |
15 |
| 1% |
51 |
2 |
15 |
Table 4.13: Summary: Testing for predictive ability, Sharpe ratio criterion. For each transaction cost case, the table shows the number of data series for which the nominal (pn), White's (2000) Reality Check (pW) or Hansen's (2001) Superior Predictive Ability test (pH) p-value is smaller than 0.10. Note that the number of data series analyzed is equal to 51 (50 stocks and the AEX-index).
4.4 A recursive out-of-sample forecasting approach
In section 3.7 we argued to apply a recursive out-of-sample forecasting approach to test whether technical trading rules have true out-of-sample forecasting power. For example, recursively at the beginning of each month it is investigated which technical trading rule performed the best in the preceding six months (training period) and this strategy is used to generate trading signals during the coming month (testing period). In this section we apply the recursive out-of-sample forecasting procedure to the data series examined in this chapter.
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 a 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 a and b are found at the 10% significance level. In the case of zero transaction costs for 31 data series out of 51 the estimate of a is significantly positive at the 10% significance level. This number decreases to 21 (10, 4, 3, 2) if 0.10% (0.25, 0.50, 0.75, 1%) costs per trade are implemented. Table 4.15B shows the results of the CAPM estimation for the case that the best strategy in the training period is selected by the Sharpe ratio criterion. Now in the case of zero transaction costs for 33 data series it is found that the estimate of a is significantly positive at the 10% significance level. If transaction costs increase to 0.10% (0.25, 0.50, 0.75, 1%), then for 24 (11, 2, 2, 2) out of 51 data series the estimate of a is significantly positive. Hence, after correction for 1% transaction costs and risk it can be concluded, independently of the selection criterion used, that the best recursive optimizing and testing procedure shows no statistically significant out-of-sample forecasting power.
| |
Selection criterion: mean return |
| costs |
a<0 |
a>0 |
b<1 |
b>1 |
a>0 Ù |
a>0 Ù |
| |
|
|
|
|
b<1 |
b>1 |
| 0% |
1 |
31 |
35 |
2 |
25 |
0 |
| 0.10% |
1 |
21 |
32 |
3 |
15 |
0 |
| 0.25% |
1 |
10 |
34 |
4 |
8 |
0 |
| 0.50% |
2 |
4 |
31 |
3 |
1 |
0 |
| 0.75% |
3 |
3 |
29 |
4 |
1 |
1 |
| 1% |
3 |
2 |
30 |
2 |
1 |
0 |
| |
Selection criterion: Sharpe ratio |
| costs |
a<0 |
a>0 |
b<1 |
b>1 |
a>0 Ù |
a>0 Ù |
| |
|
|
|
|
b<1 |
b>1 |
| 0% |
0 |
33 |
42 |
2 |
30 |
1 |
| 0.10% |
0 |
24 |
39 |
1 |
21 |
0 |
| 0.25% |
0 |
11 |
40 |
2 |
10 |
0 |
| 0.50% |
0 |
2 |
36 |
2 |
1 |
0 |
| 0.75% |
0 |
2 |
34 |
2 |
1 |
0 |
| 1% |
0 |
2 |
35 |
2 |
1 |
0 |
Table 4.16: Summary: significance CAPM estimates for best out-of-sample testing procedure. 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. Columns 1 and 2 show the number of data series for which the estimate of a is significantly negative and positive. Columns 3 and 4 show the number of data series for which the estimate of b is significantly smaller and larger than one. Column 5 shows the number of data series for which the estimate of a is significantly positive as well as the estimate of b is significantly smaller than one. Column 6 shows the number of data series for which the estimate of a is significantly positive as well as the estimate of b is significantly larger than one. Note that the number of data series analyzed is equal to 51 (50 stocks and the AEX-index).
4.5 Conclusion
In this chapter we apply a set of 787 objective computerized trend-following technical trading techniques to the Amsterdam Stock Exchange Index (AEX-index) and to 50 stocks listed in the AEX-index in the period January 1983 through May 2002. For each data series the best technical trading strategy is selected by the mean return or Sharpe ratio criterion. The advantage of the Sharpe ratio selection criterion over the mean return selection criterion is that it selects the strategy with the highest return/risk pay-off. Although for 12 stocks it is found that they could not even beat a continuous risk free investment, we find for both selection criteria that for each data series a technical trading strategy can be selected that is capable of beating the buy-and-hold benchmark, even after correction for transaction costs. For example, if the best strategy is selected by the mean return criterion, then on average, the best strategy beats the buy-and-hold benchmark with 152, 141, 135, 131, 127 and 124% yearly in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% transaction costs. However these extremely high numbers are mainly caused by IT and telecommunications related companies. If we discard these companies from the calculations, then still on average, the best strategy beats the buy-and-hold benchmark with 32, 22, 19, 17, 16 and 15% for the six different costs cases. These are quite substantial numbers.
The profits generated by the technical trading strategies could be the reward necessary to attract investors to bear the risk of holding the asset. To test this hypothesis we estimate Sharpe-Lintner CAPMs. For each data series the daily return of the best strategy in excess of the risk-free interest rate is regressed against a constant (a) and the daily return of the market-weighted AEX-index in excess of the risk-free interest rate. The coefficient of the last regression term is called b and measures the riskiness of the strategy relatively to buying and holding the market portfolio. If technical trading rules do not generate excess profits after correction for risk, then a should not be significantly different from zero. In the case of zero transaction costs it is found for the mean return as well as the Sharpe ratio criterion that for respectively 37 and 39 data series the estimate of a is significantly positive at the 10% significance level. Even if transaction costs are increased to 1% per trade, then we find for half of the data series that the estimate of a is still significantly positive. Moreover it is found that simultaneously the estimate of b is significantly smaller than one for many data series. Thus for both selection criteria we find for approximately half of the data series that in the presence of transaction costs the best technical trading strategies have forecasting power and even reduce risk.
An important question is whether the positive results found in favour of technical trading are due to chance or the fact that the best strategy has genuine superior forecasting power over the buy-and-hold benchmark. This is called the danger of data snooping. We apply White's (2000) Reality Check (RC) and Hansen's (2001) Superior Predictive Ability (SPA) test, to test the null hypothesis that the best strategy found in a specification search is not superior to the benchmark of a buy-and-hold if a correction is made for data snooping. Hansen (2001) showed that White's RC is biased in the direction of one, caused by the inclusion of poor strategies. Because we compute p-values for both tests, we can investigate whether the two test procedures result in different inferences about forecasting ability of technical trading. If zero transaction costs are implemented, then we find for the mean return selection criterion that the RC and the SPA-test in some cases lead to different conclusions. The SPA-test finds in numerous cases that the best strategy does beat the buy-and-hold significantly after correction for data snooping and the inclusion of bad strategies. Thus the biased RC misguides the researcher in several cases by not rejecting the null. However, if as little as 0.10% costs per trade are implemented, then both tests lead for almost all data series to the same conclusion: the best technical trading strategy selected by the mean return criterion is not capable of beating the buy-and-hold benchmark after correcting for the specification search that is used to find the best strategy. In contrast, for the Sharpe ratio selection criterion we find totally different results. Now the SPA-test rejects its null for 30 data series in the case of zero transaction costs, while the RC rejects its null for only 10 data series. If transaction costs are increased further to even 1% per trade, then for approximately one third of the stocks analyzed, the SPA-test rejects the null of no superior predictive ability at the 10% significance level, while the RC rejects the null for only two data series. We find for the Sharpe ratio selection criterion large differences between the two testing procedures. Thus the inclusion of poor performing strategies for which the SPA-test is correcting, can indeed influence the inferences about the predictive ability of technical trading rules.
The results show that technical trading has forecasting power for a certain group of stocks listed in the AEX-index. Further the best way to select technical trading strategies is on the basis of the Sharpe ratio criterion. However the testing procedures are mainly done in sample. Therefore next we apply a recursive optimizing and testing method to test whether the best strategy found in a specification search during a training period shows also forecasting power during a testing period thereafter. For example, every month the best strategy from the last 6 months is selected to generate trading signals during that month. In total we examine 28 different training and testing period combinations. In the case of zero transaction costs the best recursive optimizing and testing procedure yields on average an excess return over the buy-and-hold of 32.23% yearly, if the best strategy in the training period is selected by the mean return criterion. Thus the best strategy found in the past continues to generate good results in the future. If 0.50% (1%) transaction costs are implemented, then the excess return decreases to 15.05% (8.02%). These are quite substantial numbers.
Estimation of Sharpe-Lintner CAPMs shows that, after correction for 0.10% transaction costs and risk, the best recursive optimizing and testing procedure has significant forecasting power for more than 40% of the data series examined. However, if transaction costs increase to 1%, then for almost all data series the best recursive optimizing and testing procedure has no statistically significant forecasting power anymore.
Hence, in short, after correcting for sufficient transaction costs, risk, data snooping and out-of-sample forecasting, we conclude that objective trend-following technical trading techniques applied to the AEX-index and to stocks listed in the AEX-index in the period 1983-2002 are not genuine superior, as suggested by their performances, to the buy-and-hold benchmark. Only for transaction costs below 0.10% technical trading is statistically profitable, if the best strategy is selected by the Sharpe ratio criterion.
Appendix
A. Tables
| Table |
| 4.1 |
Overview of stocks entering and leaving the AEX-index |
| 4.2 |
Data series examined, sample and largest cumulative loss |
| 4.3 |
Summary statistics |
| 4.4 |
Statistics best strategy: mean return criterion, 0% costs |
| 4.5 |
Statistics best strategy: mean return criterion, 0.25% costs |
| 4.6 |
Statistics best strategy: Sharpe ratio criterion, 0 and 0.25% costs |
| 4.7A |
Mean return best strategy in excess of mean return buy-and-hold |
| 4.7B |
Sharpe ratio best strategy in excess of Sharpe ratio buy-and-hold |
| 4.8A |
Estimation results CAPM: mean return criterion |
| 4.8B |
Estimation results CAPM: Sharpe ratio criterion |
| 4.9A |
Testing for predictive ability: mean return criterion |
| 4.9B |
Testing for predictive ability: Sharpe ratio criterion |
| 4.10 |
Summary: significance CAPM estimates, mean return criterion |
| 4.11 |
Summary: Testing for predictive ability, mean return criterion |
| 4.12 |
Summary: significance CAPM estimates, Sharpe ratio criterion |
| 4.13 |
Summary: Testing for predictive ability, Sharpe Ratio criterion |
| 4.14A |
Mean return best out-of-sample testing procedure in excess of mean return buy-and-hold |
| 4.14B |
Sharpe ratio best out-of-sample testing procedure in excess of Sharpe ratio buy-and-hold |
| 4.15A |
Estimation results CAPM for best out-of-sample testing procedure: mean return criterion |
| 4.15B |
Estimation results CAPM for best out-of-sample testing procedure: Sharpe ratio criterion |
| 4.16 |
Summary: significance CAPM estimates for best out-of-sample testing procedure |
Table 4.1: Overview of stocks entering and leaving the AEX-index. Column 1 shows the names of all stocks listed in the AEX-index in the period January 3, 1983 through March 1, 2002. Columns 2 and 3 show the dates when a stock entered or left the index. Column 4 shows the reason. Source: Euronext.
| Fund name |
In |
Out |
What happened? |
| Algemene Bank Nederland (ABN) |
01/03/83 |
08/27/90 |
Merger with AMRO bank |
| Ahold (AH) |
01/03/83 |
|
|
| Akzo (AKZ) |
01/03/83 |
|
|
| Amro (ARB) |
01/03/83 |
08/27/90 |
Merger with ABN |
| Koninklijke Gist-Brocades (GIS) |
01/03/83 |
02/20/98 |
|
| Heineken (HEI) |
01/03/83 |
|
|
| Hoogovens (HO) |
01/03/83 |
10/06/99 |
Merger with British Steel, name change to Corus Group |
| KLM |
01/03/83 |
02/18/00 |
|
| Royal Dutch (RD) |
01/03/83 |
|
|
| Nationale Nederlanden (NN) |
01/03/83 |
03/01/91 |
Merger with NMB |
| Philips (PHI) |
01/03/83 |
|
|
| Unilever (UNI) |
01/03/83 |
|
|
| Koninklijke Nedlloyd (NED) (NDL after Sept 30, 1994) |
01/03/83 |
02/20/98 |
|
| Aegon (AGN) |
05/29/84 |
|
|
| Robeco (ROB) |
01/03/85 |
09/01/86 |
|
| Amev (AMV) |
01/03/86 |
06/20/94 |
Name change in Fortis Amev |
| Fortis Amev (FOR) (name change in Fortis (NL) Jan 11, 1999) |
06/20/94 |
12/17/01 |
Combing of shares Fortis Netherlands |
| and Fortis Belgium |
| Fortis (FORA) |
12/17/01 |
|
Result of combining shares Fortis |
| Netherlands and Fortis Belgium |
| Elsevier (ELS) |
09/01/86 |
|
|
| Koninklijke Nederlandse |
| Papierfabrieken (KNP) |
09/01/86 |
03/09/93 |
Merger with Buhrmann Tettenrode |
| Buhrmann Tettenrode (BT) |
12/01/86 |
03/09/93 |
Merger with Koninklijke Nederlandse |
| Papierfabrieken |
| Nederlandse Middenstands Bank |
| (NMB) |
12/01/86 |
06/20/88 |
|
| Nederlandse Middenstands Bank |
| (NMB) |
10/05/89 |
03/01/91 |
Merger with Nationale Nederlanden |
| Oce van der Grinten (OCE) |
12/01/86 |
06/20/88 |
|
| Oce van der Grinten (OCE) |
02/21/97 |
05/01/97 |
Name change in OCE |
| Oce (OCE) |
05/01/97 |
02/18/00 |
|
| Van Ommeren Ceteco N.V. (VOC) |
06/20/88 |
02/18/94 |
|
| Wessanen N.V. (WES) |
06/20/88 |
04/07/93 |
Merger with Bols |
| DAF |
10/05/89 |
02/04/93 |
|
| DSM |
10/05/89 |
|
|
| Fokker (FOK) |
10/05/89 |
02/17/95 |
|
| Verenigd bezit VNU (name change to VNU July 31, 1998) |
10/05/89 |
|
|
| ABN AMRO Bank (AAB) |
08/27/90 |
|
Result of merger ABN and AMRO |
| Polygram (PLG) |
08/27/90 |
12/08/98 |
Take over by The Seagram Company Ltd. |
| Internationale Nederlanden Groep |
| (ING) |
03/01/91 |
|
Result of merger NMB with NN |
| Wolters Kluwer (WKL) |
04/19/91 |
|
|
| Stork (STO) |
02/04/93 |
02/19/96 |
|
Table 4.1 continued.
| Fund name |
In |
Out |
What happened? |
| KNP BT (KKB) (name change |
| to Buhrmann July 31, 1998) |
03/09/93 |
08/31/98 |
Result of merger KNP and BT |
| Buhrmann (BUHR) |
08/31/98 |
02/18/00 |
|
| Buhrmann (BUHR) |
03/01/01 |
|
|
| Koninklijke BolsWessanen (BSW) |
04/07/93 |
02/20/98 |
Result of merger Bols and Wessanen |
| CSM |
02/18/94 |
02/21/97 |
|
| Pakhoed (PAK) |
02/18/94 |
02/19/96 |
|
| Koninklijke PTT Nederland (KPN) |
02/17/95 |
06/29/98 |
Split in Koninklijke KPN and |
| TNT Post Group |
| Hagemeyer (HGM) |
02/19/96 |
|
|
| Koninklijke Verenigde Bedrijven Nutricia (NUT) |
02/19/96 |
01/26/98 |
Name change in Koninklijke Numico |
| Koninklijke Numico (NUM) |
01/26/98 |
|
|
| ASM Lithography (ASML) (name |
| change to ASML Holding NV June 13, 2001) |
02/20/98 |
|
|
| Baan Company (BAAN) |
02/20/98 |
08/04/00 |
Take over by Invensys plc |
| Vendex International (VI) |
02/20/98 |
06/25/98 |
Split in Vendex and Vedior |
| Vendex (VDX) |
06/25/98 |
03/01/01 |
Result of split Vendex International |
| Vedior (VDOR) |
06/25/98 |
02/19/99 |
Result of split Vendex International |
| Koninklijke KPN (KPN) |
06/29/98 |
|
Result of split Koninklijke PTT |
| Nederland |
| TNT Post Group (TPG) (name |
| change to TPG NV August 6, 2001) |
06/29/98 |
|
Result of split Koninklijke PTT |
| Nederland |
| Corus Group (CORS) |
10/06/99 |
03/01/01 |
Result of merger Hoogovens |
| with British Steel |
| Getronics (GTN) |
02/18/00 |
|
|
| United Pan-Europe |
| Communications (UPC) |
02/18/00 |
02/14/02 |
|
| Gucci |
02/18/00 |
|
|
| KPNQWEST (KQIP) |
03/01/01 |
06/06/02 |
|
| Versatel (VERS) |
03/01/01 |
03/01/02 |
|
| CMG |
03/01/02 |
|
|
| Van der Moolen (MOO) |
03/01/02 |
|
|
Table 4.2: Data series examined, sample and largest cumulative loss. Column 1 shows the names of the data series that are examined in this chapter. Column 2 shows their respective sample periods. Columns 3 and 4 show the largest cumulative loss of the data series in %/100 terms and the period during which this decline occurred.
| Data set |
Sample period |
Max. loss |
Period of max. loss |
| AEX |
12/30/83 - 05/31/02 |
-0.4673 |
08/12/87 - 11/10/87 |
| ABN |
12/30/83 - 08/21/90 |
-0.3977 |
08/14/86 - 11/10/87 |
| AMRO |
12/30/83 - 08/21/90 |
-0.4824 |
01/17/86 - 11/30/87 |
| ABN AMRO |
08/20/91 - 05/31/02 |
-0.4821 |
04/15/98 - 10/05/98 |
| AEGON |
12/30/83 - 05/31/02 |
-0.5748 |
01/06/86 - 11/10/87 |
| AHOLD |
12/30/83 - 05/31/02 |
-0.4754 |
08/13/87 - 01/04/88 |
| AKZO NOBEL |
12/30/83 - 05/31/02 |
-0.5646 |
09/24/87 - 11/08/90 |
| ASML |
03/13/96 - 05/31/02 |
-0.7866 |
03/13/00 - 09/21/01 |
| BAAN |
05/17/96 - 08/03/00 |
-0.9743 |
04/22/98 - 05/22/00 |
| BUHRMANN |
12/30/83 - 05/31/02 |
-0.8431 |
07/25/00 - 09/21/01 |
| CETECO |
05/23/95 - 05/31/02 |
-0.9988 |
03/30/98 - 07/19/01 |
| CMG |
11/29/96 - 05/31/02 |
-0.928 |
02/18/00 - 05/30/02 |
| CORUS |
10/03/00 - 05/31/02 |
-0.512 |
05/23/01 - 09/21/01 |
| CSM |
12/30/83 - 05/31/02 |
-0.343 |
05/23/86 - 11/10/87 |
| DAF |
05/31/90 - 08/31/93 |
-0.9986 |
06/27/90 - 08/20/93 |
| DSM |
02/02/90 - 05/31/02 |
-0.4008 |
05/21/92 - 03/01/93 |
| REED ELSEVIER |
12/30/83 - 05/31/02 |
-0.5169 |
08/11/87 - 11/10/87 |
| FOKKER |
12/30/83 - 03/04/98 |
-0.9965 |
06/23/86 - 10/30/97 |
| FORTIS |
12/30/83 - 05/31/02 |
-0.6342 |
01/17/86 - 12/10/87 |
| GETRONICS |
05/23/86 - 05/31/02 |
-0.9279 |
03/07/00 - 09/20/01 |
| GIST BROCADES |
12/30/83 - 08/27/98 |
-0.6121 |
01/06/86 - 12/29/87 |
| GUCCI |
10/21/96 - 05/31/02 |
-0.5938 |
04/08/97 - 10/08/98 |
| HAGEMEYER |
12/30/83 - 05/31/02 |
-0.7398 |
07/24/97 - 09/21/01 |
| HEINEKEN |
12/30/83 - 05/31/02 |
-0.4398 |
08/12/87 - 11/10/87 |
| HOOGOVENS |
12/30/83 - 12/09/99 |
-0.8104 |
05/23/86 - 11/10/87 |
| ING |
02/28/92 - 05/31/02 |
-0.5442 |
07/21/98 - 10/05/98 |
| KLM |
12/30/83 - 05/31/02 |
-0.7843 |
07/16/98 - 09/18/01 |
| KON. PTT NED. |
06/09/95 - 06/26/98 |
-0.1651 |
07/18/97 - 09/11/97 |
| KPN |
06/25/99 - 05/31/02 |
-0.9692 |
03/13/00 - 09/05/01 |
| KPNQWEST |
11/03/00 - 05/31/02 |
-0.9929 |
01/25/01 - 05/29/02 |
| VAN DER MOOLEN |
12/15/87 - 05/31/02 |
-0.6871 |
07/09/98 - 10/05/98 |
| NAT. NEDERLANDEN |
12/30/83 - 04/11/91 |
-0.4803 |
05/23/86 - 11/10/87 |
| NEDLLOYD |
12/30/83 - 05/31/02 |
-0.7844 |
04/18/90 - 10/08/98 |
| NMB POSTBANK |
12/30/83 - 03/01/91 |
-0.5057 |
01/07/86 - 01/14/88 |
| NUMICO |
12/30/83 - 05/31/02 |
-0.683 |
11/05/86 - 01/04/88 |
| OCE |
12/30/83 - 05/31/02 |
-0.8189 |
05/26/98 - 09/21/01 |
| PAKHOED |
12/30/83 - 11/03/99 |
-0.4825 |
04/23/98 - 10/01/98 |
| PHILIPS |
12/30/83 - 05/31/02 |
-0.6814 |
09/05/00 - 09/21/01 |
| POLYGRAM |
12/13/90 - 12/14/98 |
-0.3275 |
08/08/97 - 04/29/98 |
| ROBECO |
12/30/83 - 05/31/02 |
-0.4363 |
09/13/00 - 09/21/01 |
| ROYAL DUTCH |
12/30/83 - 05/31/02 |
-0.3747 |
10/13/00 - 09/21/01 |
| STORK |
12/30/83 - 05/31/02 |
-0.7591 |
10/06/97 - 09/21/01 |
| TPG |
06/25/99 - 05/31/02 |
-0.4174 |
01/24/00 - 09/14/01 |
| UNILEVER |
12/30/83 - 05/31/02 |
-0.4541 |
07/07/98 - 03/13/00 |
| UPC |
02/10/00 - 05/31/02 |
-0.999 |
03/09/00 - 04/16/02 |
| VEDIOR |
06/03/98 - 05/31/02 |
-0.7169 |
09/10/98 - 02/22/00 |
| VENDEX KBB |
05/29/96 - 05/31/02 |
-0.7781 |
10/26/99 - 09/21/01 |
| VERSATEL |
07/20/00 - 05/31/02 |
-0.9932 |
07/26/00 - 05/22/02 |
| VNU |
12/30/83 - 05/31/02 |
-0.6589 |
02/25/00 - 10/03/01 |
| WESSANEN |
12/30/83 - 05/31/02 |
-0.5711 |
07/28/97 - 10/05/98 |
| WOLTERS KLUWER |
12/30/83 - 05/31/02 |
-0.5789 |
01/05/99 - 03/15/00 |
Table 4.3: Summary statistics. The first column shows the names of the data series examined. Columns 2 to 7 show the number of observations, the mean yearly effective return in %/100 terms, the mean, standard deviation, skewness and kurtosis of the daily logarithmic return. Column 8 shows the t-ratio testing whether the mean daily return is significantly different from zero. Column 9 shows the Sharpe ratio. Column 10 shows the largest cumulative loss in %/100 terms. Column 11 shows the Ljung-Box (1978) Q-statistic testing whether the first 20 autocorrelations of the return series as a whole are significantly different from zero. Column 12 shows the heteroskedasticity adjusted Box-Pierce (1970) Q-statistic, as derived by Diebold (1986). The final column shows the Ljung-Box (1978) Q-statistic for testing autocorrelations in the squared returns. Significance level of the (adjusted) Q(20)-test statistic can be evaluated based on the following chi-squared values: a) chi-squared(0.99,20)=37.57, b) chi-squared(0.95,20)=31.41, c) chi-squared(0.90,20)=28.41.
| Data set |
N |
Yearly |
Mean |
Std.Dev. |
Skew. |
Kurt. |
t-ratio |
Sharpe |
Max.loss |
Q20 |
Adj Q20 |
Q20 r2 |
| AEX |
4805 |
0.1042 |
0.000393 |
0.012051 |
-0.558 |
13.195 |
2.26b |
0.014661 |
-0.4673 |
70.78a |
21.34 |
4375.57a |
| ABN |
1732 |
0.0427 |
0.000166 |
0.012829 |
-0.13 |
8.929 |
0.54 |
-0.005931 |
-0.3977 |
22.22 |
9.94 |
1114.12a |
| AMRO |
1732 |
0.0679 |
0.000261 |
0.014559 |
-0.276 |
10.168 |
0.74 |
0.001286 |
-0.4824 |
27.36 |
12.57 |
454.18a |
| ABN AMRO |
2813 |
0.2012 |
0.000727 |
0.016749 |
-0.336 |
8.248 |
2.30b |
0.032169 |
-0.4821 |
49.55a |
23.21 |
1601.92a |
| AEGON |
4805 |
0.2033 |
0.000735 |
0.017084 |
-0.239 |
11.98 |
2.98a |
0.030316 |
-0.5748 |
59.60a |
20.6 |
2383.74a |
| AHOLD |
4805 |
0.1701 |
0.000624 |
0.0162 |
-0.305 |
12.509 |
2.67a |
0.025118 |
-0.4754 |
86.40a |
31.45b |
3844.46a |
| AKZO NOBEL |
4805 |
0.1215 |
0.000455 |
0.016427 |
-0.494 |
11.253 |
1.92c |
0.014513 |
-0.5646 |
86.16a |
27.63 |
3432.03a |
| ASML |
1622 |
0.3809 |
0.001281 |
0.041354 |
0.155 |
6.225 |
1.25 |
0.027639 |
-0.7866 |
50.77a |
38.62a |
89.48a |
| BAAN |
1099 |
-0.3075 |
-0.001458 |
0.048042 |
1.147 |
38.714 |
-1.01 |
-0.032987 |
-0.9743 |
44.12a |
18.95 |
39.16a |
| BUHRMANN |
4805 |
0.1031 |
0.000389 |
0.023772 |
-1.31 |
47.813 |
1.13 |
0.007261 |
-0.8431 |
38.95a |
19.78 |
47.41a |
| CETECO |
1833 |
-0.5427 |
-0.003104 |
0.06784 |
-3.278 |
62.774 |
-1.96c |
-0.047808 |
-0.9988 |
104.66a |
28.09 |
203.54a |
| CMG |
1435 |
0.0775 |
0.000296 |
0.037376 |
-0.206 |
9.389 |
0.3 |
0.004156 |
-0.928 |
72.96a |
48.56a |
139.65a |
| CORUS |
433 |
0.3054 |
0.001058 |
0.030171 |
0.338 |
4.99 |
0.73 |
0.029612 |
-0.512 |
27.11 |
25.17 |
15.78 |
| CSM |
4805 |
0.1596 |
0.000587 |
0.014589 |
1.327 |
36.456 |
2.79a |
0.025423 |
-0.343 |
60.70a |
24.08 |
812.42a |
| DAF |
848 |
-0.8565 |
-0.007703 |
0.097302 |
-3.33 |
36.55 |
-2.31b |
-0.082711 |
-0.9986 |
97.94a |
13.2 |
286.71a |
| DSM |
3215 |
0.1429 |
0.00053 |
0.015778 |
0.198 |
8.193 |
1.90c |
0.020398 |
-0.4008 |
38.75a |
22.1 |
569.54a |
| REED ELSEVIER |
4805 |
0.192 |
0.000697 |
0.018464 |
0.055 |
13.556 |
2.62a |
0.026015 |
-0.5169 |
82.77a |
25.57 |
2277.49a |
| FOKKER |
3698 |
-0.2133 |
-0.000952 |
0.057443 |
-3.733 |
71.209 |
-1.01 |
-0.020722 |
-0.9965 |
115.12a |
24.86 |
546.71a |
| FORTIS |
4805 |
0.1473 |
0.000545 |
0.017203 |
0.167 |
9.926 |
2.20b |
0.019107 |
-0.6342 |
34.52b |
13.56 |
2097.37a |
| GETRONICS |
4180 |
0.0949 |
0.00036 |
0.025214 |
-2.483 |
60.334 |
0.92 |
0.005826 |
-0.9279 |
61.16a |
17.65 |
120.88a |
| GIST BROCADES |
3824 |
0.0695 |
0.000267 |
0.017398 |
-0.39 |
11.739 |
0.95 |
0.001842 |
-0.6121 |
47.05a |
25.94 |
499.63a |
| GUCCI |
1464 |
0.1289 |
0.000481 |
0.026198 |
0.507 |
10.817 |
0.7 |
0.013003 |
-0.5938 |
25.72 |
16.94 |
177.81a |
| HAGEMEYER |
4805 |
0.1437 |
0.000533 |
0.020354 |
-0.767 |
20.041 |
1.81c |
0.015534 |
-0.7398 |
48.75a |
21.26 |
924.57a |
| HEINEKEN |
4805 |
0.1726 |
0.000632 |
0.015468 |
0.067 |
9.687 |
2.83a |
0.026842 |
-0.4398 |
65.52a |
27.37 |
2358.85a |
| HOOGOVENS |
4159 |
0.1018 |
0.000385 |
0.024165 |
-0.773 |
17.372 |
1.03 |
0.006609 |
-0.8104 |
57.43a |
28.62c |
250.82a |
| ING |
2675 |
0.2286 |
0.000817 |
0.017917 |
-0.682 |
11.917 |
2.36b |
0.035597 |
-0.5442 |
95.04a |
32.78b |
1685.41a |
| KLM |
4805 |
0.0145 |
0.000057 |
0.022555 |
-0.407 |
13.283 |
0.18 |
-0.007074 |
-0.7843 |
43.88a |
23.15 |
721.16a |
Table 4.3 continued.
| Data set |
N |
Yearly |
Mean |
Std.Dev. |
Skew. |
Kurt. |
t-ratio |
Sharpe |
Max.loss |
Q20 |
Adj Q20 |
Q20 r2 |
| KON. PTT NED. |
795 |
0.3279 |
0.001125 |
0.01434 |
0.287 |
5.656 |
2.21b |
0.069431 |
-0.1651 |
53.09a |
35.91b |
170.80a |
| KPN |
765 |
-0.3959 |
-0.002 |
0.045616 |
-0.128 |
6.22 |
-1.21 |
-0.047207 |
-0.9692 |
32.65b |
22.13 |
172.90a |
| KPNQWEST |
410 |
-0.9399 |
-0.011158 |
0.087222 |
-3.346 |
32.22 |
-2.59a |
-0.129789 |
-0.9929 |
54.54a |
14.83 |
108.71a |
| VAN DER MOOLEN |
3773 |
0.2731 |
0.000958 |
0.021531 |
0.045 |
12.922 |
2.73a |
0.03462 |
-0.6871 |
71.79a |
27.05 |
1177.84a |
| NAT. NEDERLANDEN |
1899 |
0.1055 |
0.000398 |
0.015855 |
-0.071 |
17.589 |
1.09 |
0.009266 |
-0.4803 |
26.94 |
8.78 |
1245.69a |
| NEDLLOYD |
4805 |
0.0786 |
0.0003 |
0.023107 |
1.292 |
43.435 |
0.9 |
0.003627 |
-0.7844 |
48.49a |
25 |
127.26a |
| NMB POSTBANK |
1870 |
0.1135 |
0.000427 |
0.015695 |
-0.111 |
8.606 |
1.18 |
0.011297 |
-0.5057 |
22.67 |
16.29 |
148.46a |
| NUMICO |
4805 |
0.1988 |
0.000719 |
0.017808 |
-0.665 |
24.203 |
2.80a |
0.028239 |
-0.683 |
40.15a |
20.39 |
158.90a |
| OCE |
4805 |
0.0748 |
0.000286 |
0.019629 |
-0.48 |
18.012 |
1.01 |
0.003546 |
-0.8189 |
75.60a |
26.28 |
873.42a |
| PAKHOED |
4133 |
0.1503 |
0.000556 |
0.01781 |
-0.111 |
10.48 |
2.01b |
0.018523 |
-0.4825 |
23.4 |
14.65 |
383.09a |
| PHILIPS |
4805 |
0.1356 |
0.000505 |
0.023059 |
-0.401 |
9.391 |
1.52 |
0.012486 |
-0.6814 |
62.15a |
28.46c |
1386.88a |
| POLYGRAM |
2087 |
0.1824 |
0.000665 |
0.015905 |
0.267 |
7.009 |
1.91c |
0.027906 |
-0.3275 |
27.46 |
20.9 |
116.65a |
| ROBECO |
4805 |
0.1003 |
0.000379 |
0.009457 |
-0.495 |
10.909 |
2.78a |
0.017202 |
-0.4363 |
56.62a |
23.75 |
1585.92a |
| ROYAL DUTCH |
4805 |
0.16 |
0.000589 |
0.013469 |
-0.088 |
7.549 |
3.03a |
0.027653 |
-0.3747 |
35.86b |
16.22 |
2875.11a |
| STORK |
4805 |
0.0823 |
0.000314 |
0.020289 |
-1.356 |
30.27 |
1.07 |
0.004791 |
-0.7591 |
52.41a |
18.22 |
702.99a |
| TPG |
765 |
-0.0129 |
-0.000052 |
0.020926 |
-0.093 |
5.47 |
-0.07 |
-0.009794 |
-0.4174 |
23.2 |
18.63 |
119.38a |
| UNILEVER |
4805 |
0.1726 |
0.000632 |
0.016744 |
0.019 |
11.955 |
2.62a |
0.024806 |
-0.4541 |
98.23a |
45.94a |
731.96a |
| UPC |
601 |
-0.9212 |
-0.010084 |
0.079572 |
-0.187 |
6.552 |
-3.11a |
-0.128788 |
-0.999 |
33.40b |
24.82 |
109.25a |
| VEDIOR |
1042 |
-0.1174 |
-0.000496 |
0.034184 |
-0.049 |
13.428 |
-0.47 |
-0.018754 |
-0.7169 |
29.83c |
25.06 |
29.96c |
| VENDEX KBB |
1567 |
0.1287 |
0.000481 |
0.023202 |
-0.035 |
10.019 |
0.82 |
0.014741 |
-0.7781 |
38.24a |
19.91 |
227.98a |
| VERSATEL |
486 |
-0.9173 |
-0.009892 |
0.069301 |
0.629 |
10.696 |
-3.15a |
-0.145133 |
-0.9932 |
19.02 |
18.61 |
30.71c |
| VNU |
4805 |
0.2045 |
0.000738 |
0.019594 |
0.049 |
11.399 |
2.61a |
0.026633 |
-0.6589 |
56.62a |
24.11 |
1379.96a |
| WESSANEN |
4805 |
0.0656 |
0.000252 |
0.016082 |
-0.351 |
15.195 |
1.09 |
0.002214 |
-0.5711 |
82.28a |
33.19b |
1055.89a |
| WOLTERS KLUWER |
4805 |
0.2097 |
0.000755 |
0.017947 |
-1.459 |
29.33 |
2.92a |
0.030022 |
-0.5789 |
81.27a |
28.16 |
635.78a |
Table 4.4: Statistics best strategy: mean return criterion, 0% costs.
Statistics of the best strategy, selected by the mean return criterion, if no transaction costs are implemented, for each data series listed in the first column. Column 2 shows the strategy parameters. Columns 3 and 4 show the mean return and excess mean return on a yearly basis in %/100 terms. Columns 5 and 6 show the Sharpe and excess Sharpe ratio. Column 7 shows the largest cumulative loss of the strategy in %/100 terms. Columns 8, 9 and 10 show the number of trades, the percentage of profitable trades and the percentage of days these profitable trades lasted. The last column shows the standard deviation of returns during profitable trades divided by the standard deviation of returns during non-profitable trades.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| AEX |
[ MA: 1, 25, 0.000, 0, 0, 0.100] |
0.2502 |
0.1323 |
0.0454 |
0.0307 |
-0.4387 |
411 |
0.659 |
0.849 |
1.2064 |
Table 4.4 continued.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| ABN |
[ MA: 1, 10, 0.010, 0, 0, 0.000] |
0.2862 |
0.2336 |
0.0467 |
0.0527 |
-0.3076 |
100 |
0.730 |
0.842 |
1.2766 |
| AMRO |
[ MA: 1, 5, 0.005, 0, 0, 0.000] |
0.3874 |
0.2992 |
0.0563 |
0.0550 |
-0.3216 |
234 |
0.718 |
0.838 |
1.2825 |
| ABN AMRO |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.4982 |
0.2473 |
0.0628 |
0.0307 |
-0.4880 |
1114 |
0.713 |
0.825 |
1.1275 |
| AEGON |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.5412 |
0.2808 |
0.0637 |
0.0334 |
-0.5826 |
1870 |
0.718 |
0.830 |
1.1375 |
| AHOLD |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
0.4030 |
0.1990 |
0.0490 |
0.0239 |
-0.6745 |
2230 |
0.686 |
0.790 |
1.1167 |
| AKZO NOBEL |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.5598 |
0.3908 |
0.0686 |
0.0541 |
-0.5888 |
1834 |
0.713 |
0.830 |
1.1438 |
| ASML |
[ MA: 2, 50, 0.000, 4, 0, 0.000] |
1.3426 |
0.6965 |
0.0757 |
0.0481 |
-0.5728 |
29 |
0.759 |
0.890 |
1.4775 |
| BAAN |
[ FR: 0.005, 0, 0 ] |
0.5678 |
1.2641 |
0.0248 |
0.0577 |
-0.7490 |
436 |
0.706 |
0.804 |
1.2107 |
| BUHRMANN |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
0.5494 |
0.4047 |
0.0512 |
0.0439 |
-0.5858 |
2128 |
0.699 |
0.810 |
1.3945 |
| CETECO |
[ MA: 10, 200, 0.000, 2, 0, 0.000] |
0.1616 |
1.5398 |
0.0194 |
0.0672 |
-0.5315 |
12 |
0.750 |
0.886 |
2.9653 |
| CMG |
[ MA: 1, 5, 0.000, 0, 0, 0.075] |
1.2144 |
1.0551 |
0.0659 |
0.0618 |
-0.7236 |
326 |
0.709 |
0.833 |
1.1708 |
| CORUS |
[ MA: 1, 25, 0.000, 0, 25, 0.000] |
1.2393 |
0.7154 |
0.0810 |
0.0514 |
-0.3774 |
21 |
0.667 |
0.744 |
1.1468 |
| CSM |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.2764 |
0.1008 |
0.0362 |
0.0108 |
-0.5294 |
1837 |
0.684 |
0.802 |
1.2955 |
| DAF |
[ MA: 10, 25, 0.025, 0, 0, 0.000] |
0.0994 |
6.6594 |
0.0005 |
0.0832 |
-0.8171 |
15 |
0.667 |
0.779 |
2.6064 |
| DSM |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
0.5287 |
0.3376 |
0.0693 |
0.0489 |
-0.3549 |
1527 |
0.692 |
0.815 |
1.3443 |
| REED ELSEVIER |
[ FR: 0.005, 0, 0 ] |
0.3404 |
0.1245 |
0.0375 |
0.0114 |
-0.6546 |
1562 |
0.703 |
0.824 |
1.0731 |
| FOKKER |
[short ] |
0.0618 |
0.3498 |
0.0000 |
0.0207 |
0.0000 |
1 |
1.000 |
1.000 |
NA |
| FORTIS |
[ FR: 0.005, 0, 0 ] |
0.4224 |
0.2397 |
0.0508 |
0.0316 |
-0.6734 |
1540 |
0.708 |
0.820 |
1.2021 |
| GETRONICS |
[ FR: 0.005, 0, 0 ] |
0.6024 |
0.4634 |
0.0518 |
0.0460 |
-0.8127 |
1384 |
0.697 |
0.815 |
1.3690 |
| GIST BROCADES |
[ MA: 1, 25, 0.000, 0, 0, 0.000] |
0.2548 |
0.1733 |
0.0286 |
0.0268 |
-0.4897 |
332 |
0.666 |
0.864 |
0.9720 |
| GUCCI |
[ FR: 0.010, 0, 0, ] |
0.5011 |
0.3298 |
0.0414 |
0.0284 |
-0.5883 |
407 |
0.703 |
0.829 |
1.2138 |
| HAGEMEYER |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.6217 |
0.4180 |
0.0636 |
0.0481 |
-0.6414 |
1793 |
0.694 |
0.810 |
1.2510 |
| HEINEKEN |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.4010 |
0.1948 |
0.0527 |
0.0258 |
-0.5536 |
1858 |
0.700 |
0.819 |
1.1882 |
| HOOGOVENS |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.4010 |
0.1948 |
0.0527 |
0.0258 |
-0.5536 |
1858 |
0.700 |
0.819 |
1.1882 |
| ING |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.8105 |
0.4736 |
0.0951 |
0.0595 |
-0.5247 |
994 |
0.728 |
0.852 |
1.3545 |
| KLM |
[ FR: 0.010, 0, 0 ] |
0.2234 |
0.2060 |
0.0199 |
0.0270 |
-0.6926 |
1305 |
0.707 |
0.833 |
1.1918 |
| KON. PTT NED. |
[ FR: 0.005, 0, 0 ] |
0.5792 |
0.1892 |
0.0832 |
0.0137 |
-0.2851 |
247 |
0.725 |
0.836 |
1.2906 |
| KPN |
[ FR: 0.035, 0, 0 ] |
1.1403 |
2.5429 |
0.0538 |
0.1010 |
-0.4628 |
143 |
0.748 |
0.865 |
1.2871 |
| KPNQWEST |
[ SR 15, 0.025, 0, 0, 0.000 ] |
0.2783 |
20.2694 |
0.0176 |
0.1474 |
-0.5794 |
9 |
0.889 |
0.988 |
2.5531 |
| VAN DER MOOLEN |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.8905 |
0.4850 |
0.0806 |
0.0460 |
-0.5842 |
1361 |
0.696 |
0.809 |
1.3909 |
| NAT. NEDERLANDEN |
[ MA: 1, 5, 0.001, 0, 0, 0.000] |
0.4646 |
0.3248 |
0.0639 |
0.0546 |
-0.3051 |
384 |
0.688 |
0.834 |
1.4260 |
| NEDLLOYD |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.5838 |
0.4683 |
0.0489 |
0.0452 |
-0.6774 |
1953 |
0.683 |
0.816 |
1.2050 |
| NMB POSTBANK |
[ SR 5, 0.000, 0, 0, 0.000 ] |
0.4532 |
0.3050 |
0.0590 |
0.0477 |
-0.4431 |
215 |
0.726 |
0.865 |
1.3831 |
| NUMICO |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.5488 |
0.2920 |
0.0599 |
0.0316 |
-0.8071 |
1763 |
0.700 |
0.820 |
1.0522 |
| OCE |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.4986 |
0.3943 |
0.0506 |
0.0471 |
-0.7918 |
1814 |
0.695 |
0.822 |
1.0832 |
| PAKHOED |
[ SR 25, 0.000, 0, 0, 0.075 ] |
0.3294 |
0.1557 |
0.0389 |
0.0204 |
-0.3689 |
126 |
0.714 |
0.831 |
1.0275 |
Table 4.4 continued.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| PHILIPS |
[ FR: 0.005, 0, 0 ] |
0.6646 |
0.4659 |
0.0587 |
0.0462 |
-0.6383 |
1639 |
0.719 |
0.837 |
1.1255 |
| POLYGRAM |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
0.4626 |
0.2369 |
0.0571 |
0.0292 |
-0.3543 |
985 |
0.694 |
0.790 |
1.2574 |
| ROBECO |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.3591 |
0.2352 |
0.0791 |
0.0619 |
-0.3168 |
1626 |
0.726 |
0.839 |
1.1705 |
| ROYAL DUTCH |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.2841 |
0.1069 |
0.0415 |
0.0138 |
-0.4719 |
1926 |
0.707 |
0.815 |
1.1878 |
| STORK |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
0.3152 |
0.2152 |
0.0292 |
0.0244 |
-0.8669 |
2253 |
0.679 |
0.802 |
0.9364 |
| TPG |
[ FR: 0.025, 0, 25 ] |
0.2077 |
0.2235 |
0.0213 |
0.0311 |
-0.3973 |
49 |
0.633 |
0.754 |
0.9465 |
| UNILEVER |
[ FR: 0.200, 4, 0 ] |
0.2591 |
0.0737 |
0.0276 |
0.0027 |
-0.5251 |
15 |
0.933 |
0.985 |
0.8096 |
| UPC |
[short ] |
0.0422 |
12.2299 |
0.0000 |
0.1288 |
0.0000 |
1 |
1.000 |
1.000 |
NA |
| VEDIOR |
[ MA: 2, 5, 0.000, 0, 25, 0.000] |
0.4764 |
0.6728 |
0.0332 |
0.0520 |
-0.5683 |
58 |
0.707 |
0.844 |
1.6142 |
| VENDEX KBB |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.6473 |
0.4594 |
0.0603 |
0.0456 |
-0.7064 |
634 |
0.689 |
0.806 |
1.4021 |
| VERSATEL |
[ FR: 0.120, 0, 0, ] |
0.5762 |
18.0630 |
0.0207 |
0.1658 |
-0.5642 |
27 |
0.704 |
0.872 |
1.6760 |
| VNU |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.6397 |
0.3613 |
0.0641 |
0.0375 |
-0.5945 |
1874 |
0.709 |
0.830 |
1.1521 |
| WESSANEN |
[ MA: 1, 2, 0.001, 0, 0, 0.000] |
0.3572 |
0.2736 |
0.0448 |
0.0426 |
-0.5854 |
1902 |
0.680 |
0.815 |
1.1492 |
| WOLTERS KLUWER |
[ MA: 1 , 2, 0.001, 0, 0, 0.000] |
0.5224 |
0.2585 |
0.0609 |
0.0309 |
-0.6480 |
1864 |
0.697 |
0.820 |
1.1813 |
Table 4.5: Statistics best strategy: mean return criterion, 0.25% costs. Statistics of the best strategy, selected by the mean return criterion, if 0.25% costs per trade are implemented, for each data series listed in the first column. Column 2 shows the strategy parameters. Columns 3 and 4 show the mean return and excess mean return on a yearly basis in %/100 terms. Columns 5 and 6 show the Sharpe and excess Sharpe ratio. Column 7 shows the largest cumulative loss of the strategy in %/100 terms. Columns 8, 9 and 10 show the number of trades, the percentage of profitable trades and the percentage of days these profitable trades lasted. The last column shows the standard deviation of returns during profitable trades divided by the standard deviation of returns during non-profitable trades.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| AEX |
[ MA: 5, 25, 0.050, 0, 0, 0.000] |
0.2060 |
0.0923 |
0.0335 |
0.0188 |
-0.4148 |
13 |
1.000 |
1.000 |
NA |
| ABN |
[ MA: 5, 10, 0.025, 0, 0, 0.000] |
0.2262 |
0.1764 |
0.0431 |
0.0492 |
-0.2649 |
11 |
0.727 |
0.983 |
0.6278 |
| AMRO |
[ MA: 10, 50, 0.025, 0, 0, 0.000] |
0.2935 |
0.2118 |
0.0463 |
0.0451 |
-0.4307 |
14 |
0.786 |
0.925 |
1.2234 |
| ABN AMRO |
[ FR: 0.090, 4, 0 ] |
0.3003 |
0.0828 |
0.0355 |
0.0034 |
-0.6587 |
53 |
0.321 |
0.749 |
0.6190 |
| AEGON |
[ MA: 25, 50, 0.050, 0, 0, 0.000] |
0.3104 |
0.0891 |
0.0407 |
0.0104 |
-0.6193 |
10 |
0.700 |
0.884 |
0.7975 |
| AHOLD |
[ SR: 10, 0.000, 0, 50, 0.000 ] |
0.3020 |
0.1129 |
0.0414 |
0.0163 |
-0.6203 |
145 |
0.703 |
0.808 |
0.9048 |
| AKZO NOBEL |
[ MA: 1, 10, 0.001, 0, 0, 0.000] |
0.2555 |
0.1196 |
0.0322 |
0.0177 |
-0.4911 |
611 |
0.239 |
0.468 |
1.0644 |
| ASML |
[ MA: 2, 50, 0.000, 4, 0, 0.000] |
1.2941 |
0.6620 |
0.0738 |
0.0462 |
-0.5971 |
29 |
0.552 |
0.855 |
1.2261 |
| BAAN |
[ FR: 0.045, 0, 25, ] |
0.5004 |
1.1679 |
0.0245 |
0.0575 |
-0.6185 |
65 |
0.415 |
0.435 |
1.1170 |
| BUHRMANN |
[ MA: 1, 2, 0.050, 0, 0, 0.000] |
0.3279 |
0.2040 |
0.0395 |
0.0323 |
-0.5189 |
7 |
1.000 |
1.000 |
NA |
| CETECO |
[ MA: 10, 200, 0.000, 2, 0, 0.000] |
0.1526 |
1.5211 |
0.0181 |
0.0659 |
-0.5315 |
12 |
0.583 |
0.878 |
1.9772 |
Table 4.5 continued.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| CMG |
[ MA: 25, 50, 0.050, 0, 0, 0.000] |
0.9756 |
0.8343 |
0.0727 |
0.0686 |
-0.6357 |
8 |
0.875 |
0.989 |
0.7260 |
| CORUS |
[ MA: 1, 25, 0.000, 0, 25, 0.000] |
1.1715 |
0.6658 |
0.0777 |
0.0482 |
-0.3819 |
21 |
0.429 |
0.455 |
1.0574 |
| CSM |
[ MA: 10, 100, 0.050, 0, 0, 0.000] |
0.2242 |
0.0559 |
0.0286 |
0.0032 |
-0.5071 |
17 |
0.941 |
0.959 |
1.1744 |
| DAF |
[short ] |
0.0908 |
6.6050 |
0.0000 |
0.0827 |
0.0000 |
1 |
1.000 |
1.000 |
NA |
| DSM |
[ MA: 2, 100, 0.000, 0, 0, 0.100] |
0.3218 |
0.1568 |
0.0444 |
0.0241 |
-0.3954 |
91 |
0.407 |
0.809 |
0.8567 |
| REED ELSEVIER |
[ FR: 0.040, 0, 50 ] |
0.2583 |
0.0558 |
0.0276 |
0.0016 |
-0.7002 |
133 |
0.767 |
0.891 |
0.6184 |
| FOKKER |
[short ] |
0.0618 |
0.3500 |
0.0000 |
0.0207 |
0.0000 |
1 |
1.000 |
1.000 |
NA |
| FORTIS |
[ FR: 0.140, 3, 0 ] |
0.2129 |
0.0573 |
0.0235 |
0.0044 |
-0.7970 |
46 |
0.522 |
0.843 |
0.6970 |
| GETRONICS |
[ MA: 5, 100, 0.025, 0, 0, 0.000] |
0.3160 |
0.2021 |
0.0345 |
0.0287 |
-0.5473 |
40 |
0.625 |
0.904 |
1.2430 |
| GIST BROCADES |
[ MA: 10, 200, 0.000, 0, 50, 0.000] |
0.2053 |
0.1271 |
0.0263 |
0.0245 |
-0.4796 |
45 |
0.733 |
0.728 |
0.9605 |
| GUCCI |
[ SR: 5, 0.000, 0, 50, 0.000 ] |
0.4345 |
0.2713 |
0.0388 |
0.0259 |
-0.4526 |
49 |
0.673 |
0.867 |
0.9805 |
| HAGEMEYER |
[ MA: 25, 100, 0.000, 0, 0, 0.100] |
0.2687 |
0.1094 |
0.0315 |
0.0160 |
-0.6601 |
75 |
0.480 |
0.667 |
0.8419 |
| HEINEKEN |
[ MA: 1, 2, 0.000, 0, 50, 0.000] |
0.2509 |
0.0669 |
0.0363 |
0.0095 |
-0.4846 |
120 |
0.708 |
0.893 |
1.0301 |
| HOOGOVENS |
[ MA: 1, 2, 0.000, 0, 50, 0.000] |
0.2509 |
0.0669 |
0.0363 |
0.0095 |
-0.4846 |
120 |
0.708 |
0.893 |
1.0301 |
| ING |
[ FR: 0.100, 4, 0 ] |
0.4265 |
0.1613 |
0.0515 |
0.0160 |
-0.4403 |
42 |
0.500 |
0.772 |
0.9916 |
| KLM |
[ FR: 0.100, 0, 50 ] |
0.1514 |
0.1351 |
0.0147 |
0.0218 |
-0.6026 |
110 |
0.709 |
0.821 |
1.0300 |
| KON. PTT NED. |
[ MA: 25, 200, 0.000, 3, 0, 0.000] |
0.5422 |
0.1623 |
0.0673 |
-0.0019 |
-0.2701 |
5 |
0.800 |
0.996 |
1.1393 |
| KPN |
[ FR: 0.035, 0, 0 ] |
0.7261 |
1.8596 |
0.0375 |
0.0848 |
-0.5333 |
143 |
0.217 |
0.320 |
0.8791 |
| KPNQWEST |
[ SR: 15, 0.025, 0, 0, 0.000 ] |
0.2502 |
19.8348 |
0.0157 |
0.1455 |
-0.5858 |
9 |
0.889 |
0.988 |
2.5531 |
| VAN DER MOOLEN |
[ FR: 0.200, 0, 0 ] |
0.4967 |
0.1759 |
0.0508 |
0.0162 |
-0.5865 |
21 |
0.857 |
0.937 |
0.9624 |
| NAT. NEDERLANDEN |
[ SR: 5, 0.010, 0, 0, 0.000 ] |
0.2544 |
0.1350 |
0.0326 |
0.0234 |
-0.3684 |
99 |
0.434 |
0.705 |
1.0256 |
| NEDLLOYD |
[ MA: 2, 25, 0.000, 0, 0, 0.000] |
0.3615 |
0.2624 |
0.0341 |
0.0305 |
-0.6414 |
288 |
0.316 |
0.695 |
1.2790 |
| NMB POSTBANK |
[ SR: 20, 0.000, 0, 0, 0.000 ] |
0.3816 |
0.2412 |
0.0480 |
0.0368 |
-0.4116 |
45 |
0.689 |
0.866 |
1.0019 |
| NUMICO |
[ FR: 0.160, 4, 0, ] |
0.3788 |
0.1503 |
0.0463 |
0.0181 |
-0.5632 |
26 |
0.808 |
0.951 |
0.8727 |
| OCE |
[ SR: 50, 0.010, 0, 0, 0.000 ] |
0.3427 |
0.2494 |
0.0464 |
0.0429 |
-0.7001 |
28 |
0.786 |
0.920 |
1.2531 |
| PAKHOED |
[ SR: 25, 0.000, 0, 0, 0.075 ] |
0.2954 |
0.1263 |
0.0344 |
0.0159 |
-0.4018 |
126 |
0.540 |
0.742 |
1.0265 |
| PHILIPS |
[ MA: 5, 100, 0.050, 0, 0, 0.000] |
0.3584 |
0.1964 |
0.0368 |
0.0244 |
-0.5935 |
30 |
0.833 |
0.925 |
1.2026 |
| POLYGRAM |
[ MA: 1, 2, 0.025, 0, 0, 0.000] |
0.3427 |
0.1359 |
0.0412 |
0.0133 |
-0.4702 |
12 |
0.583 |
0.937 |
0.6775 |
| ROBECO |
[ MA: 5, 25, 0.000, 0, 0, 0.075] |
0.2036 |
0.0941 |
0.0424 |
0.0252 |
-0.3751 |
218 |
0.353 |
0.664 |
0.8953 |
| ROYAL DUTCH |
[ SR: 100, 0.000, 0, 0, 0.100 ] |
0.2339 |
0.0639 |
0.0374 |
0.0098 |
-0.3284 |
40 |
0.575 |
0.814 |
0.7354 |
| STORK |
[ SR: 20, 0.010, 0, 0, 0.000 ] |
0.2771 |
0.1801 |
0.0309 |
0.0262 |
-0.5738 |
83 |
0.590 |
0.836 |
1.0104 |
| TPG |
[ FR: 0.025, 0, 25 ] |
0.1587 |
0.1749 |
0.0155 |
0.0254 |
-0.3973 |
49 |
0.408 |
0.395 |
0.8050 |
| UNILEVER |
[ FR: 0.200, 4, 0 ] |
0.2543 |
0.0698 |
0.0270 |
0.0022 |
-0.5298 |
15 |
0.800 |
0.977 |
0.5217 |
| UPC |
[short ] |
0.0422 |
12.2439 |
0.0000 |
0.1288 |
0.0000 |
1 |
1.000 |
1.000 |
NA |
| VEDIOR |
[ MA: 2, 5, 0.000, 0, 25, 0.000] |
0.4251 |
0.6157 |
0.0299 |
0.0487 |
-0.5789 |
58 |
0.466 |
0.518 |
1.0279 |
| VENDEX KBB |
[ SR: 25, 0.050, 0, 0, 0.000 ] |
0.4469 |
0.2824 |
0.0531 |
0.0384 |
-0.3155 |
4 |
1.000 |
1.000 |
NA |
Table 4.5 continued.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| VERSATEL |
[ FR: 0.120, 0, 0 ] |
0.4777 |
16.8951 |
0.0174 |
0.1626 |
-0.5717 |
27 |
0.444 |
0.730 |
1.4834 |
| VNU |
[ MA: 1, 2, 0.050, 0, 0, 0.000] |
0.3448 |
0.1166 |
0.0420 |
0.0154 |
-0.5302 |
6 |
0.667 |
0.995 |
0.2966 |
| WESSANEN |
[ MA: 1, 2, 0.025, 0, 0, 0.000] |
0.2000 |
0.1263 |
0.0254 |
0.0232 |
-0.5345 |
29 |
0.552 |
0.963 |
0.4049 |
| WOLTERS KLUWER |
[ MA: 2, 5, 0.050, 0, 0, 0.000] |
0.2778 |
0.0564 |
0.0322 |
0.0022 |
-0.6267 |
13 |
0.538 |
0.917 |
0.5323 |
Table 4.6: Statistics best strategy: Sharpe ratio criterion, 0 and 0.25% costs. Statistics of the best strategy, selected by the Sharpe ratio criterion, if 0 and 0.25% costs per trade are implemented, for each data series listed in the first column. Column 2 shows the strategy parameters. Columns 3 and 4 show the mean return and excess mean return on a yearly basis in %/100 terms. Columns 5 and 6 show the Sharpe and excess Sharpe ratio. Column 7 shows the largest loss of the strategy in %/100 terms. Columns 8, 9 and 10 show the number of trades, the percentage of profitable trades and the percentage of days these profitable trades lasted. The last column shows the standard deviation of returns during profitable trades divided by the standard deviation of returns during non-profitable trades. Results are only shown for those data series for which a different best strategy is selected by the Sharpe ratio criterion than by the mean return criterion.
| 0% costs per trade |
|
|
|
|
|
|
|
|
|
|
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| AEX |
[ MA: 1, 25, 0.000, 0, 0, 0.000] |
0.2475 |
0.1298 |
0.0454 |
0.0308 |
-0.4444 |
408 |
0.657 |
0.849 |
1.2064 |
| BAAN |
[ MA: 1, 2, 0.000, 0, 50, 0.000] |
0.4911 |
1.1534 |
0.0593 |
0.0923 |
-0.4425 |
27 |
0.741 |
0.990 |
1.6964 |
| CMG |
[ MA: 25, 50, 0.050, 0, 0, 0.000] |
0.9886 |
0.8456 |
0.0735 |
0.0693 |
-0.6322 |
8 |
0.875 |
0.989 |
0.7260 |
| CORUS |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
1.1930 |
0.6799 |
0.0813 |
0.0517 |
-0.4660 |
176 |
0.705 |
0.829 |
1.5341 |
| DAF |
[ SR: 20, 0.050, 0, 0, 0.000 ] |
0.0989 |
6.6563 |
0.0005 |
0.0833 |
-0.5781 |
9 |
0.778 |
0.782 |
3.8140 |
| GIST BROCADES |
[ MA: 2, 25, 0.000, 0, 0, 0.000] |
0.2547 |
0.1731 |
0.0289 |
0.0270 |
-0.5015 |
246 |
0.711 |
0.856 |
1.0282 |
| GUCCI |
[ FR: 0.200, 0, 50 ] |
0.4060 |
0.2455 |
0.0470 |
0.0340 |
-0.2944 |
19 |
0.842 |
0.701 |
1.2907 |
| VAN DER MOOLEN |
[ MA: 1, 2, 0.000, 0, 0, 0.000] |
0.8182 |
0.4282 |
0.0808 |
0.0462 |
-0.5137 |
1653 |
0.674 |
0.816 |
1.3728 |
| NMB POSTBANK |
[ SR: 5, 0.001, 0, 0, 0.000 ] |
0.4489 |
0.3012 |
0.0592 |
0.0479 |
-0.4275 |
201 |
0.731 |
0.873 |
1.4092 |
| PAKHOED |
[ MA: 10, 25, 0.000, 0, 50, 0.000] |
0.2739 |
0.1075 |
0.0392 |
0.0207 |
-0.4607 |
116 |
0.690 |
0.823 |
1.0159 |
| STORK |
[ SR: 20, 0.010, 0, 0, 0.000 ] |
0.3046 |
0.2054 |
0.0345 |
0.0297 |
-0.5606 |
83 |
0.819 |
0.908 |
0.9992 |
| TPG |
[ SR: 5, 0.000, 0, 50, 0.000 ] |
0.1531 |
0.1682 |
0.0251 |
0.0349 |
-0.2260 |
25 |
0.760 |
0.988 |
1.8030 |
| UNILEVER |
[ MA: 10, 25, 0.000, 0, 5, 0.000] |
0.2134 |
0.0348 |
0.0295 |
0.0047 |
-0.4496 |
342 |
0.705 |
0.663 |
0.8162 |
| 0.25% costs per trade |
|
|
|
|
|
|
|
|
|
|
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| AEX |
[ FR: 0.120, 0, 50 ] |
0.1572 |
0.0482 |
0.0345 |
0.0199 |
-0.2724 |
42 |
0.786 |
0.808 |
1.3628 |
| ABN AMRO |
[ SR: 150, 0.000, 0, 0, 0.100 ] |
0.2915 |
0.0754 |
0.0457 |
0.0136 |
-0.3828 |
13 |
0.615 |
0.924 |
0.7539 |
| AEGON |
[ SR: 250, 0.010, 0, 0, 0.000 ] |
0.2914 |
0.0733 |
0.0449 |
0.0146 |
-0.4530 |
4 |
1.000 |
1.000 |
NA |
| BAAN |
[ MA: 1, 2 0.000, 0, 50, 0.000] |
0.4670 |
1.1197 |
0.0566 |
0.0897 |
-0.4425 |
27 |
0.741 |
0.990 |
1.6964 |
Table 4.6 continued.
| Data set |
Strategy parameters |
r |
re |
S |
Se |
ML |
# tr. |
%tr.>0 |
%d > 0 |
SDR |
| CETECO |
[ SR: 250, 0.025 0, 0, 0.000 ] |
0.1341 |
1.4806 |
0.0182 |
0.0661 |
-0.4751 |
3 |
1.000 |
1.000 |
NA |
| CSM |
[ SR: 200, 0.000, 0, 50, 0.000 ] |
0.1871 |
0.0238 |
0.0321 |
0.0067 |
-0.3105 |
18 |
0.833 |
0.873 |
0.8999 |
| DAF |
[ SR: 20, 0.050, 0, 0, 0.000 ] |
0.0874 |
6.5818 |
-0.0002 |
0.0825 |
-0.5823 |
9 |
0.778 |
0.782 |
3.8140 |
| REED ELSEVIER |
[ FR: 0.140, 0, 50 ] |
0.2264 |
0.0290 |
0.0307 |
0.0047 |
-0.5967 |
45 |
0.756 |
0.914 |
0.8124 |
| FORTIS |
[ MA: 2, 100, 0.000, 0, 50, 0.000] |
0.1978 |
0.0441 |
0.0293 |
0.0102 |
-0.5023 |
86 |
0.733 |
0.846 |
0.9443 |
| GETRONICS |
[ SR: 50, 0.050, 0, 0, 0.000 ] |
0.3134 |
0.1997 |
0.0355 |
0.0297 |
-0.6535 |
10 |
0.900 |
0.982 |
0.6250 |
| GUCCI |
[ FR: 0.200, 0, 50, ] |
0.3952 |
0.2364 |
0.0459 |
0.0329 |
-0.2980 |
19 |
0.789 |
0.667 |
1.3484 |
| ING |
[ MA: 25, 100, 0.000, 0, 0, 0.100] |
0.4013 |
0.1408 |
0.0574 |
0.0219 |
-0.4027 |
48 |
0.583 |
0.774 |
0.8523 |
| KON. PTT NED. |
[ FR: 0.050, 0, 50 ] |
0.4075 |
0.0608 |
0.0763 |
0.0071 |
-0.1439 |
19 |
0.789 |
0.889 |
1.1433 |
| PAKHOED |
[ MA: 10, 25, 0.000, 0, 50, 0.000] |
0.2516 |
0.0883 |
0.0355 |
0.0170 |
-0.4661 |
116 |
0.681 |
0.811 |
1.0157 |
| POLYGRAM |
[ FR: 0.050, 0, 25 ] |
0.3190 |
0.1158 |
0.0415 |
0.0137 |
-0.3669 |
98 |
0.561 |
0.604 |
0.9687 |
| ROBECO |
[ SR: 25, 0.025, 0, 0, 0.000 ] |
0.1686 |
0.0622 |
0.0435 |
0.0264 |
-0.3793 |
7 |
0.857 |
0.968 |
1.0651 |
| TPG |
[ FR: 0.035, 0, 50 ] |
0.1581 |
0.1742 |
0.0202 |
0.0302 |
-0.3420 |
25 |
0.680 |
0.838 |
1.2569 |
| VENDEX KBB |
[ FR: 0.400, 2, 0 ] |
0.4458 |
0.2814 |
0.0536 |
0.0389 |
-0.4861 |
3 |
1.000 |
1.000 |
NA |
| WOLTERS KLUWER |
[ MA: 1, 200 , 0.000, 0, 5, 0.000] |
0.2448 |
0.0292 |
0.0372 |
0.0072 |
-0.3897 |
106 |
0.453 |
0.856 |
0.5689 |
Table 4.7: Performance best strategy in excess of performance buy-and-hold. Panel A shows the mean return of the best strategy, selected by the mean return criterion after implementing 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade, in excess of the mean return of the buy-and-hold benchmark for each data series listed in the first column. Panel B shows the Sharpe ratio of the best strategy, selected by the Sharpe ratio criterion after implementing 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade, in excess of the Sharpe ratio of the buy-and-hold benchmark for each data series listed in the first column.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| Data set |
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
|
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
| AEX |
0.1323 |
0.0943 |
0.0923 |
0.0889 |
0.0856 |
0.0822 |
|
0.0308 |
0.0216 |
0.0199 |
0.0180 |
0.0172 |
0.0164 |
| ABN |
0.2336 |
0.1988 |
0.1764 |
0.1686 |
0.1608 |
0.1530 |
|
0.0527 |
0.0504 |
0.0492 |
0.0471 |
0.0451 |
0.0430 |
| AMRO |
0.2992 |
0.2289 |
0.2118 |
0.2003 |
0.1889 |
0.1776 |
|
0.0550 |
0.0464 |
0.0451 |
0.0429 |
0.0406 |
0.0384 |
| ABN AMRO |
0.2473 |
0.1042 |
0.0828 |
0.0725 |
0.0695 |
0.0666 |
|
0.0307 |
0.0166 |
0.0136 |
0.0130 |
0.0124 |
0.0118 |
| AEGON |
0.2808 |
0.1117 |
0.0891 |
0.0865 |
0.0840 |
0.0814 |
|
0.0334 |
0.0147 |
0.0146 |
0.0144 |
0.0143 |
0.0141 |
| AHOLD |
0.1990 |
0.1256 |
0.1129 |
0.0920 |
0.0803 |
0.0760 |
|
0.0239 |
0.0185 |
0.0163 |
0.0125 |
0.0096 |
0.0074 |
| AKZO NOBEL |
0.3908 |
0.2251 |
0.1196 |
0.1123 |
0.1065 |
0.1008 |
|
0.0541 |
0.0346 |
0.0177 |
0.0144 |
0.0129 |
0.0114 |
| ASML |
0.6965 |
0.6826 |
0.6620 |
0.6281 |
0.5948 |
0.5621 |
|
0.0481 |
0.0473 |
0.0462 |
0.0442 |
0.0423 |
0.0403 |
| BAAN |
1.2641 |
1.2199 |
1.1679 |
1.0865 |
1.0538 |
1.0215 |
|
0.0923 |
0.0912 |
0.0897 |
0.0871 |
0.0844 |
0.0818 |
Table 4.7 continued.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| Data set |
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
|
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
| BUHRMANN |
0.4047 |
0.2050 |
0.2040 |
0.2023 |
0.2006 |
0.1989 |
|
0.0439 |
0.0324 |
0.0323 |
0.0320 |
0.0318 |
0.0315 |
| CETECO |
1.5398 |
1.5323 |
1.5211 |
1.5025 |
1.4839 |
1.4733 |
|
0.0672 |
0.0667 |
0.0661 |
0.0658 |
0.0656 |
0.0653 |
| CMG |
1.0551 |
0.8963 |
0.8343 |
0.8231 |
0.8118 |
0.8007 |
|
0.0693 |
0.0690 |
0.0686 |
0.0679 |
0.0671 |
0.0664 |
| CORUS |
0.7154 |
0.6954 |
0.6658 |
0.6176 |
0.5706 |
0.5248 |
|
0.0517 |
0.0501 |
0.0482 |
0.0451 |
0.0419 |
0.0387 |
| CSM |
0.1008 |
0.0586 |
0.0559 |
0.0514 |
0.0470 |
0.0425 |
|
0.0108 |
0.0071 |
0.0067 |
0.0061 |
0.0054 |
0.0048 |
| DAF |
6.6594 |
6.6264 |
6.6050 |
6.6106 |
6.6162 |
6.6218 |
|
0.0833 |
0.0830 |
0.0825 |
0.0818 |
0.0810 |
0.0828 |
| DSM |
0.3376 |
0.1753 |
0.1568 |
0.1317 |
0.1123 |
0.0932 |
|
0.0489 |
0.0272 |
0.0241 |
0.0188 |
0.0136 |
0.0108 |
| REED ELSEVIER |
0.1245 |
0.0670 |
0.0558 |
0.0413 |
0.0407 |
0.0400 |
|
0.0114 |
0.0055 |
0.0047 |
0.0035 |
0.0024 |
0.0015 |
| FOKKER |
0.3498 |
0.3499 |
0.3500 |
0.3503 |
0.3505 |
0.3507 |
|
0.0207 |
0.0207 |
0.0207 |
0.0207 |
0.0208 |
0.0208 |
| FORTIS |
0.2397 |
0.0969 |
0.0573 |
0.0551 |
0.0547 |
0.0544 |
|
0.0316 |
0.0118 |
0.0102 |
0.0075 |
0.0054 |
0.0053 |
| GETRONICS |
0.4634 |
0.3040 |
0.2021 |
0.1965 |
0.1934 |
0.1902 |
|
0.0460 |
0.0334 |
0.0297 |
0.0293 |
0.0288 |
0.0283 |
| GIST BROCADES |
0.1733 |
0.1484 |
0.1271 |
0.1193 |
0.1114 |
0.1036 |
|
0.0270 |
0.0253 |
0.0245 |
0.0230 |
0.0216 |
0.0201 |
| GUCCI |
0.3298 |
0.2870 |
0.2713 |
0.2455 |
0.2201 |
0.2096 |
|
0.0340 |
0.0336 |
0.0329 |
0.0318 |
0.0307 |
0.0295 |
| HAGEMEYER |
0.4180 |
0.2307 |
0.1094 |
0.0975 |
0.0856 |
0.0739 |
|
0.0481 |
0.0271 |
0.0160 |
0.0141 |
0.0122 |
0.0103 |
| HEINEKEN |
0.1948 |
0.0784 |
0.0669 |
0.0480 |
0.0340 |
0.0333 |
|
0.0258 |
0.0118 |
0.0095 |
0.0056 |
0.0022 |
0.0019 |
| HOOGOVENS |
0.1948 |
0.0784 |
0.0669 |
0.0480 |
0.0340 |
0.0333 |
|
0.0258 |
0.0118 |
0.0095 |
0.0056 |
0.0022 |
0.0019 |
| ING |
0.4736 |
0.2656 |
0.1613 |
0.1391 |
0.1173 |
0.0979 |
|
0.0595 |
0.0326 |
0.0219 |
0.0201 |
0.0185 |
0.0168 |
| KLM |
0.2060 |
0.1545 |
0.1351 |
0.1192 |
0.1065 |
0.0992 |
|
0.0270 |
0.0233 |
0.0218 |
0.0194 |
0.0170 |
0.0146 |
| KON. PTT NED. |
0.1892 |
0.1673 |
0.1623 |
0.1541 |
0.1492 |
0.1446 |
|
0.0137 |
0.0095 |
0.0071 |
0.0035 |
0.0021 |
0.0008 |
| KPN |
2.5429 |
2.2521 |
1.8596 |
1.6628 |
1.6541 |
1.6455 |
|
0.1010 |
0.0945 |
0.0848 |
0.0842 |
0.0839 |
0.0836 |
| KPNQWEST |
20.2694 |
20.0946 |
19.8348 |
19.5219 |
19.2272 |
18.9362 |
|
0.1474 |
0.1466 |
0.1455 |
0.1440 |
0.1427 |
0.1414 |
| VAN DER MOOLEN |
0.4850 |
0.2799 |
0.1759 |
0.1686 |
0.1613 |
0.1541 |
|
0.0462 |
0.0252 |
0.0162 |
0.0153 |
0.0144 |
0.0134 |
| NAT. NEDERLANDEN |
0.3248 |
0.2081 |
0.1350 |
0.1018 |
0.0943 |
0.0869 |
|
0.0546 |
0.0358 |
0.0234 |
0.0213 |
0.0208 |
0.0203 |
| NEDLLOYD |
0.4683 |
0.3177 |
0.2624 |
0.2350 |
0.2268 |
0.2186 |
|
0.0452 |
0.0363 |
0.0305 |
0.0278 |
0.0269 |
0.0259 |
| NMB POSTBANK |
0.3050 |
0.2632 |
0.2412 |
0.2052 |
0.1702 |
0.1361 |
|
0.0479 |
0.0401 |
0.0368 |
0.0313 |
0.0258 |
0.0203 |
| NUMICO |
0.2920 |
0.1589 |
0.1503 |
0.1429 |
0.1356 |
0.1282 |
|
0.0316 |
0.0192 |
0.0181 |
0.0170 |
0.0158 |
0.0147 |
| OCE |
0.3943 |
0.2546 |
0.2494 |
0.2409 |
0.2325 |
0.2240 |
|
0.0471 |
0.0437 |
0.0429 |
0.0415 |
0.0401 |
0.0387 |
| PAKHOED |
0.1557 |
0.1438 |
0.1263 |
0.1159 |
0.1119 |
0.1079 |
|
0.0207 |
0.0192 |
0.0170 |
0.0162 |
0.0155 |
0.0148 |
| PHILIPS |
0.4659 |
0.2740 |
0.1964 |
0.1879 |
0.1794 |
0.1709 |
|
0.0462 |
0.0282 |
0.0244 |
0.0233 |
0.0223 |
0.0216 |
| POLYGRAM |
0.2369 |
0.1401 |
0.1359 |
0.1289 |
0.1220 |
0.1151 |
|
0.0292 |
0.0169 |
0.0137 |
0.0122 |
0.0111 |
0.0100 |
| ROBECO |
0.2352 |
0.1298 |
0.0941 |
0.0798 |
0.0706 |
0.0613 |
|
0.0619 |
0.0357 |
0.0264 |
0.0257 |
0.0251 |
0.0245 |
| ROYAL DUTCH |
0.1069 |
0.0674 |
0.0639 |
0.0580 |
0.0554 |
0.0537 |
|
0.0138 |
0.0106 |
0.0098 |
0.0084 |
0.0071 |
0.0057 |
| STORK |
0.2152 |
0.1952 |
0.1801 |
0.1552 |
0.1309 |
0.1106 |
|
0.0297 |
0.0283 |
0.0262 |
0.0227 |
0.0191 |
0.0182 |
| TPG |
0.2235 |
0.2038 |
0.1749 |
0.1527 |
0.1317 |
0.1109 |
|
0.0349 |
0.0329 |
0.0302 |
0.0268 |
0.0233 |
0.0199 |
Table 4.7 continued.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| Data set |
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
|
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
| UNILEVER |
0.0737 |
0.0721 |
0.0698 |
0.0659 |
0.0619 |
0.0580 |
|
0.0047 |
0.0025 |
0.0022 |
0.0018 |
0.0017 |
0.0017 |
| UPC |
12.2299 |
12.2355 |
12.2439 |
12.2579 |
12.2720 |
12.2862 |
|
0.1288 |
0.1288 |
0.1288 |
0.1289 |
0.1289 |
0.1290 |
| VEDIOR |
0.6728 |
0.6498 |
0.6157 |
0.5604 |
0.5069 |
0.4551 |
|
0.0520 |
0.0506 |
0.0487 |
0.0454 |
0.0421 |
0.0388 |
| VENDEX KBB |
0.4594 |
0.2836 |
0.2824 |
0.2803 |
0.2782 |
0.2761 |
|
0.0456 |
0.0391 |
0.0389 |
0.0387 |
0.0384 |
0.0381 |
| VERSATEL |
18.0630 |
17.5873 |
16.8951 |
15.7960 |
14.7618 |
13.7890 |
|
0.1658 |
0.1646 |
0.1626 |
0.1595 |
0.1563 |
0.1531 |
| VNU |
0.3613 |
0.1797 |
0.1166 |
0.1154 |
0.1143 |
0.1131 |
|
0.0375 |
0.0174 |
0.0154 |
0.0152 |
0.0150 |
0.0148 |
| WESSANEN |
0.2736 |
0.1554 |
0.1263 |
0.1184 |
0.1107 |
0.1029 |
|
0.0426 |
0.0280 |
0.0232 |
0.0218 |
0.0203 |
0.0189 |
| WOLTERS KLUWER |
0.2585 |
0.0929 |
0.0564 |
0.0531 |
0.0498 |
0.0464 |
|
0.0309 |
0.0092 |
0.0072 |
0.0041 |
0.0035 |
0.0035 |
| Average |
1.5103 |
1.4049 |
1.3492 |
1.3038 |
1.2671 |
1.2332 |
|
0.0477 |
0.0388 |
0.0357 |
0.0339 |
0.0323 |
0.0311 |
Table 4.8: Estimation results CAPM. Coefficient estimates of the Sharpe-Lintner CAPM: rti-rtf=a + b (rtAEX-rtf) + et.
That is, the return of the best recursive optimizing and testing procedure, when selection is done in the optimizing period by the mean return criterion (Panel A) or by the Sharpe ratio criterion (Panel B), in excess of the risk-free interest rate is regressed against a constant and the return of the AEX-index in excess of the risk-free interest rate. Estimation results for the 0 and 0.50% costs per trade cases are shown. a, b, c indicates that the corresponding coefficient is, in the case of a, significantly different from zero, or in the case of b, significantly different from one, at the 1, 5, 10% significance level. Estimation is done with Newey-West (1987) heteroskedasticity and autocorrelation consistent (HAC) standard errors.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| costs per trade |
0% |
0.50% |
|
0% |
0.50% |
| Data set |
a |
b |
a |
b |
|
a |
b |
a |
b |
| AEX |
0.000527a |
0.809b |
0.000340b |
0.996 |
|
0.000526a |
0.767a |
0.000340b |
0.996 |
| ABN |
0.000734b |
0.501a |
0.000544c |
0.372a |
|
0.000734b |
0.501a |
0.000544c |
0.372a |
| AMRO |
0.001014b |
0.537a |
0.000702c |
0.494a |
|
0.001014b |
0.537a |
0.000702c |
0.494a |
| ABN AMRO |
0.001125a |
0.954 |
0.000489c |
1.086 |
|
0.001125a |
0.954 |
0.000489c |
1.086 |
| AEGON |
0.001309a |
0.934 |
0.000672b |
0.852c |
|
0.001309a |
0.934 |
0.000630a |
0.797b |
| AHOLD |
0.000958a |
0.875a |
0.000618b |
0.740a |
|
0.000958a |
0.875a |
0.000618b |
0.740a |
| AKZO NOBEL |
0.001414a |
0.759a |
0.00047 |
0.991 |
|
0.001414a |
0.759a |
0.000347 |
0.621a |
| ASML |
0.002888a |
1.158 |
0.002722a |
1.159 |
|
0.002888a |
1.158 |
0.002722a |
1.159 |
| BAAN |
0.000724 |
1.066 |
0.00116 |
0.226a |
|
0.001289c |
0.227a |
0.00116 |
0.226a |
| BUHRMANN |
0.001383a |
0.744a |
0.000820a |
0.442a |
|
0.001383a |
0.744a |
0.000820a |
0.442a |
Table 4.8 continued.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| costs per trade |
0% |
0.50% |
|
0% |
0.5% |
| Data set |
a |
b |
a |
b |
|
a |
b |
a |
b |
| CETECO |
0.000398 |
0.150a |
0.000341 |
0.151a |
|
0.000398 |
0.150a |
0.000298 |
0.161a |
| CMG |
0.002793b |
0.967 |
0.002371a |
0.702a |
|
0.002417a |
0.701a |
0.002371a |
0.702a |
| CORUS |
0.003574b |
0.642b |
0.003337c |
0.639b |
|
0.003202c |
0.383a |
0.003337c |
0.639b |
| CSM |
0.000673b |
0.449a |
0.000483c |
0.495a |
|
0.000673b |
0.449a |
0.000386b |
0.390a |
| DAF |
6.38E-05 |
0.448a |
-6.00E-08a |
4.53E-08a |
|
8.06E-05 |
0.7 |
-3.08E-06 |
0.698 |
| DSM |
0.001366a |
0.541a |
0.000682c |
0.633a |
|
0.001366a |
0.541a |
0.000677b |
0.568a |
| REED ELSEVIER |
0.000807b |
0.785a |
0.000436 |
1.160a |
|
0.000807b |
0.785a |
0.000436c |
0.762a |
| FOKKER |
-3.15E-08a |
6.55E-08a |
-3.15E-08a |
6.55E-08a |
|
-3.15E-08a |
6.55E-08a |
-3.15E-08a |
6.55E-08a |
| FORTIS |
0.001026a |
0.825a |
0.000341 |
1.103 |
|
0.001026a |
0.825a |
0.000335 |
0.649a |
| GETRONICS |
0.001581a |
0.717a |
0.000800b |
0.565a |
|
0.001581a |
0.717a |
0.000800b |
0.565a |
| GIST BROCADES |
0.000495 |
0.587a |
0.000273 |
0.740a |
|
0.000495 |
0.583a |
0.000273 |
0.740a |
| GUCCI |
0.001316 |
0.599a |
0.001018 |
0.731b |
|
0.001089 |
0.476a |
0.001031 |
0.476a |
| HAGEMEYER |
0.001593a |
0.618a |
0.000566c |
0.669a |
|
0.001593a |
0.618a |
0.000566c |
0.669a |
| HEINEKEN |
0.001005a |
0.660a |
0.000516b |
0.476a |
|
0.001005a |
0.660a |
0.000516b |
0.476a |
| HOOGOVENS |
0.001565a |
1.122c |
0.000888b |
0.855 |
|
0.001565a |
1.122c |
0.000888b |
0.855 |
| ING |
0.001886a |
1.016 |
0.000829b |
1.144 |
|
0.001886a |
1.016 |
0.000651b |
0.97 |
| KLM |
0.000445 |
0.784a |
0.000173 |
0.618a |
|
0.000445 |
0.784a |
0.000173 |
0.618a |
| KON. PTT NED. |
0.000845 |
0.738a |
6.19E-05 |
1.341a |
|
0.000845 |
0.738a |
0.000128 |
0.819a |
| KPN |
0.003498b |
1.786a |
0.002349 |
1.775a |
|
0.003498b |
1.786a |
0.001615 |
1.008 |
| KPNQWEST |
0.001679 |
0.842 |
0.001611 |
0.926 |
|
0.001679 |
0.842 |
0.001611 |
0.926 |
| VAN DER MOOLEN |
0.002127a |
0.706a |
0.001160b |
0.762a |
|
0.001989a |
0.642a |
0.001160b |
0.762a |
| NAT. NEDERLANDEN |
0.001228a |
0.577a |
0.000494 |
0.671b |
|
0.001228a |
0.577a |
0.000365 |
0.325a |
| NEDLLOYD |
0.001470a |
0.782a |
0.000805c |
0.621a |
|
0.001470a |
0.782a |
0.000805c |
0.621a |
| NMB POSTBANK |
0.001215b |
0.531a |
0.000901c |
0.507a |
|
0.001203b |
0.511a |
0.000901c |
0.507a |
| NUMICO |
0.001427a |
0.523a |
0.000921a |
0.559a |
|
0.001427a |
0.523a |
0.000921a |
0.559a |
| OCE |
0.001257a |
0.655a |
0.000825a |
0.491a |
|
0.001257a |
0.655a |
0.000825a |
0.491a |
| PAKHOED |
0.000721b |
0.631a |
0.000579c |
0.611a |
|
0.000600b |
0.455a |
0.000579c |
0.611a |
| PHILIPS |
0.001616a |
1.076 |
0.000788b |
1.031 |
|
0.001616a |
1.076 |
0.000788b |
1.031 |
| POLYGRAM |
0.000932b |
0.717a |
0.000504 |
0.837b |
|
0.000932b |
0.717a |
0.000504 |
0.837b |
| ROBECO |
0.000921a |
0.438a |
0.000394b |
0.410a |
|
0.000921a |
0.438a |
0.000350a |
0.259a |
| ROYAL DUTCH |
0.000669a |
0.571a |
0.000474b |
0.674a |
|
0.000669a |
0.571a |
0.000474b |
0.674a |
| STORK |
0.0007 |
0.807 |
0.000544c |
0.558a |
|
0.000712b |
0.558a |
0.000544c |
0.558a |
| TPG |
0.000721 |
0.291a |
0.000412 |
0.167a |
|
0.000484 |
0.203a |
0.000412 |
0.167a |
Table 4.8 continued.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| costs per trade |
0% |
0.50% |
|
0% |
0.5% |
| Data set |
a |
b |
a |
b |
|
a |
b |
a |
b |
| UNILEVER |
0.000606b |
0.519a |
0.000578b |
0.518a |
|
0.000476b |
0.427a |
0.000451b |
0.532a |
| UPC |
-1.37E-08a |
1.38E-08a |
-1.37E-08a |
1.38E-08a |
|
-1.37E-08a |
1.38E-08a |
-1.37E-08a |
1.38E-08a |
| VEDIOR |
0.001478 |
0.302a |
0.001198 |
0.306a |
|
0.001478 |
0.302a |
0.001198 |
0.306a |
| VENDEX KBB |
0.001724b |
0.426a |
0.001172b |
0.558a |
|
0.001724b |
0.426a |
0.001169c |
0.560a |
| VERSATEL |
0.002604 |
1.086 |
0.00211 |
1.085 |
|
0.002604 |
1.086 |
0.00211 |
1.085 |
| VNU |
0.001604a |
0.752a |
0.000803a |
0.838b |
|
0.001604a |
0.752a |
0.000803a |
0.838b |
| WESSANEN |
0.000877a |
0.629a |
0.000363 |
0.622a |
|
0.000877a |
0.629a |
0.000363 |
0.622a |
| WOLTERS KLUWER |
0.001325a |
0.585a |
0.000590c |
0.747a |
|
0.001325a |
0.585a |
0.000473b |
0.635a |
Table 4.9: Testing for predictive ability. Nominal (pn), White's (2000) Reality Check (pW) and Hansen's (2001) Superior Predictive Ability test (pH) p-values, if the best strategy is selected by the mean return criterion (Panel A) or if the best strategy is selected by the Sharpe ratio criterion, in the case of 0 and 0.10% costs per trade.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| costs per trade |
0% |
0.10% |
|
0% |
0.10% |
| Data set |
pn |
pW |
pH |
pn |
pW |
pH |
|
pn |
pW |
pH |
pn |
pW |
pH |
| AEX |
0 |
0.93 |
0.08 |
0 |
1 |
0.28 |
|
0 |
0.77 |
0.08 |
0 |
0.96 |
0.25 |
| ABN |
0 |
0.65 |
0.36 |
0 |
0.9 |
0.59 |
|
0 |
0.42 |
0.13 |
0 |
0.52 |
0.12 |
| AMRO |
0 |
0.99 |
0.84 |
0 |
1 |
0.94 |
|
0 |
0.78 |
0.13 |
0 |
0.94 |
0.26 |
| ABN AMRO |
0 |
0.51 |
0.04 |
0 |
1 |
0.88 |
|
0 |
0.96 |
0.21 |
0 |
1 |
0.71 |
| AEGON |
0 |
0.26 |
0.06 |
0 |
1 |
0.94 |
|
0 |
0.77 |
0.03 |
0 |
1 |
0.45 |
| AHOLD |
0 |
0.47 |
0.15 |
0 |
0.99 |
0.64 |
|
0.01 |
0.88 |
0.12 |
0 |
0.98 |
0.19 |
| AKZO NOBEL |
0 |
1 |
0 |
0 |
1 |
0.4 |
|
0 |
0.01 |
0 |
0 |
0.57 |
0.02 |
| ASML |
0 |
1 |
0.96 |
0 |
1 |
0.96 |
|
0 |
0.98 |
0.02 |
0 |
0.98 |
0.02 |
| BAAN |
0.01 |
1 |
0.96 |
0 |
1 |
0.97 |
|
0 |
0.06 |
0.03 |
0 |
0.06 |
0.02 |
| BUHRMANN |
0 |
1 |
0.39 |
0 |
1 |
0.98 |
|
0 |
0.1 |
0 |
0 |
0.63 |
0.03 |
| CETECO |
0 |
1 |
0.51 |
0 |
1 |
0.51 |
|
0 |
0.45 |
0.01 |
0 |
0.46 |
0.01 |
| CMG |
0 |
1 |
0.99 |
0 |
1 |
1 |
|
0 |
0.63 |
0.05 |
0 |
0.61 |
0.03 |
| CORUS |
0 |
1 |
1 |
0 |
1 |
1 |
|
0.04 |
1 |
0.82 |
0 |
1 |
0.8 |
| CSM |
0.02 |
1 |
0.86 |
0 |
1 |
0.98 |
|
0.07 |
1 |
0.73 |
0 |
1 |
0.7 |
| DAF |
0 |
1 |
0.27 |
0 |
1 |
0.27 |
|
0 |
0.32 |
0.29 |
0 |
0.36 |
0.28 |
| DSM |
0 |
0.05 |
0 |
0 |
0.99 |
0.3 |
|
0 |
0.35 |
0.01 |
0 |
1 |
0.2 |
| REED ELSEVIER |
0.01 |
1 |
0.95 |
0 |
1 |
1 |
|
0.05 |
1 |
0.63 |
0.01 |
1 |
0.88 |
| FOKKER |
0.04 |
1 |
0.79 |
0.04 |
1 |
0.76 |
|
0.04 |
0.8 |
0.38 |
0.04 |
0.77 |
0.3 |
| FORTIS |
0 |
0.94 |
0.92 |
0 |
1 |
0.99 |
|
0 |
0.89 |
0.03 |
0 |
1 |
0.58 |
| GETRONICS |
0 |
1 |
0.29 |
0 |
1 |
0.79 |
|
0 |
0.24 |
0 |
0 |
0.78 |
0.08 |
| GIST BROCADES |
0 |
1 |
0.92 |
0 |
1 |
0.96 |
|
0 |
0.97 |
0.22 |
0 |
0.99 |
0.22 |
| GUCCI |
0.04 |
1 |
0.93 |
0 |
1 |
0.98 |
|
0 |
1 |
0.36 |
0 |
1 |
0.32 |
| HAGEMEYER |
0 |
1 |
0.91 |
0 |
1 |
0.96 |
|
0 |
0.22 |
0 |
0 |
0.96 |
0.04 |
| HEINEKEN |
0 |
0.31 |
0 |
0 |
1 |
0.78 |
|
0 |
0.7 |
0.03 |
0 |
1 |
0.43 |
| HOOGOVENS |
0 |
0.31 |
0 |
0 |
1 |
0.78 |
|
0 |
0.7 |
0.03 |
0 |
1 |
0.43 |
| ING |
0 |
0.99 |
0 |
0 |
1 |
0.34 |
|
0 |
0.32 |
0 |
0 |
1 |
0.12 |
KLM |
0 |
1 |
0.98 |
0 |
1 |
0.99 |
|
0 |
0.68 |
0.22 |
0 |
0.84 |
0.34 |
| KON. PTT NED. |
0.15 |
1 |
0.84 |
0 |
1 |
0.84 |
|
0.44 |
1 |
0.97 |
0.02 |
1 |
0.97 |
| KPN |
0 |
1 |
0.96 |
0 |
1 |
0.98 |
|
0 |
0.23 |
0.05 |
0 |
0.31 |
0.08 |
| KPNQWEST |
0 |
1 |
0.3 |
0 |
1 |
0.3 |
|
0 |
0.08 |
0.08 |
0 |
0.08 |
0.08 |
| VAN DER MOOLEN |
0 |
1 |
0.07 |
0 |
1 |
0.8 |
|
0 |
0.8 |
0 |
0 |
1 |
0.33 |
| NAT. NEDERLANDEN |
0 |
0.28 |
0.11 |
0 |
0.99 |
0.66 |
|
0 |
0.32 |
0.08 |
0.01 |
0.83 |
0.42 |
| NEDLLOYD |
0 |
1 |
0.13 |
0 |
1 |
0.65 |
|
0 |
0.16 |
0 |
0 |
0.55 |
0.02 |
| NMB POSTBANK |
0 |
0.66 |
0.12 |
0 |
0.85 |
0.24 |
|
0 |
0.71 |
0.15 |
0 |
0.89 |
0.25 |
| NUMICO |
0 |
1 |
0.4 |
0 |
1 |
0.95 |
|
0 |
0.88 |
0.05 |
0 |
1 |
0.32 |
| OCE |
0 |
1 |
0.38 |
0 |
1 |
0.86 |
|
0 |
0.1 |
0.01 |
0 |
0.17 |
0 |
| PAKHOED |
0 |
1 |
0.75 |
0 |
1 |
0.77 |
|
0 |
1 |
0.21 |
0 |
1 |
0.14 |
| PHILIPS |
0 |
1 |
0.01 |
0 |
1 |
0.52 |
|
0 |
0.1 |
0 |
0 |
0.87 |
0.03 |
| POLYGRAM |
0 |
0.86 |
0.12 |
0 |
1 |
0.58 |
|
0.03 |
0.99 |
0.39 |
0 |
1 |
0.73 |
| ROBECO |
0 |
0 |
0 |
0 |
0.75 |
0 |
|
0 |
0.02 |
0 |
0 |
0.74 |
0.02 |
| ROYAL DUTCH |
0.01 |
0.95 |
0.36 |
0 |
1 |
0.86 |
|
0.05 |
1 |
0.45 |
0 |
1 |
0.42 |
| STORK |
0.01 |
1 |
0.9 |
0 |
1 |
0.94 |
|
0 |
0.83 |
0.1 |
0 |
0.88 |
0.08 |
| TPG |
0 |
1 |
1 |
0 |
1 |
1 |
|
0 |
1 |
0.82 |
0 |
1 |
0.8 |
| UNILEVER |
0 |
1 |
0.87 |
0 |
1 |
0.82 |
|
0 |
1 |
0.85 |
0.04 |
1 |
0.92 |
| UPC |
0 |
1 |
0.1 |
0 |
1 |
0.1 |
|
0 |
0.06 |
0.02 |
0 |
0.06 |
0.03 |
| VEDIOR |
0 |
1 |
0.98 |
0 |
1 |
0.98 |
|
0 |
0.92 |
0.33 |
0 |
0.94 |
0.33 |
| VENDEX KBB |
0 |
1 |
0.94 |
0 |
1 |
0.99 |
|
0 |
0.94 |
0.27 |
0 |
0.98 |
0.34 |
| VERSATEL |
0 |
1 |
0.42 |
0 |
1 |
0.43 |
|
0 |
0.03 |
0.03 |
0 |
0.03 |
0.03 |
| VNU |
0 |
1 |
0.01 |
0 |
1 |
0.9 |
|
0 |
0.85 |
0 |
0.02 |
1 |
0.28 |
| WESSANEN |
0 |
0.96 |
0.02 |
0 |
0.99 |
0.62 |
|
0 |
0.06 |
0 |
0 |
0.62 |
0.19 |
| WOLTERS KLUWER |
0 |
1 |
0.89 |
0 |
1 |
1 |
|
0 |
1 |
0.03 |
0 |
1 |
0.64 |
Table 4.14: Excess performance best out-of-sample testing procedure. Panel A shows the yearly mean return of the best recursive out-of-sample testing procedure, selected by the mean return criterion, in excess of the yearly mean return of the buy-and-hold. Panel B shows the Sharpe ratio of the best recursive out-of-sample testing procedure, selected by the Sharpe ratio criterion, in excess of the Sharpe ratio of the buy-and-hold. Results are presented for the 0, 0.10, 0.25 and 0.50% transaction costs cases. The row labeled ``Average: out-of-sample'' shows the average over the results as presented in the table. The row labeled ``Average: in sample'' shows the average over the results of the best strategy selected in sample for each data series.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| Data set |
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
|
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
| AEX |
0.1076 |
0.0871 |
0.0171 |
-0.0107 |
-0.0352 |
-0.0515 |
|
0.0314 |
0.0216 |
0.0136 |
0.0013 |
-0.0108 |
-0.0047 |
| ABN |
0.1972 |
0.1771 |
0.1186 |
0.1383 |
0.0658 |
0.0179 |
|
0.0266 |
0.0207 |
0.0210 |
0.0116 |
0.0075 |
0.0068 |
| AMRO |
0.3002 |
0.1491 |
0.1741 |
0.1264 |
0.0717 |
0.0558 |
|
0.0452 |
0.0373 |
0.0309 |
0.0245 |
0.0163 |
0.0117 |
| ABN AMRO |
0.2317 |
0.1750 |
0.1174 |
0.0595 |
-0.0095 |
-0.0285 |
|
0.0165 |
0.0115 |
-0.0021 |
-0.0047 |
-0.0017 |
-0.0066 |
| AEGON |
0.2579 |
0.2387 |
0.1866 |
0.1315 |
0.1033 |
0.0975 |
|
0.0303 |
0.0170 |
0.0076 |
0.0049 |
0.0016 |
-0.0005 |
| AHOLD |
0.2115 |
0.1758 |
0.1583 |
0.1218 |
0.0990 |
0.1005 |
|
0.0187 |
0.0152 |
0.0122 |
0.0000 |
0.0018 |
-0.0074 |
| AKZO NOBEL |
0.4165 |
0.3126 |
0.1861 |
0.0107 |
-0.0376 |
-0.0479 |
|
0.0455 |
0.0356 |
0.0227 |
0.0095 |
-0.0008 |
-0.0115 |
| ASML |
0.0997 |
0.2644 |
0.3582 |
0.5279 |
0.2838 |
0.3105 |
|
-0.0009 |
0.0051 |
0.0026 |
-0.0116 |
-0.0038 |
-0.0006 |
| BAAN |
0.2921 |
0.3498 |
0.4187 |
0.2578 |
0.2401 |
0.1432 |
|
0.0582 |
0.0550 |
0.0505 |
0.0423 |
0.0377 |
0.0399 |
| BUHRMANN |
0.2906 |
0.2232 |
0.1459 |
0.0737 |
-0.0374 |
-0.0020 |
|
0.0263 |
0.0145 |
0.0074 |
0.0030 |
0.0029 |
-0.0077 |
| CETECO |
0.5496 |
0.3833 |
0.3638 |
0.3601 |
0.2866 |
0.2533 |
|
0.0539 |
0.0443 |
0.0380 |
0.0355 |
0.0304 |
0.0304 |
| CMG |
1.2489 |
1.1705 |
1.0928 |
0.7014 |
0.4715 |
0.3412 |
|
0.0818 |
0.0724 |
0.0628 |
0.0407 |
0.0179 |
0.0312 |
| CORUS |
1.4040 |
1.2349 |
1.0419 |
0.8183 |
0.6792 |
0.5440 |
|
0.0039 |
-0.0023 |
-0.0090 |
-0.0140 |
-0.0182 |
-0.0053 |
| CSM |
0.0723 |
0.0287 |
-0.0231 |
-0.0577 |
-0.0822 |
-0.0948 |
|
0.0085 |
0.0004 |
-0.0029 |
-0.0076 |
-0.0175 |
-0.0218 |
| DAF |
0.2506 |
0.2016 |
0.1937 |
0.1595 |
0.1768 |
0.1745 |
|
0.0775 |
0.0879 |
0.0873 |
0.0831 |
0.0861 |
0.0785 |
| DSM |
0.2766 |
0.1723 |
0.1690 |
0.0134 |
0.0024 |
-0.0069 |
|
0.0370 |
0.0221 |
0.0029 |
-0.0103 |
-0.0088 |
-0.0057 |
| REED ELSEVIER |
0.1636 |
0.1153 |
0.0256 |
-0.0815 |
-0.0725 |
-0.0743 |
|
0.0021 |
0.0045 |
-0.0009 |
-0.0160 |
-0.0200 |
-0.0261 |
| FOKKER |
0.1708 |
0.1059 |
0.0537 |
-0.0234 |
-0.0495 |
-0.0200 |
|
0.0082 |
0.0082 |
0.0082 |
0.0083 |
0.0083 |
0.0083 |
| FORTIS |
0.1929 |
0.0948 |
0.0509 |
-0.0469 |
-0.0914 |
-0.1267 |
|
0.0163 |
0.0071 |
-0.0007 |
-0.0117 |
-0.0181 |
-0.0264 |
| GETRONICS |
0.3375 |
0.2511 |
0.1869 |
0.1444 |
-0.0070 |
-0.0373 |
|
0.0388 |
0.0322 |
0.0251 |
0.0226 |
0.0229 |
0.0177 |
| GIST BROCADES |
0.0856 |
0.0508 |
0.0424 |
-0.0051 |
0.0089 |
-0.0695 |
|
0.0225 |
0.0190 |
0.0131 |
0.0029 |
-0.0036 |
0.0024 |
| GUCCI |
0.3182 |
0.2343 |
0.2869 |
0.4464 |
0.2923 |
0.2365 |
|
0.0373 |
0.0337 |
0.0315 |
0.0289 |
0.0158 |
0.0209 |
| HAGEMEYER |
0.2593 |
0.1657 |
0.0707 |
0.0353 |
0.0128 |
0.0056 |
|
0.0348 |
0.0258 |
0.0036 |
-0.0039 |
-0.0086 |
-0.0129 |
| HEINEKEN |
0.1277 |
0.0950 |
0.0196 |
-0.0685 |
-0.1205 |
-0.1161 |
|
0.0326 |
0.0044 |
-0.0077 |
-0.0259 |
-0.0299 |
-0.0284 |
| HOOGOVENS |
0.4009 |
0.3061 |
0.2213 |
0.1763 |
0.0450 |
-0.0246 |
|
0.0440 |
0.0313 |
0.0251 |
0.0133 |
0.0018 |
-0.0058 |
| ING |
0.2090 |
0.1260 |
0.1028 |
-0.0142 |
-0.0632 |
-0.0732 |
|
0.0220 |
0.0137 |
0.0009 |
-0.0101 |
-0.0151 |
-0.0278 |
| KLM |
0.1803 |
0.1128 |
0.0896 |
0.0630 |
0.0024 |
0.0114 |
|
0.0319 |
0.0180 |
0.0130 |
0.0071 |
0.0036 |
0.0001 |
Table 4.14 continued.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| Data set |
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
|
0% |
0.10% |
0.25% |
0.50% |
0.75% |
1% |
| KON. PTT NED. |
0.1292 |
0.1599 |
0.1350 |
0.0943 |
0.1270 |
0.0800 |
|
0.0086 |
-0.0056 |
-0.0269 |
-0.0373 |
-0.0482 |
-0.0484 |
| KPN |
1.0787 |
0.9829 |
0.9163 |
0.8445 |
0.5666 |
0.5991 |
|
0.1425 |
0.1185 |
0.1015 |
0.1068 |
0.0992 |
0.0841 |
| KPNQWEST |
0.4183 |
0.4129 |
0.4049 |
0.3920 |
0.6060 |
0.5880 |
|
0.1640 |
0.1622 |
0.1596 |
0.1550 |
0.1506 |
0.1221 |
| VAN DER MOOLEN |
0.3970 |
0.3502 |
0.2888 |
0.1832 |
0.1401 |
0.0841 |
|
0.0297 |
0.0193 |
0.0100 |
-0.0044 |
-0.0079 |
-0.0123 |
| NAT. NEDERLANDEN |
0.2439 |
0.2009 |
0.1045 |
0.0048 |
-0.0163 |
-0.0339 |
|
0.0567 |
0.0436 |
0.0289 |
0.0193 |
0.0014 |
-0.0036 |
| NEDLLOYD |
0.4392 |
0.3444 |
0.2632 |
0.0531 |
0.0285 |
-0.0165 |
|
0.0383 |
0.0321 |
0.0175 |
0.0093 |
0.0062 |
0.0002 |
| NMB POSTBANK |
0.4363 |
0.3660 |
0.1964 |
0.1044 |
0.1101 |
0.0271 |
|
0.0346 |
0.0330 |
0.0273 |
0.0213 |
0.0062 |
-0.0057 |
| NUMICO |
0.2212 |
0.1330 |
0.0904 |
0.0561 |
-0.0047 |
-0.0645 |
|
0.0275 |
0.0139 |
0.0036 |
-0.0032 |
-0.0078 |
-0.0159 |
| OCE |
0.3564 |
0.2763 |
0.1655 |
0.1684 |
0.0872 |
0.0875 |
|
0.0605 |
0.0434 |
0.0252 |
0.0054 |
0.0069 |
0.0046 |
| PAKHOED |
0.1123 |
0.0757 |
0.0582 |
0.0341 |
0.0176 |
-0.0403 |
|
0.0188 |
0.0109 |
0.0023 |
-0.0099 |
-0.0100 |
-0.0170 |
| PHILIPS |
0.3218 |
0.1933 |
0.1035 |
-0.0149 |
-0.0481 |
-0.0986 |
|
0.0166 |
0.0167 |
-0.0001 |
0.0001 |
-0.0056 |
-0.0113 |
| POLYGRAM |
0.2305 |
0.1006 |
-0.0283 |
-0.1426 |
-0.1913 |
-0.1345 |
|
0.0023 |
0.0061 |
0.0035 |
-0.0156 |
-0.0225 |
-0.0254 |
| ROBECO |
0.1745 |
0.0954 |
0.0293 |
0.0040 |
0.0043 |
-0.0169 |
|
0.0517 |
0.0301 |
0.0000 |
-0.0114 |
-0.0178 |
-0.0235 |
| ROYAL DUTCH |
0.0240 |
0.0118 |
-0.0237 |
-0.0225 |
-0.0615 |
-0.0810 |
|
0.0060 |
-0.0044 |
-0.0073 |
-0.0157 |
-0.0167 |
-0.0263 |
| STORK |
0.1774 |
0.1206 |
0.1702 |
-0.0440 |
-0.0074 |
-0.0077 |
|
0.0264 |
0.0224 |
0.0071 |
-0.0086 |
-0.0085 |
-0.0071 |
| TPG |
0.3160 |
0.3458 |
0.1942 |
0.0607 |
0.0126 |
-0.0601 |
|
0.0474 |
0.0419 |
0.0344 |
0.0239 |
0.0139 |
0.0169 |
| UNILEVER |
-0.0213 |
-0.0429 |
-0.0775 |
-0.1083 |
-0.1045 |
-0.1347 |
|
-0.0076 |
-0.0108 |
-0.0212 |
-0.0239 |
-0.0296 |
-0.0341 |
| UPC |
0.5227 |
0.5098 |
0.4911 |
1.0538 |
1.0499 |
1.0460 |
|
0.1255 |
0.1421 |
0.1295 |
0.1165 |
0.1414 |
0.1312 |
| VEDIOR |
-0.1383 |
-0.1671 |
-0.1786 |
-0.2218 |
-0.1493 |
-0.1302 |
|
0.0078 |
0.0074 |
0.0096 |
0.0073 |
0.0036 |
0.0093 |
| VENDEX KBB |
0.2894 |
0.2136 |
0.0585 |
0.0427 |
-0.0590 |
-0.0659 |
|
0.0346 |
0.0284 |
0.0210 |
0.0216 |
0.0113 |
0.0094 |
| VERSATEL |
1.2925 |
1.2756 |
1.2508 |
1.2103 |
1.1710 |
1.1329 |
|
0.1079 |
0.1071 |
0.1122 |
0.1060 |
0.1044 |
0.1029 |
| VNU |
0.3450 |
0.2892 |
0.1556 |
0.0298 |
-0.0018 |
0.0161 |
|
0.0232 |
0.0153 |
-0.0012 |
-0.0097 |
-0.0117 |
-0.0224 |
| WESSANEN |
0.2391 |
0.1542 |
0.0414 |
-0.0364 |
-0.0675 |
-0.0965 |
|
0.0333 |
0.0211 |
0.0048 |
0.0014 |
-0.0082 |
-0.0188 |
| WOLTERS KLUWER |
0.1809 |
0.0842 |
-0.0472 |
-0.1254 |
-0.1280 |
-0.1059 |
|
0.0170 |
0.0101 |
-0.0110 |
-0.0271 |
-0.0306 |
-0.0319 |
| Average: out-of-sample |
0.3223 |
0.2645 |
0.2085 |
0.1505 |
0.1043 |
0.0802 |
|
0.0377 |
0.0306 |
0.0213 |
0.0128 |
0.0082 |
0.0044 |
| Average: in sample |
6.8571 |
6.7184 |
6.6225 |
6.5136 |
6.4123 |
6.3151 |
|
0.0522 |
0.0431 |
0.0402 |
0.0380 |
0.0363 |
0.0350 |
Table 4.15: Estimation results CAPM for best out-of-sample testing procedure. Coefficient estimates of the Sharpe-Lintner CAPM:
rti-rtf=a + b (rtAEX-rtf) + et.
That is, the return of the best recursive optimizing and testing procedure, when selection is done in the optimizing period by the mean return criterion (Panel A) or by the Sharpe ratio criterion (Panel B), in excess of the risk-free interest rate is regressed against a constant and the return of the AEX-index in excess of the risk-free interest rate. Estimation results for the 0 and 0.50% costs per trade cases are shown. a, b, c indicates that the corresponding coefficient is, in the case of a, significantly different from zero, or in the case of b, significantly different from one, at the 1, 5, 10% significance level. Estimation is done with Newey-West (1987) heteroskedasticity and autocorrelation consistent (HAC) standard errors.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| costs per trade |
0% |
0.50% |
|
0% |
0.50% |
| Data set |
a |
b |
a |
b |
|
a |
b |
a |
b |
| AEX |
0.000371b |
0.99 |
-5.39E-05 |
1.082 |
|
0.000493a |
0.730a |
7.98E-05 |
0.846c |
| ABN |
0.000663c |
0.662b |
0.000467 |
0.637b |
|
0.000366 |
0.546a |
0.00014 |
0.651b |
| AMRO |
0.001047b |
0.525a |
0.0005 |
0.522a |
|
0.000736c |
0.412a |
0.000467 |
0.523a |
| ABN AMRO |
0.000935b |
0.879c |
0.00036 |
1.074 |
|
0.000627c |
0.898c |
0.000242 |
0.949 |
| AEGON |
0.001116a |
1.005 |
0.000746b |
1.062 |
|
0.001038a |
0.687a |
0.000602b |
0.866 |
| AHOLD |
0.000972a |
0.816b |
0.000699b |
0.876 |
|
0.000789a |
0.610a |
0.00044 |
0.696a |
| AKZO NOBEL |
0.001397a |
0.624a |
0.000168 |
0.728a |
|
0.001022a |
0.558a |
0.000432 |
0.768a |
| ASML |
0.001011 |
1.556a |
0.002076 |
1.489a |
|
0.000959 |
1.497a |
0.000337 |
1.431b |
| BAAN |
-0.00158 |
0.958 |
-0.00172 |
0.909 |
|
-6.01E-05 |
0.685b |
-0.001048 |
0.693b |
| BUHRMANN |
0.000956b |
0.831b |
0.000248 |
1.045 |
|
0.000759b |
0.621a |
0.000157 |
0.856b |
| CETECO |
-0.000523 |
0.259a |
-0.001442 |
0.291a |
|
-0.000159 |
0.290a |
-0.001581 |
0.094a |
| CMG |
0.002969b |
1.181 |
0.001839 |
1.176 |
|
0.003175b |
0.919 |
0.001406 |
0.921 |
| CORUS |
0.004795c |
0.616c |
0.004226 |
0.560c |
|
0.005136c |
0.626c |
0.004563 |
0.635 |
| CSM |
0.000537b |
0.360a |
8.29E-05 |
0.441a |
|
0.000593b |
0.355a |
0.000248 |
0.387a |
| DAF |
-0.005082c |
1.422 |
-0.006421b |
1.497 |
|
-0.002042 |
1.373 |
-0.001437 |
1.566 |
| DSM |
0.001089a |
0.524a |
0.00029 |
0.522a |
|
0.000981a |
0.464a |
0.000113 |
0.607a |
| REED ELSEVIER |
0.000846a |
0.722a |
7.95E-06 |
0.964 |
|
0.000466 |
0.816a |
3.84E-05 |
1.091 |
| FORTIS |
0.000785a |
0.764a |
-3.76E-05 |
0.97 |
|
0.000564b |
0.699a |
-2.84E-05 |
0.911c |
| GETRONICS |
0.001028b |
0.678a |
0.000432 |
0.739b |
|
0.001171a |
0.708a |
0.000665 |
0.965 |
| GIST BROCADES |
0.00016 |
0.714a |
-0.00016 |
0.697a |
|
0.000365 |
0.645a |
-5.60E-05 |
0.656a |
| GUCCI |
0.001627 |
0.570a |
0.001947c |
0.838 |
|
0.002076b |
0.473a |
0.001732c |
0.488a |
| HAGEMEYER |
0.001091a |
0.726a |
0.000434 |
0.617a |
|
0.001156a |
0.553a |
0.000326 |
0.607a |
| HEINEKEN |
0.000728a |
0.615a |
6.66E-05 |
0.689a |
|
0.000966a |
0.527a |
-6.22E-05 |
0.551a |
| HOOGOVENS |
0.001074b |
0.943 |
0.000437 |
0.89 |
|
0.001159a |
0.818c |
0.000258 |
0.779a |
| ING |
0.000900b |
1.01 |
0.000143 |
1.236c |
|
0.000820b |
0.881c |
0.000193 |
0.954 |
Table 4.15 continued.
| |
Panel A |
|
Panel B |
| selection criterion |
Mean return |
|
Sharpe ratio |
| costs per trade |
0% |
0.50% |
|
0% |
0.50% |
| Data set |
a |
b |
a |
b |
|
a |
b |
a |
b |
| KLM |
0.000336 |
0.746a |
-0.000104 |
0.904 |
|
0.000493 |
0.713a |
-0.000205 |
0.935 |
| KON. PTT NED. |
0.000539 |
0.843 |
0.000164 |
1.074 |
|
0.00084 |
0.751b |
-2.57E-05 |
0.638a |
| KPN |
0.00245 |
1.706b |
0.0023 |
2.244a |
|
0.003785c |
1.731b |
0.001819 |
1.705c |
| KPNQWEST |
-0.00421 |
1.182 |
-0.004448 |
1.174 |
|
-0.000803 |
0.647 |
-0.001073 |
0.636 |
| VAN DER MOOLEN |
0.001618a |
0.811b |
0.001064c |
0.837c |
|
0.001406a |
0.662a |
0.000632 |
0.810b |
| NAT. NEDERLANDEN |
0.000818c |
0.639a |
1.36E-05 |
0.549a |
|
0.000929b |
0.506a |
0.000358 |
0.577a |
| NEDLLOYD |
0.001282a |
0.639a |
9.88E-05 |
0.647a |
|
0.001015b |
0.578a |
0.000175 |
0.622a |
| NMB POSTBANK |
0.001547a |
0.491a |
0.000611 |
0.529a |
|
0.000880b |
0.481a |
0.00072 |
0.417a |
| NUMICO |
0.001061a |
0.504a |
0.000558 |
0.558a |
|
0.001020a |
0.450a |
0.000436 |
0.484a |
| OCE |
0.001104a |
0.553a |
0.000521 |
0.679a |
|
0.001301a |
0.533a |
8.51E-05 |
0.630a |
| PAKHOED |
0.000508 |
0.540a |
0.000243 |
0.569a |
|
0.000617c |
0.538a |
-5.79E-05 |
0.771b |
| PHILIPS |
0.001068a |
1.025 |
-1.57E-05 |
1.203 |
|
0.000580c |
0.94 |
0.00014 |
1.083 |
| POLYGRAM |
0.000849c |
0.495a |
-0.000475 |
0.657a |
|
0.000219 |
0.766a |
-0.000175 |
0.694a |
| ROBECO |
0.000681a |
0.413a |
0.000106 |
0.470a |
|
0.000670a |
0.369a |
5.77E-06 |
0.415a |
| ROYAL DUTCH |
0.00035 |
0.493a |
0.000184 |
0.528a |
|
0.000452b |
0.484a |
9.14E-05 |
0.532a |
| STORK |
0.000525 |
0.834 |
-0.000206 |
0.568a |
|
0.000550c |
0.580a |
-0.000235 |
0.490a |
| TPG |
0.001137 |
0.450a |
0.000209 |
0.568a |
|
0.001019 |
0.571a |
0.000232 |
0.374a |
| UNILEVER |
0.000264 |
0.370a |
-5.50E-05 |
0.402a |
|
0.000269 |
0.403a |
-7.37E-05 |
0.399a |
| UPC |
-0.001767 |
0.736 |
0.000276 |
0.071a |
|
-0.001142 |
1.158 |
-0.00182 |
0.301a |
| VEDIOR |
-0.000718 |
0.467a |
-0.001119 |
0.548a |
|
0.00023 |
0.689c |
0.000203 |
0.703c |
| VENDEX KBB |
0.000876 |
0.464a |
2.81E-05 |
0.632a |
|
0.000891 |
0.363a |
0.000519 |
0.480a |
| VERSATEL |
0.00177 |
0.598 |
0.001552 |
0.594 |
|
0.000621 |
0.485 |
0.000526 |
0.579 |
| VNU |
0.001359a |
0.700a |
0.000422 |
0.846c |
|
0.001129a |
0.825b |
0.000225 |
0.795a |
| WESSANEN |
0.000706b |
0.602a |
-0.000231 |
0.520a |
|
0.000541c |
0.546a |
-6.58E-05 |
0.552a |
| WOLTERS KLUWER |
0.000978a |
0.542a |
-6.04E-05 |
0.799c |
|
0.000873a |
0.507a |
-7.49E-05 |
0.602a |
B. Parameters of recursive optimizing and testing procedure
This appendix presents the parameter values of the recursive optimizing and testing procedures applied in section 4.4. The two parameters are the length of the training period, TR, and the length of the testing period, Te. The following 28 combinations of training and testing periods, [Tr,Te], are used:
|
|
| Train |
Test |
| 5 |
1 |
| 10 |
1 |
| 21 |
1 |
| 42 |
1 |
| 63 |
1 |
| 126 |
1 |
| 252 |
1 |
| 10 |
5 |
| 21 |
5 |
| 42 |
5 |
| 63 |
5 |
| 126 |
5 |
| 252 |
5 |
| 21 |
10 |
|
|
| Train |
Test |
| 42 |
10 |
| 63 |
10 |
| 126 |
10 |
| 252 |
10 |
| 42 |
21 |
| 63 |
21 |
| 126 |
21 |
| 252 |
21 |
| 63 |
42 |
| 126 |
42 |
| 252 |
42 |
| 126 |
63 |
| 252 |
63 |
| 252 |
126 |
|
- 1
- At the moment of writing the stock exchanges were reaching new lows, which is not visible in these data until May 2002.
- 2
- See section 3.2, page ??, for an explanation. Separate ACFs of the returns are computed for each data series, but not presented here to save space. The tables are available upon request from the author.
- 3
- We also estimated the Sharpe-Lintner CAPMs for the 0.10, 0.25, 0.75 and 1% transaction costs cases. The estimation results for the separate stocks are not presented here to save space.
|
