Gerwin Griffioen's Technical Analysis Pages

Griffioen, G.A.W. (2003), "Technical Analysis in Financial Markets", PhD thesis, University of Amsterdam.

Chapter 5
Technical Trading Rule Performance in Local Main Stock Market Indices

5.1 Introduction

Brock, Lakonishok and LeBaron (1992) found that technical trading rules show forecasting power when applied to the Dow-Jones Industrial Average (DJIA) in the period 1896-1986. Sullivan, Timmermann and White (1999) confirmed their results for the same period, after they made a correction for data snooping. However they noticed that the forecasting power seems to disappear in the period after 1986. Next, Bessembinder and Chan (1998) found that break even transaction costs, that is costs for which trading rule profits disappear, are lower than real transaction costs in the period 1926-1991 and that therefore the technical trading rules examined by Brock et al. (1992) are not economically significant when applied to the DJIA. The trading rule set of Brock et al. (1992) has been applied to many other local main stock market indices. For example, to Asian stock markets by Bessembinder and Chan (1995), to the UK stock market by Hudson, Dempsey and Keasey (1996) and Mills (1997), to the Spanish stock market by Fernández-Rodríguez, Sosvilla-Rivero, and Andrada-Félix (2001), to Latin-American stock markets by Ratner and Leal (1999) and to the Hong Kong stock market by Coutts and Cheung (2000).

In this chapter we test whether objective computerized trend-following technical trading techniques can profitably be exploited after correction for risk and transaction costs when applied to the local main stock market indices of 50 countries and the MSCI World Index. Firstly, we do as if we are a local trader and we apply the technical trading rules to the indices in local currency and we compute the profits in local currency. However these profits could be spurious if the local currencies weakened against other currencies. Therefore, secondly, we do as if we are an US-based trader and we calculate the profits that could be made by technical trading rules in US Dollars. For this second case we generate technical trading signals in two different ways. Firstly by using the local main stock market index in local currency and secondly by using the local main stock market index recomputed in US Dollars. Observed technical trading rule profits could be the reward for risk. Therefore we test by estimating a Sharpe-Lintner capital asset pricing model (CAPM) whether the best technical trading rule selected for each stock market index is also profitable after correction for risk. Both the local index and the MSCI World Index are used as the benchmark market portfolio in the CAPM estimation equation. If the technical trading rules show economically significant forecasting power after correction for risk and transaction costs, then further it is tested whether the best strategy found for each local main stock market index is indeed superior to the buy-and-hold benchmark after correction for data snooping. This chapter may therefore be seen as an empirical application of White's (2000) Reality Check and Peter Hansen's (2001) test for superior predictive ability. Further we test by recursively optimizing our technical trading rule set whether technical analysis shows true out-of-sample forecasting power.

In section 5.2 we list the local main stock market indices examined in this chapter and we show the summary statistics. We refer to the sections 3.3, 3.4 and 3.5 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 5.3 presents the empirical results of our study. In section 5.4 we test whether recursively optimizing and updating our technical trading rule set shows genuine out-of-sample forecasting ability. Finally, section 5.5 summarizes and concludes.

5.2 Data and summary statistics

The data series examined in this chapter are the daily closing levels of local main stock market indices in Africa, the Americas, Asia, Europe, the Middle East and the Pacific in the period January 2, 1981 through June 28, 2002. Local main stock market indices are intended to show a representative picture of the local economy by including the most important or most traded stocks in the index. The MSCI¹ World Index is a market capitalization index that is designed to measure global developed market equity performance. In this chapter we analyze in total 51 indices. Column 1 of table 5.1 shows for each country which local main stock market index is chosen. Further for each country data is collected on the exchange rate against the US Dollar. As a proxy for the risk-free interest rate we use for most countries daily data on 1-month interbank interest rates when available or otherwise rates on 1-month certificates of deposits. Table 5.1 shows the summary statistics of the stock market indices expressed in local currency, while table 5.2 shows the summary statistics if the stock market indices are expressed in US Dollars. Hence in table 5.2 it can be seen whether the behavior of the exchange rates of the local currencies against the US Dollar alters the features of the local main stock market data. Because the first 260 data points are used for initializing the technical trading strategies, the summary statistics are shown from January 1, 1982. In the tables the first and second column show the names of the indices 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 daily logarithmic 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. The tenth column shows the largest cumulative loss, that is the largest decline from a peak to a through, of the indices in percentage/100 terms. The eleventh column shows for each stock market index 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 MSCI World Index during the 1982-2002 period is equal to 8.38% and the yearly standard deviation of the returns is approximately equal to 12%. Measured in local currency 7 indices show a negative mean yearly effective return, although not significantly. These are stock market indices mainly in Asia, Eastern Europe and Latin America. For 17 indices a significantly positive mean return is found, mainly for the West European and US indices, but also for the Egyptian CMA and the Israeli TA100 index. If measured in US Dollars, then the number of indices which show a negative mean return more than doubles and increases to 16, while the number of indices which show a significantly positive mean return declines from 17 to 10. Especially for the Asian and Latin American stock market indices the results in US Dollars are worse than in local currency. For example, in the Latin American stock markets the Brazilian Bovespa shows a considerable positive mean yearly return of 13.85% if measured in Brazilian Reals, while it shows a negative mean yearly return of -2.48% if measured in US Dollars. In the Asian stock markets it is remarkable that the results for the Chinese Shanghai Composite, the Hong Kong Hang Seng and the Singapore Straits Times are not affected by a recomputation in US Dollars, despite the Asian crises. The separate indices are more risky than the MSCI World Index, as can be seen by the standard deviations and the largest cumulative loss numbers. Thus it is clear that country specific risks are reduced by the broad diversified world index. The return distribution is strongly leptokurtic for all indices and is negatively skewed for a majority of the indices. Thus large negative shocks occur more frequently than large positive shocks. The local interest rates are used for computing the Sharpe ratio (i.e. the extra return over the risk-free interest rate per extra point of risk as measured by the standard deviation) in local currency, while the rates on 1-month US certificates of deposits are used for computing the Sharpe ratio in US Dollars. The Sharpe ratio is negative for 23 indices, if expressed in local currency or in US Dollars, indicating that these indices were not able to beat a continuous risk free investment. Only the European and US stock market indices as well as the Egyptian and Israeli stock market indices were able in generating a positive excess return over the risk-free interest rate. For more than half of the indices the largest cumulative loss is larger than 50% if expressed in local currency or US Dollars. For example, during the Argentine economic crises the Merval lost 77% of its value in local currency and 91% of its value in US Dollars. The Russian Moscow Times lost 94% of its value in US Dollars in a short period of approximately one year between August 1997 and October 1998. The largest decline of the MSCI World Index is equal to 39% and occurred in the period March 27, 2000 through September 21, 2001. Of the 14 indices for which we have data preceding the year 1987, only for 4 indices, namely the DJIA, the NYSE Composite, the Australian ASX and the Dutch AEX, the largest cumulative loss, when measured in local currency, occurred preceding and during the crash of 1987. If measured in US Dollars, only the largest decline for the Dutch AEX changes and took place in the period January 4, 2000 through September 21, 2001. Remarkably for most indices the largest decline started well before the terrorist attack against the US on September 11, 2001, but stopped only 10 days after it². With hindsight, the overall picture is that the European and US stock markets performed the best, but also the Egyptian and Israeli stock markets show remarkably good 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 errors³. Typically autocorrelations of the returns are small with only few lags being significant. Without correcting for heteroskedasticity we find for 35 of the 51 indices a significant first order autocorrelation both in local and US currency, while when corrected for heteroskedasticity we find for 30 (23) indices measured in local (US) currency a significant first order autocorrelation at the 10% significance level. It is noteworthy that for more than half of the indices the second order autocorrelation is negative. In contrast, the first order autocorrelation is negative for only 5 (10) indices in local (US) currency. The Ljung-Box (1978) Q-statistics in the second to last columns of tables 5.1 and 5.2 reject for almost all indices the null hypothesis that the first 20 autocorrelations of the returns as a whole are equal to zero. For only 3 (5) indices the null is not rejected in the local (US) currency case, see for example New Zealand's NZSE30 and the Finnish HEX. 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. Now for 26 (34) indices the null of no autocorrelation is not rejected in the local (US) currency case. The autocorrelation functions of the squared returns show that for all indices the autocorrelations are high and significant up to order 20. The Ljung-Box (1978) statistics reject the null of no autocorrelation in the squared returns firmly, except for the Venezuela Industrial if expressed in US Dollars. Hence, almost all indices exhibit significant volatility clustering, that is large (small) shocks are likely to be followed by large (small) shocks.

5.3 Empirical results

5.3.1 Results for the mean return criterion

Technical trading rule performance

In section 5.2 we showed that almost half of the local main stock market indices could not even beat a continuous risk free investment. Further we showed that for half of the indices 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. If technical trading rules can capture dependence, which they can profitably trade upon, the question remains whether the profits disappear after implementing transaction costs. Furthermore, it is necessary to test whether the profits are just the compensation for bearing the risk of holding the risky asset during certain periods.

In total we apply 787 objective computerized trend-following technical trading techniques with and without transaction costs to the 51 market indices (see sections 2.3 and 3.3 and Appendix B of Chapter 3 for the technical trading rule parameterizations). We consider three different trading cases. First we do as if we are a local trader and we apply our technical trading rule set to the indices expressed in local currency and we compute the profits expressed in local currency. If no trading position in the stock market index is held, then the local risk-free interest rate is earned. Due to depreciation however, it is possible that profits in local currencies disappear when recomputed in US Dollars. Therefore we also consider the problem from the perspective of an US-based trader. Trading signals are then generated in two different ways: firstly on the indices expressed in local currency and secondly on the indices recomputed in US Dollars. Recomputation of local indices in US Dollars is done to correct for possible trends in the levels of stock market indices caused by a declining or advancing exchange rate of the local currency against the US Dollar. If the US-based trader holds no trading position in the stock market index, then the US risk-free interest rate is earned. Summarized we examine the following trading cases:

	Trader	Index in	Profits in
Trading case 1	local trader	local currency	local currency
Trading case 2	US trader	local currency	US Dollars
Trading case 3	US trader	US Dollars	US Dollars

We refer to section 3.4 for a discussion on how the technical trading rule profits are computed. If 0 and 0.25% costs per trade are implemented, then for trading case 3 tables 5.3 and 5.4 show for each local main stock market index some statistics of the best strategy selected by the mean return criterion. 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 cumulative 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 indices during profitable trades divided by the standard deviation of the returns of the indices during non-profitable trades.

To summarize, for trading case 3 table 5.6A (i.e. table 5.6 panel A) shows for each index 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. At the bottom of table 5.6A, the row labeled ``Average 3'' shows for each transaction cost case the average over the results for trading case 3 as presented in the table. For comparison with the other two trading cases the row labeled ``Average 1'' shows the average over the results if trading case 1 is examined and the row labeled ``Average 2'' shows the average over the results if trading case 2 is examined.

Table 5.6A clearly shows that for each stock market index the best technical trading strategy selected by the mean return criterion is capable of beating the buy-and-hold benchmark, even after correction for transaction costs. If transaction costs increase from 0 to 1% per trade, then it can be seen that the excess returns decline on average from 49.14 to 17.22%. However, even in the large 1% costs per trade case, the best technical trading strategy is superior to the buy-and-hold strategy. The lowest excess returns are found for the West European stock market indices, while the highest excess returns are found for the Asian and Latin American stock market indices. No large differences are found between the three trading cases. The results, as summarized by the averages in the bottom rows of table 5.6A, are similar.

From table 5.3 it can be seen that in the case of zero transaction costs the best-selected strategies are mainly strategies that generate a lot of signals. Trading positions are held for only a few days. For example, the best technical trading strategy found for the MSCI World Index is a single crossover moving-average rule, with no extra refinements, which generates a signal when the price series crosses a 2-day moving average. The mean yearly return is equal to 52%, which corresponds with a mean yearly excess return of 40%. The Sharpe ratio is equal to 0.1461 and the excess Sharpe ratio is equal to 0.1349. These excess performance measures are considerably large. The maximum loss of the strategy is 18.7%, half less than the maximum loss of buying and holding the MSCI World Index, which is equal to 38.7%. The number of trades is very large, once every 2.4 days, but also the percentage of profitable trades is very large, namely 74.8%. These profitable trades span 86% of the total number of trading days. Similar good results are also found for the other stock market indices. For 42 of the 51 indices the maximum loss of the best strategy is less than the largest cumulative loss of the buy-and-hold strategy. For most indices the percentage of profitable trades is larger than 70% and these profitable trades span more than 80% of the total number of trading days. Although the Sharpe ratio of the buy-and-hold was negative for 23 indices, indicating that these indices were not able in beating a continuous risk free investment, it is found for all indices that the best-selected strategy shows a positive Sharpe ratio.

If transaction costs are increased to 0.25% per trade, then table 5.4 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 period. For example, the best strategy found for the MSCI World Index is a single crossover moving-average rule which generates signals if the price series crosses a 200-day moving average and where the single refinement is a 2.5%-band filter. This strategy generates a trade every 13 months. However due to transaction costs the performance of the technical trading rules decreases and also the percentage of profitable trades and the percentage of days profitable trades last decreases for most indices in comparison with the zero transaction costs case. However for all indices, the Sharpe ratio of the best strategy is still positive. This continues to be the case even if costs are increased to 1% per trade. Similar results are found for the two other trading cases.

CAPM

If no transaction costs are implemented, then for trading case 3 it can be seen from the last column in table 5.3 that the standard deviations of the daily returns during profitable trades are higher than the standard deviations of the daily returns during non-profitable trades for almost all stock market indices, except for the Indonesian Jakarta Composite, the Finnish HEX, the Swiss SMI and the Irish ISEQ. However, if 0.25% costs per trade are calculated, then for only 24 indices out of 51 the standard deviation ratio is larger than one. Similar results are found for the other two trading cases. According to the efficient markets hypothesis it is not possible to exploit a data set with past information to predict future price changes. The good performance of the technical trading rules could therefore be the reward for holding a risky asset needed to attract investors to bear the risk. Since the technical trading rule forecasts only depend on past price history, it seems unlikely that they should result in unusual risk-adjusted profits. To test this hypothesis we regress Sharpe-Lintner capital asset pricing models (CAPMs)

r_tⁱ-r_t^f=a + b (r_t^M-r_t^f) + e_t. (1)

Here r_tⁱ is the return on day t of the best strategy applied to index i, r_t^M is the return on day t of a (preferably broad) market portfolio M and r_t^f is the risk-free interest rate. As proxy for the market portfolio M we use the local index itself or the MSCI World Index, both expressed in the same currency according to which the return of the best strategy is computed. Because we considered three different trading cases for computing r_tⁱ, and combine these with two different choices for the market portfolio M, we estimated in total six different CAPMs for each index. 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.

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

Trading case 1 a<0 a>0 b<1 b>1 a>0 Ù a>0 Ù

b<1 b>1

0% 0 51 23 0 23 0

0.10% 0 46 30 0 27 0

0.25% 0 45 29 0 26 0

0.50% 0 36 31 5 22 3

0.75% 0 30 31 6 19 2

1% 1 25 30 7 15 3

Trading case 2

0% 0 50 19 0 18 0

0.10% 0 44 23 1 20 0

0.25% 0 41 25 1 22 0

0.50% 0 35 25 4 20 1

0.75% 0 29 28 4 17 1

1% 1 27 28 6 16 2

Trading case 3

0% 0 51 29 0 29 0

0.10% 0 45 28 1 25 0

0.25% 0 44 28 2 26 0

0.50% 0 37 28 3 23 0

0.75% 1 32 33 3 24 0

1% 2 27 34 4 20 1

Table 5.9: Summary: significance CAPM estimates, mean return criterion. For each transaction cost case, the table shows the number of indices for which significant estimates are found at the 10% significance level for the coefficients in the Sharpe-Lintner CAPM. The local main stock market index is taken to be the market portfolio in the CAPM estimations. Columns 1 and 2 show the number of indices for which the estimate of a is significantly negative and positive. Columns 3 and 4 show the number of indices for which the estimate of b is significantly smaller and larger than one. Column 5 shows the number of indices 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 indices 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 indices analyzed is equal to 51.

For example, for the best strategy applied to the MSCI World Index in the case of zero transaction costs, the estimate of a is significantly positive at the 1% significance level and equal to 13.42 basis points per day, that is approximately 33.8% on a yearly basis. The estimate of b is significantly smaller than one at the 10% 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% per trade, then a decreases to 1.82 basis points (4.6% yearly), but still is significantly positive at the 10% significance level. However, the estimate of b is not significantly smaller than one anymore, if as little as 0.25% costs per trade are charged. It becomes even significantly larger than one if 1% transaction costs are implemented, which indicates that the strategy applied to the MSCI World Index is riskier than buying and holding the market index.

If the local main stock market index is taken to be the market portfolio in the CAPM estimations and if zero transaction costs are implemented, then, as further can be seen in the tables, also for the other indices the estimate of a is significantly positive at the 10% significance level. Further the estimate of b is significantly smaller than one for 29 indices. For none of the indices the estimate of b is significantly larger than one. The estimate of a in general decreases as costs per trade increases and becomes less significant for more indices. However in the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade cases for example, still for respectively 45, 44, 37, 32 and 27 indices out of 51 the estimate of a is significantly positive at the 10% significance level. The estimate of b is significantly smaller than one for 28, 28, 28, 33 and 34 indices, in the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade cases, indicating that even in the presence of high costs, the best selected technical trading strategies are less risky than the buy-and-hold strategy. The number of data series for which the estimate of b is significantly smaller than one increases as transaction costs increase. This is mainly caused because as transaction costs increase, by the selection criteria strategies are selected which trade less frequently and are thus less risky. Notice that for a large number of cases it is found that the estimate of 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. The results for the two other trading cases are similar.

If the MSCI World Index is used as market portfolio in the CAPM estimations, then the results for a become less strong⁴. In the case of zero transaction costs for 46 stock market indices it is found that the estimate of a is significantly different from zero. In the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade cases, for respectively 40, 34, 24, 24 and 19 indices out of 51 the estimate of a is significantly positive at the 10% significance level. However still the estimate of b is significantly smaller than one for 41, 41, 40, 40 and 42 indices in the 0.10, 0.25, 0.50, 0.75 and 1% costs per trade case.

From these findings we conclude that there are trend-following technical trading techniques which can profitably be exploited, even after correction for transaction costs, when applied to local main stock market indices. As transaction costs increase, the best strategies selected are those which trade less frequently. Furthermore, if a correction is made for risk by estimating Sharpe-Lintner CAPMs, then it is found for many local main stock market indices that the best strategy has forecasting power, i.e. a>0. It is also found that in general the best strategy is less risky, i.e. b<1, than buying and holding the market portfolio. Hence, for most stock market indices, we can reject the null hypothesis that the profits of technical trading are just the reward for bearing risk.

Data snooping

The question remains open whether the findings in favour of technical trading for particular indices 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 0.25% transaction costs table 5.8 shows for trading case 3 the nominal, RC and SPA-test p-values, if the best strategy is selected by the mean return criterion⁵. Table 5.10 summarizes the results for all transaction cost cases by showing the number of indices 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.

Trading case 3

costs p_n p_W p_H

0% 51 8 27

0.10% 51 6 15

0.25% 51 2 6

0.50% 51 0 2

0.75% 51 0 1

1% 51 0 1

Table 5.10: Summary: Testing for predictive ability, mean return criterion. For each transaction cost case, the table shows the number of indices for which the nominal (p_n), White's (2000) Reality Check (p_W) or Hansen's (2001) Superior Predictive Ability test (p_H) p-value is smaller than 0.10. Note that the number of indices analyzed is equal to 51.

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 all indices in all cost cases at the 10% significance level. However, if we correct for data snooping, then in the case of zero transaction costs we find for only 8 of the stock market indices that 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 27 indices 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 19 indices. Thus the RC misguides the researcher in several cases by not rejecting the null. The number of contradictory results decreases to 9 if 0.10% costs per trade are implemented and to 4, 2, 1 and 1 if 0.25, 0.50, 0.75 and 1% costs per trade are implemented. In the 0.10% costs per trade case, the SPA-test rejects for 15 indices its null hypothesis, but this number declines to 2 in the 0.50% costs per trade case. Remarkably, only for the Egyptian CMA the SPA-test does reject its null hypothesis, even in the 1% costs per trade case. Hence we conclude that for all but one of the market indices 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.

5.3.2 Results for the Sharpe ratio criterion

Technical trading rule performance

Similar to tables 5.3 and 5.4, table 5.5 shows for trading case 3 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 indices are shown for which the best strategy selected by the Sharpe ratio criterion differs from the best strategy selected by the mean return criterion. Further, to summarize, table 5.6B shows for each index 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 index and for each transaction costs case it is found that the excess Sharpe ratio is considerably positive. In the last row of table 5.6B it can be seen that on average the excess Sharpe ratio declines from 0.0672 to 0.0320 if transaction costs increase from 0 to 1% per trade. Table 5.5 shows that the best strategies selected in the case of zero transaction costs are mainly strategies which trade frequently. For most indices, except 10, the best-selected strategy is the same as in the case that the best strategy is selected by the mean return criterion. If costs are increased to 0.25%, then the best strategies selected are those which trade less frequently. Now for 22 indices the best-selected strategy differs from the case when the best strategy is selected by the mean return criterion. The results for the two other trading cases are similar.

As for the mean return criterion it is found that for each stock market index 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 shown in tables 5.7B and 5.11 for the Sharpe ratio selection criterion are similar to the estimation results shown in tables 5.7A and 5.9 for the mean return selection criterion. If zero transaction costs are implemented, then it is found for trading case 3 that for all 51 indices the estimate of a is significantly positive at the 10% significance level. This number decreases from 37 to 28 if transaction costs increase from 0.50 to 1% per trade. As for the mean return selection criterion, for many indices it is found that the estimate of a is significantly positive and that simultaneously the estimate of b is significantly smaller than one. Thus, after correction for transaction costs and risk, for more than half of the indices it is found that the best technical trading strategy selected by the Sharpe ratio criterion significantly outperforms the buy-and-hold benchmark strategy and is even significantly less risky.

If the MSCI World Index is taken to be the market portfolio, then the results for a become less strong, as in the mean return selection criterion case. If transaction costs increase from 0% to 0.50 and 1%, then the number of indices for which a significant estimate of a is found declines from 46 to 25 and 18.

Trading case 1 a<0 a>0 b<1 b>1 a>0 Ù a>0 Ù

b<1 b>1

0% 0 50 26 0 25 0

0.10% 0 46 34 0 29 0

0.25% 0 46 37 0 32 0

0.50% 0 39 43 0 32 0

0.75% 0 33 43 1 28 1

1% 1 27 42 1 22 1

Trading case 2

0% 0 50 21 0 20 0

0.10% 0 46 30 1 26 0

0.25% 0 43 36 1 30 0

0.50% 0 38 39 1 30 0

0.75% 0 33 37 1 26 0

1% 0 31 36 3 23 1

Trading case 3

0% 0 51 28 0 28 0

0.10% 0 45 37 0 31 0

0.25% 0 42 41 0 33 0

0.50% 0 37 43 1 33 0

0.75% 1 33 47 1 32 0

1% 2 28 47 1 26 0

Table 5.11: Summary: significance CAPM estimates, Sharpe ratio criterion. For each transaction cost case, the table shows the number of indices for which significant estimates are found at the 10% significance level for the coefficients in the Sharpe-Lintner CAPM. The local main stock market index is taken to be the market portfolio in the CAPM estimations. Columns 1 and 2 show the number of indices for which the estimate of a is significantly negative and positive. Columns 3 and 4 show the number of indices for which the estimate of b is significantly smaller and larger than one. Column 5 shows the number of indices 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 indices 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 indices analyzed is equal to 51.

Data snooping

In the case of 0 and 0.25% transaction costs table 5.8B shows for trading case 3 the nominal, White's RC and Hansen's SPA-test p-values, if the best strategy is selected by the Sharpe ratio criterion. For trading case 3 table 5.12 summarizes the results for all transaction cost cases by showing the number of indices for which the corresponding p-value is smaller than 0.10.

Trading case 3

costs p_n p_W p_H

0% 51 24 35

0.10% 51 17 28

0.25% 51 7 23

0.50% 51 3 16

0.75% 51 3 15

1% 51 1 13

Table 5.12: Summary: Testing for predictive ability, Sharpe ratio criterion. For each transaction cost case, the table shows the number of indices for which the nominal (p_n), White's (2000) Reality Check (p_W) or Hansen's (2001) Superior Predictive Ability test (p_H) p-value is smaller than 0.10. Note that the number of indices analyzed is equal to 51.

The results for the Sharpe ratio selection criterion differ from the results for the mean return selection criterion. If the nominal p-value is used to test the null hypothesis that the best strategy is not superior to the benchmark of buy-and-hold, then the null is rejected for all indices at the 10% significance level for all cost cases. If a correction is made for data snooping, then it is found in the case of zero transaction costs that for 24 indices the null hypothesis that the best strategy is not superior to the buy-and-hold benchmark is rejected by the RC. However, for 35 indices 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. Thus for half of the indices we find that the best technical trading rule has forecasting power even when correcting for the specification search. These numbers are higher than for the mean return selection criterion. In total we find for 11 indices contradictory results, which is less than for the mean return selection criterion. Even in the case of 0.10% costs per trade, the number of indices for which the RC and the SPA-test reject the null is high, namely for 17 and 28 indices respectively. However, if transaction costs are increased any further, then the number of indices for which the RC rejects its null declines sharply: to 7, 3, 3, 1 in the 0.25, 0.50, 0.75 and 1% transaction costs cases. In contrast, the SPA-test rejects its null for 23, 16, 15 and 13 indices in the 0.25, 0.50, 0.75 and 1% transaction costs cases. Note that these results differ substantially from the mean return selection criterion in which case under 0.25, 0.50, 0.75 and 1% costs per trade the null of no superior predictive ability was rejected for respectively 6, 2, 1 and 1 indices by the SPA-test. Hence we conclude, after a correction is made for transaction costs and data snooping, that the best strategy selected by the Sharpe ratio criterion is capable of beating the benchmark of a buy-and-hold strategy for approximately 25% of the indices analyzed. These results are mainly found for the Asian stock market indices, but also for some European stock market indices, such as Italy and Portugal.

5.4 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 main local stock market indices 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 of Chapter 4.

If trading case 3 is applied, then in the case of 0.25% transaction costs, tables 5.13 and 5.14 show for the local main stock market indices some statistics of the best recursive optimizing and testing procedure, if the best strategy in the training period is selected by the mean return and Sharpe ratio criterion respectively. Because the longest training period is one year, the results are computed for the period 1983:1-2002:6. Tables 5.15A and 5.15B summarize the results for both selection criteria in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade. In the second to last row of table 5.15A 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, 37.72, 30.60, 21.41, 12.4, 7.05 and 4.47% yearly in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade. If transaction costs increase, then the best recursive optimizing and testing procedure becomes less profitable. Good results, also after correction for transaction costs, are mainly found for the Asian, Latin American, Middle East and Russian stock market indices. For example, the best recursive optimizing and testing procedure generates an excess return over the buy-and-hold of 43.52, 32.42, 20.99, 12.61, 7.50 and 4.88% yearly for the Argentinean Merval, after implementing 0, 0.10, 0.25, 0.50, 0.75 and 1% transaction costs. However, for the US, Japanese and most Western European stock market indices the recursive out-of-sample forecasting procedure does not show to be profitable, after implementing transaction costs.

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 0.0544, 0.0419, 0.0298, 0.0164, 0.0086 and 0.0052 in the case of 0, 0.10, 0.25, 0.50, 0.75 and 1% costs per trade (see second to last row of table 5.15B). As for the mean return selection criterion, the best recursive optimizing and testing procedure does not generate excess Sharpe ratios over the buy-and-hold for the US and most Western European indices in the presence of transaction costs. The best results are mainly found for the Latin American, Egyptian and Asian stock market indices.

For comparison, the last rows in tables 5.15A and 5.15B show the average over the results of the best strategies selected by the mean return or Sharpe ratio criterion in sample for each index tabulated. As can be seen, clearly the results of the best strategies selected in sample are better than the results of the best recursive out-of-sample forecasting procedure.

A: Local index as benchmark market portfolio

Selection criterion: mean return

costs a<0 a>0 b<1 b>1 a>0 Ù a>0 Ù

b<1 b>1

0% 0 37 20 1 15 1

0.10% 0 29 21 1 11 0

0.25% 0 26 16 2 9 0

0.50% 3 16 17 2 6 0

0.75% 3 10 17 2 3 0

1% 4 7 13 3 2 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 40 39 0 30 0

0.10% 0 33 34 0 23 0

0.25% 1 28 36 1 20 0

0.50% 4 15 29 1 9 0

0.75% 6 9 26 0 5 0

1% 6 6 23 1 3 0

B: MSCI World Index as benchmark market portfolio

Selection criterion: mean return

costs a<0 a>0 b<1 b>1 a>0 Ù a>0 Ù

b<1 b>1

0% 0 31 41 1 26 1

0.10% 0 24 40 0 21 0

0.25% 0 18 39 0 15 0

0.50% 2 7 40 1 6 0

0.75% 2 4 39 1 4 0

1% 3 1 38 3 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 45 0 28 0

0.10% 0 24 44 0 21 0

0.25% 0 17 42 0 16 0

0.50% 0 8 42 1 8 0

0.75% 0 2 42 0 2 0

1% 2 2 41 1 2 0

Table 5.17: Summary: significance CAPM estimates for best out-of-sample testing procedure. For each transaction cost case, the table shows the number of indices for which significant estimates are found at the 10% significance level for the coefficients in the Sharpe-Lintner CAPM. In panel A the local main stock market index and in panel B the MSCI World Index is taken to be the market portfolio in the CAPM estimations. Columns 1 and 2 show the number of indices for which the estimate of a is significantly negative and positive. Columns 3 and 4 show the number of indices for which the estimate of b is significantly smaller and larger than one. Column 5 shows the number of indices 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 indices 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 indices analyzed is equal to 51.

For the cases that the best strategy in the optimizing period is selected by the mean return and Sharpe ratio criterion respectively, tables 5.16A and 5.16B show for the 0 and 0.50% transaction cost cases the estimation results of the Sharpe-Lintner CAPM (see equation 5.1), where the return in US Dollars of the best recursive optimizing and testing procedure in excess of the US risk-free interest rate is regressed against a constant a and the return of the local main stock market index in US Dollars in excess of the US risk-free interest rate. Tables 5.17A, B summarize the CAPM estimation results for the two possible choices of the market portfolio and for all transaction cost cases by showing the number of indices for which significant estimates of a or b are found at the 10% significance level. Estimation is done with Newey-West (1987) heteroskedasticity and autocorrelation consistent (HAC) standard errors.

If the local main stock market index is taken to be the market portfolio and if the best strategy in the training period is selected by the mean return criterion, then in the case of zero transaction costs it can be seen in table 5.17A that for 37 indices a significantly positive estimate of a is found. As can be seen in table 5.16A, mainly for the US, Japan and Western European countries the estimate of a is neither significantly negative nor positive at the 10% significance level. As transaction costs increase to 0.50%, the number of significant estimates of a decreases to 16. Significant estimates for a are then mainly found for the Asian stock market indices. As transaction costs increase even further to 1%, then the number of significant estimates of a decreases to 7. Significant estimates for a are then found only for the Peru Lima General, Indonesia Jakarta Composite, Pakistan Karachi 100, Sri Lanka CSE All Share, Thailand SET, and the Egypt CMA. If the Sharpe ratio selection criterion is used to select the best strategy in the training period of the recursive optimizing and testing procedure, then the results are similar as for the mean return selection criterion. If transaction costs increase to 1%, then significant estimates of a are found only for the Chile IPSA, Peru Lima General, Sri Lanka CSE All Share, Norway OSE All Share, Russia Moscow Times, and the Egypt CMA.

However, if the MSCI World Index is taken to be market portfolio in the CAPM regression, then the results become worse, as can be seen in table 5.17B. In the case of the mean return selection criterion the number of significant estimates of a decreases from 31 to 1 if transaction costs increase from 0 to 1%. Only for the Egypt CMA the estimate of a is significantly positive at the 10% significance level if transaction costs are equal to 1% per trade. If the Sharpe ratio selection criterion is used to select the best strategy in the training period, then also for the Russia Moscow Times the estimate of a is significantly positive at the 10% significance level.

Hence, after correction for sufficiently high 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 for local main stock market indices world wide. Only for low transaction costs (£ 0.25% per trade) technical trading shows statistically significant out-of-sample forecasting power for the Asian, Chilean, Czech, Greece, Mexican, Russian and Turkish stock market indices. In contrast, for the US, Japanese and most Western European stock market indices no significant out-of-sample forecasting power is found, even for low transaction costs.

5.5 Conclusion

In this chapter we apply a set of 787 objective computerized trend-following technical trading techniques to 50 local main stock market indices in Africa, the Americas, Asia, Europe, the Middle East and the Pacific, and to the MSCI World Index in the period January 2, 1981 through June 28, 2002. For each index 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 23 stock market indices it is found that they could not even beat a continuous risk free investment, we find for both selection criteria that for each index a technical trading strategy can be selected that is capable of beating the buy-and-hold benchmark, even after correction for transaction costs.

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 local stock market index 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 buying and holding a market portfolio 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. The market portfolio is taken to be the local stock market index, but we also examine the possibility that the market portfolio is represented by the MSCI World Index. 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 case, it is found for the mean return as well as the Sharpe ratio criterion that for all indices the estimate of a is significantly positive at the 10% significance level, if the local index is used as the market portfolio. Even if transaction costs are increased to 1% per trade, then we find for more than half of the indices that the estimate of a is still significantly positive. Moreover it is found that the estimate of b is simultaneously significantly smaller than one for most indices. Thus for both selection criteria we find for approximately half of the indices that in the presence of transaction costs the best technical trading strategies have forecasting power and even reduce risk. If the MSCI World Index is used as market portfolio in the CAPM estimations, then the results for a become less strong, but even in the 0.50% costs per trade case, for almost half of the indices the estimate of a is significantly positive.

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. If zero transaction costs are implemented, then we find for the mean return selection criterion that the RC and the SPA-test for 19 out of 51 indices lead to different conclusions. The SPA-test finds for more than half of the indices 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 0.25% costs per trade are implemented, then both tests lead for almost all indices 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. The SPA-test rejects the null hypothesis for 35 indices in the case of zero transaction costs, while the RC rejects the null hypothesis for 24 indices. If costs are increased further to even 1% per trade, then for approximately a quarter of the indices analyzed, the SPA-tests rejects the null of no superior predictive ability at the 10% significance level, while the RC rejects the null for only one index. We find for the Sharpe ratio selection criterion large differences between the two testing procedures. Thus the inclusion of poor performing strategies, for which is corrected in the SPA-test, can indeed influence the inferences about the predictive ability of technical trading rules.

Next we apply a recursive optimizing and testing method to test whether the best strategy found in a specification search during a training period also shows 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 mean return over the buy-and-hold of 37.72% 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 transaction costs increase, then the excess mean returns on average decline. In the presence of 1% transaction costs the excess mean return over the buy-and-hold benchmark is on average 4.47% yearly. For both selection criteria, mainly profitable results are found for the Asian, Latin American, Middle East and Russian stock market indices. No profitable results are found for the US, Japanese and Western European stock market indices. However, estimation of Sharpe-Lintner CAPMs indicates that the economic profits of technical trading in almost all stock market indices, except the Egypt CMA and the Russia Moscow Times, can be explained by risk, after a correction is made for sufficiently high transaction costs. Only for transaction costs below or equal to 0.25% some risk-corrected out-of-sample forecasting power is found for the Asian, Latin American, Middle East and Russian stock market indices.

Hence, in short, after correcting for sufficiently high transaction costs, risk, data-snooping and out-of-sample forecasting, we conclude that objective trend-following technical trading techniques, applied to local main stock market indices all over the world, are not genuine superior, as suggested by their in-sample performance results, to the buy-and-hold benchmark. Only for sufficiently low transaction costs some statistically significant risk-corrected out-of-sample forecasting power is found for the Asian, Latin American, Middle East and Russian stock market indices.

5.6 Comparing the US, Dutch and
Other Stock Markets

Table 5.18 summarizes for all transaction costs cases the results of testing the set of 787 trend following technical trading techniques on the DJIA and on stocks listed in the DJIA (Chapter 3), on the AEX-index and on stocks listed in the AEX-index (Chapter 4) and on 51 stock market indices world wide (Chapter 5). If the return of the best technical trading strategy, selected in sample, in excess of the risk free interest rate is regressed against a constant a and the return of a market portfolio in excess of the risk free interest rate (see CAPMs (3.5), (4.1) and (5.1)), then the rows labeled ``(1) in-sample CAPM: a > 0'' show for each chapter the fraction of data series for which the estimate of a is significantly positive at the 10% significance level. The rows labeled ``(2) p_W<0.10'' show the fraction of data series for which White's (2000) RC p-value is smaller than 0.10. The rows labeled ``(3) p_H<0.10'' show the fraction of data series for which Hansen's (2001) SPA-test p-value is smaller than 0.10. Finally, the rows labeled ``(4) out-of-sample CAPM: a > 0'' show as in the rows labeled ``(1) in-sample CAPM: a > 0'' the fraction of data series for which the estimate of a is significantly positive at the 10% significance level, but this time when the return of the best recursive optimizing and training procedure in excess of the risk free interest rate is regressed against a constant a and the return of a market portfolio in excess of the risk free interest rate. Panel A shows the results if the best technical trading strategy is selected by the mean return criterion and panel B shows the results if the best technical trading strategy is selected by the Sharpe ratio criterion.

In each chapter for all data series a technical trading strategy that is capable of beating the buy-and-hold benchmark can be selected in sample. In the case of zero transaction costs it can be seen in the rows labeled ``(1) in-sample CAPM: a>0'' that in each chapter for a majority of the data series the estimate of a is significantly positive, indicating that the best selected technical trading rule has statistically significant forecasting power after correction for risk. If transaction costs increase, then the number of data series for which a significantly positive estimate of a is found declines. This can especially be observed in the results for the US stock market in Chapter 3 for which the fraction of data series for which a significantly positive estimate of a is found declines to one quarter if 1% transaction costs are implemented. However, in the case of 1% transaction costs, for approximately half of the Dutch stock market data in Chapter 4 and for approximately half of the stock market indices in Chapter 5, the estimate of a is still significantly positive. If the in-sample CAPM estimation results are compared with the out-of-sample CAPM estimation results, then the results in favour of technical trading of the latter tests are obviously worse than the results of the former tests. However, if transaction costs are zero, then in each chapter a group of data series can be found for which technical trading shows significant out-of-sample forecasting power, after correction for risk. As transaction costs increase, this group becomes smaller and smaller.

White's (2000) RC and Hansen's (2001) SPA-test are utilized to correct for data snooping. If little costs are implemented, then for the US stock market data in Chapter 3, the RC does not reject the null of no superior forecasting ability of the best selected technical trading rule over the buy-and-hold benchmark for all data series for both selection criteria. For the Dutch stock market data in Chapter 4 the same conclusion can be made, although the results in favour of technical trading are stronger, if the Sharpe ratio criterion is used. For a group of stock market indices in Chapter 5, in the case of zero transaction costs, it is found that the null hypothesis of no superior forecasting ability is rejected, especially if the Sharpe ratio criterion is used. However, if transaction costs increase to 1%, then for almost all data series the null hypothesis is not rejected anymore. The SPA-test corrects for the inclusion of poor and irrelevant strategies. Differences between the RC and SPA-test can especially be seen in Chapters 4 and 5, if the Sharpe ratio selection criterion is used. Then, for both the Dutch stock market data and the local main stock market indices, if 1% transaction costs are implemented, for more than one quarter of the data series the null hypothesis of no superior forecasting ability is rejected. Thus the biased RC leads in numerous cases to the wrong inferences.

If no transaction costs are implemented, then technical trading shows economically and statistically significant forecasting power for a group of data series, in all three chapters. In that case, generally, the results of the Sharpe ratio selection criterion are slightly better than the results of the mean return selection criterion. However, if transaction costs increase, then in Chapters 4 and 5 the Sharpe ratio selection criterion performs better in selecting the best technical trading strategy. If the Sharpe ratio criterion is used in selecting the best strategy, then for transaction costs up to 0.25%, technical trading shows economically and statistically significant forecasting power for approximately one fourth of the Dutch stock market data in Chapter 4. This is the case for approximately one third of the local main stock market indices in Chapter 5, if 0.50% transaction costs are implemented. It can be concluded that the DJIA and stocks listed in the DJIA are weak-form efficient. That is, these data series are not predictable from their own price history at normal transaction costs. The AEX-index and stocks listed in the AEX-index are weak-form efficient, only for transaction costs above 0.25%. For transaction costs below 0.25% profit opportunities exist. From the results in Chapter 5 it can be concluded that technical analysis applied to the stock market indices of emerging markets in Asia, Latin America, the Middle East and Russia has statistically significant forecasting power only for low transaction costs (£ 0.25% per trade), while for the Japanese, Northern American and Western European stock market indices the null hypothesis of weak-form efficiency cannot be rejected for all transaction costs cases.

Appendix

A. Tables

Table
5.1	Summary statistics local main stock market indices in local currency
5.2	Summary statistics local main stock market indices in US Dollars
5.3	Statistics best strategy: mean return criterion, 0% costs
5.4	Statistics best strategy: mean return criterion, 0.25% costs
5.5	Statistics best strategy: Sharpe ratio criterion, 0 and 0.25% costs
5.6A	Mean return best strategy in excess of mean return buy-and-hold
5.6B	Sharpe ratio best strategy in excess of Sharpe ratio buy-and-hold
5.7A	Estimation results CAPM: mean return criterion
5.7B	Estimation results CAPM: Sharpe ratio criterion
5.8A	Testing for predictive ability: mean return criterion
5.8B	Testing for predictive ability: Sharpe ratio criterion
5.9	Summary: significance CAPM estimates, mean return criterion
5.10	Summary: Testing for predictive ability, mean return criterion
5.11	Summary: significance CAPM estimates, Sharpe ratio criterion
5.12	Summary: Testing for predictive ability, Sharpe Ratio criterion
5.13	Statistics best out-of-sample testing procedure: mean return criterion, 0.25% costs
5.14	Statistics best out-of-sample testing procedure: Sharpe ratio criterion, 0.25% costs
5.15A	Mean return best out-of-sample testing procedure in excess of mean return buy-and-hold
5.15B	Sharpe ratio best out-of-sample testing procedure in excess of Sharpe ratio buy-and-hold
5.16A	Estimation results CAPM for best out-of-sample testing procedure: mean return criterion
5.16B	Estimation results CAPM for best out-of-sample testing procedure: Sharpe ratio criterion
5.17	Summary: significance CAPM estimates for best out-of-sample testing procedure
5.18	Summary of the results found in Chapters 3, 4 and 5

Table 5.1: Summary statistics local main stock market indices in local currency. The first column shows the names of the indices 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

World MSCI 5346 0.0838 0.000319 0.007529 -0.844 19.639 3.10a 0.011198 -0.3872 289.84a 50.74a 2189.95a

Argentina Merval 2065 -0.0525 -0.000214 0.02492 0.002 7.814 -0.39 -0.024918 -0.7682 81.22a 37.89a 634.96a

Brazil Bovespa 1755 0.1385 0.000515 0.024989 0.519 18.044 0.86 -0.012837 -0.6504 52.54a 24.91 283.11a

Canada TSX Composite 4042 0.0542 0.000209 0.008915 -1.304 22.217 1.49 -0.004028 -0.4281 83.26a 20.6 1330.14a

Chile IPSA 1955 -0.0048 -0.000019 0.012366 0.272 10.652 -0.07 -0.004304 -0.5512 108.58a 41.66a 534.99a

Mexico IPC 1413 0.1058 0.000399 0.018576 0.003 9.272 0.81 -0.015889 -0.4681 34.17b 20.82 225.62a

Peru Lima General 2610 0.2404 0.000855 0.014208 0.372 8.661 3.07a 0.031386 -0.5015 353.19a 125.83a 983.56a

US S&P500 5346 0.1035 0.000391 0.010341 -2.229 52.477 2.76a 0.015047 -0.3677 34.84b 11.77 353.99a

US DJIA 5346 0.1175 0.000441 0.010593 -2.872 72.566 3.04a 0.019429 -0.3613 36.13b 10.49 264.85a

US Nasdaq100 4825 0.114 0.000428 0.017764 -0.112 11.043 1.68c 0.011826 -0.7826 55.27a 22.1 2940.35a

US NYSE Composite 5346 0.0996 0.000377 0.009362 -2.543 61.538 2.94a 0.015129 -0.3302 41.47a 11.61 365.68a

US Russel2000 3520 0.0853 0.000325 0.009567 -0.5 8.374 2.02b 0.013897 -0.3725 134.56a 56.12a 2980.48a

US Wilshire5000 4565 0.0993 0.000376 0.009687 -1.817 31.044 2.62a 0.0172 -0.3966 61.30a 26.46 580.38a

Venezuela Industrial 1956 0.238 0.000847 0.0253 0.721 26.063 1.48 0.014105 -0.7945 52.71a 36.70b 370.72a

Australia ASX All Ordinaries 3987 0.0424 0.000165 0.009974 -6.715 182.588 1.04 -0.014138 -0.5009 161.89a 28.03 118.71a

China Shanghai Composite 1953 0.1372 0.00051 0.019896 0.894 27.342 1.13 0.025638 -0.4245 34.67b 21.42 304.15a

Hong Kong Hang Seng 4042 0.0924 0.000351 0.01826 -3.446 77.531 1.22 0.007494 -0.6005 62.73a 19.53 75.87a

India BSE30 2478 0.0222 0.000087 0.016375 -0.064 5.6 0.26 -0.012132 -0.5618 41.68a 28.88c 259.83a

Indonesia Jakarta Composite 3260 0.0184 0.000072 0.015387 0.472 14.164 0.27 -0.036795 -0.6726 248.18a 86.34a 1030.01a

Japan Nikkei225 4042 -0.035 -0.000142 0.014357 -0.084 11.004 -0.63 -0.017261 -0.7579 53.49a 30.95c 479.80a

Malaysia KLSE Composite 4316 0.0665 0.000256 0.01681 -0.228 35.098 1 0.002812 -0.8001 98.53a 17.96 2152.29a

New Zealand NZSE30 2739 0.0137 0.000054 0.009982 -0.879 22.581 0.28 -0.020997 -0.3731 27.01 20.81 374.84a

Pakistan Karachi100 2444 0.0409 0.000159 0.017111 -0.275 10.18 0.46 -0.014939 -0.7123 59.61a 27.41 726.48a

Philippines PSE Composite 3781 0.0237 0.000093 0.016238 0.45 11.136 0.35 -0.026353 -0.7159 206.55a 110.44a 259.51a

Singapore Straits Times 3979 0.0333 0.00013 0.014729 -2.045 55.318 0.56 -0.000133 -0.6278 149.90a 25.42 756.63a

South-Korea Kospi200 2239 0.0071 0.000028 0.02288 0.144 6.939 0.06 -0.016157 -0.7521 38.11a 20.99 670.90a

Sri Lanka CSE All Share 1756 0.013 0.000051 0.009578 4.142 82.322 0.22 -0.057186 -0.5591 243.99a 42.02a 46.77a

Table 5.1 continued.

Data set N Yearly Mean Std.Dev. Skew. Kurt. t-ratio Sharpe Max.loss Q20 Adj Q20 Q20 r2

Thailand SET 2474 -0.0805 -0.000333 0.018359 0.475 7.116 -0.9 -0.037278 -0.8818 100.50a 53.14a 685.33a

Taiwan TSE Composite 1805 -0.0342 -0.000138 0.01742 -0.053 5.279 -0.34 -0.018072 -0.6446 37.91a 27.84 304.13a

Austria ATX 2625 0.0239 0.000094 0.010313 -0.468 8.71 0.47 -0.007528 -0.397 77.09a 39.04a 695.30a

Belgium Bel20 2999 0.082 0.000313 0.009315 0.015 8.035 1.84c 0.011453 -0.3692 98.69a 47.72a 876.67a

Czech Republic PX50 1711 -0.0045 -0.000018 0.012599 -0.143 5.115 -0.06 -0.029454 -0.5368 60.44a 39.38a 596.07a

Denmark KFX 3020 0.0844 0.000322 0.010205 -0.292 5.76 1.73c 0.007603 -0.3636 60.41a 33.25b 893.77a

Finland HEX General 2413 0.2032 0.000734 0.020716 -0.508 10.265 1.74c 0.027515 -0.6965 18.79 10.45 412.14a

France CAC40 2846 0.0721 0.000276 0.012618 -0.116 5.448 1.17 0.005279 -0.4731 37.56b 26.55 400.48a

Germany DAX30 2781 0.0967 0.000366 0.012964 -0.423 6.537 1.49 0.013836 -0.5304 35.81b 19.44 1370.48a

Greece ASE General 1885 0.1433 0.000532 0.018091 -0.081 6.348 1.28 0.008178 -0.6687 58.10a 29.15c 422.98a

Italy MIB30 1750 0.1028 0.000388 0.015235 -0.136 5.363 1.07 0.011711 -0.5257 51.56a 31.21c 950.01a

Netherlands AEX 4042 0.0874 0.000332 0.012368 -0.576 13.646 1.71c 0.00959 -0.4673 86.86a 25.78 3851.18a

Norway OSE All Share 1435 0.0241 0.000094 0.011935 -0.567 6.423 0.3 -0.01163 -0.4568 31.63b 17.86 596.97a

Portugal PSI General 1760 0.1122 0.000422 0.0106 -0.566 9.745 1.67c 0.021932 -0.5067 83.43a 38.09a 401.71a

Russia Moscow Times 1782 0.6278 0.001933 0.035371 -0.472 10.927 2.31b 0.024207 -0.8489 128.93a 41.12a 1372.96a

Slovakia SAX16 2016 -0.0683 -0.000281 0.013817 -0.595 11.449 -0.91 -0.052416 -0.6899 19.51 16.63 37.78a

Spain IGBM 2487 0.1308 0.000488 0.011977 -0.327 5.852 2.03b 0.020543 -0.4342 52.95a 29.59c 1202.23a

Sweden OMX 2238 0.1033 0.00039 0.015015 0.038 6.124 1.23 0.012589 -0.6316 36.84b 24.02 696.72a

Switzerland SMI 3391 0.1003 0.000379 0.011144 -0.648 11.227 1.98b 0.019659 -0.3925 33.10b 16.88 792.31a

Turkey ISE100 3520 0.7513 0.002224 0.031633 -0.076 5.904 4.17a 0.070295 -0.6343 76.84a 41.78a 840.06a

UK FTSE100 4042 0.0657 0.000252 0.010173 -0.981 16.334 1.58 -0.00539 -0.3602 57.71a 20.41 2023.87a

Ireland ISEQ 3250 0.04 0.000156 0.009608 -0.858 12.772 0.92 -0.011046 -0.4349 87.61a 43.15a 381.79a

Egypt CMA 1695 0.1734 0.000635 0.006712 1.228 12.71 3.89a 0.094564 -0.2362 314.92a 133.79a 160.04a

Israel TA100 2996 0.1489 0.000551 0.013648 -0.52 9.43 2.21b 0.004681 -0.5321 81.44a 50.49a 287.13a

Table 5.2: Summary statistics local main stock market indices in US Dollars. The stock market indices are recomputed in US Dollars. The columns are as in table 5.1. For the Sharpe ratio in column 9, the interest rate on 1-month US certificates of deposits is used. Results for the US stock market indices can be found in table 5.1.

Data set N Yearly Mean Std.Dev. Skew. Kurt. t-ratio Sharpe Max.loss Q20 Adj Q20 Q20 r2

Argentina Merval 2065 -0.1962 -0.000867 0.027511 -0.859 20.5 -1.43 -0.038201 -0.913 99.35a 31.77b 421.98a

Brazil Bovespa 1755 -0.0248 -0.0001 0.027338 0.053 9.628 -0.15 -0.010343 -0.7114 40.43a 21.32 718.38a

Canada TSX Composite 4042 0.048 0.000186 0.009801 -1.183 18.119 1.21 -0.001455 -0.4638 81.35a 22.54 1425.46a

Chile IPSA 1955 -0.0718 -0.000296 0.013714 0.09 9.553 -0.95 -0.035064 -0.6082 118.80a 53.96a 405.63a

Table 5.2 continued.

Data set N Yearly Mean Std.Dev. Skew. Kurt. t-ratio Sharpe Max.loss Q20 Adj Q20 Q20 r2

Mexico IPC 1413 0.0593 0.000229 0.021103 -0.243 10.526 0.41 0.002199 -0.6114 58.90a 33.41b 234.74a

Peru Lima General 2610 0.1128 0.000424 0.015438 0.145 8.876 1.4 0.016531 -0.6236 203.03a 81.99a 875.43a

Venezuela Industrial 1956 -0.0517 -0.000211 0.030961 -5.855 159.591 -0.3 -0.012783 -0.8263 42.49a 40.97a 2.82

Australia ASX All Ordinaries 3987 0.0294 0.000115 0.012157 -4.24 98.862 0.6 -0.006986 -0.539 97.51a 24.97 148.46a

China Shanghai Composite 1953 0.1401 0.00052 0.019893 0.885 27.243 1.16 0.016854 -0.426 34.57b 21.39 305.56a

Hong Kong Hang Seng 4042 0.0923 0.00035 0.018291 -3.457 77.541 1.22 0.008195 -0.601 63.24a 19.67 76.36a

India BSE30 2478 -0.0318 -0.000128 0.017095 -0.443 9.872 -0.37 -0.017557 -0.6359 35.01b 24.75 74.24a

Indonesia Jakarta Composite 3260 -0.0991 -0.000414 0.026494 -1.664 43.393 -0.89 -0.022479 -0.9389 236.50a 27.63 2588.78a

Japan Nikkei225 4042 -0.0181 -0.000073 0.016386 0.036 10.151 -0.28 -0.016662 -0.7425 42.46a 28.51c 325.02a

Malaysia KLSE Composite 4316 0.039 0.000152 0.018434 0.086 31.573 0.54 -0.002808 -0.8727 142.66a 22.57 2285.44a

New Zealand NZSE30 2739 0.0039 0.000015 0.011854 -0.539 11.848 0.07 -0.012825 -0.5987 21.81 17.31 264.54a

Pakistan Karachi100 2444 -0.0449 -0.000182 0.017969 -0.357 10.202 -0.5 -0.019761 -0.8156 37.78a 17.29 711.36a

Philippines PSE Composite 3781 -0.0351 -0.000142 0.018152 0.526 14.497 -0.48 -0.018701 -0.8558 220.38a 91.24a 340.05a

Singapore Straits Times 3979 0.0457 0.000177 0.015387 -1.809 49.482 0.73 -0.001464 -0.6997 148.37a 25.72 779.97a

South-Korea Kospi200 2239 -0.0372 -0.000151 0.026226 -0.037 12.275 -0.27 -0.012584 -0.878 251.77a 53.39a 3674.31a

Sri Lanka CSE All Share 1756 -0.0717 -0.000295 0.009984 3.652 70.937 -1.24 -0.047927 -0.7114 203.66a 40.36a 44.29a

Thailand SET 2474 -0.1249 -0.00053 0.020911 0.402 8.034 -1.26 -0.033558 -0.9262 117.09a 49.78a 1308.61a

Taiwan TSE Composite 1805 -0.0654 -0.000268 0.018188 -0.117 5.583 -0.63 -0.024837 -0.7058 35.12b 26.24 258.45a

Austria ATX 2625 0.0029 0.000012 0.011465 -0.321 5.263 0.05 -0.013702 -0.5183 21.67 14.91 478.74a

Belgium Bel20 2999 0.0571 0.000221 0.011007 0.043 8.093 1.1 0.004447 -0.5094 28.66c 19.44 290.86a

Czech Republic PX50 1711 -0.0203 -0.000082 0.014104 -0.197 4.689 -0.24 -0.018733 -0.6139 70.91a 50.41a 371.22a

Denmark KFX 3020 0.0607 0.000234 0.011782 -0.217 6.152 1.09 0.005221 -0.338 32.21b 22.48 359.91a

Finland HEX General 2413 0.2005 0.000725 0.021293 -0.387 9.573 1.67c 0.025897 -0.7049 20.42 12.27 342.88a

France CAC40 2846 0.0617 0.000238 0.012632 -0.13 6.179 1 0.005495 -0.4744 43.08a 30.62c 186.66a

Germany DAX30 2781 0.0804 0.000307 0.013576 -0.221 5.297 1.19 0.010269 -0.5532 39.86a 24.86 955.12a

Greece ASE General 1885 0.0788 0.000301 0.019219 -0.111 6.084 0.68 0.006072 -0.7236 46.67a 25.67 382.96a

Italy MIB30 1750 0.0711 0.000273 0.015151 -0.024 5.122 0.75 0.005911 -0.548 34.61b 23.06 642.86a

Netherlands AEX 4042 0.0858 0.000327 0.012963 -0.319 10.562 1.6 0.009747 -0.4775 59.95a 18.51 3156.92a

Norway OSE All Share 1435 -0.0013 -0.000005 0.012838 -0.345 5.55 -0.01 -0.014581 -0.4642 31.10c 16.51 926.37a

Portugal PSI General 1760 0.0655 0.000252 0.01169 -0.175 6.81 0.9 0.005878 -0.5601 39.29a 24.24 289.77a

Russia Moscow Times 1782 0.234 0.000834 0.033932 -0.288 7.915 1.04 0.01919 -0.9426 51.56a 23.27 912.28a

Slovakia SAX16 2016 -0.1082 -0.000455 0.015344 -0.525 9.145 -1.33 -0.041685 -0.7907 26.54 22.68 41.61a

Spain IGBM 2487 0.0843 0.000321 0.012772 -0.097 5.286 1.25 0.01171 -0.4622 29.22c 19.26 641.92a

Sweden OMX 2238 0.0938 0.000356 0.016323 0.023 5.806 1.03 0.01079 -0.6578 39.19a 25.64 658.19a

Switzerland SMI 3391 0.1108 0.000417 0.012252 -0.172 7.71 1.98b 0.018825 -0.4199 21.67 14.7 421.85a

Turkey ISE100 3520 0.0783 0.000299 0.034929 -0.288 7.319 0.51 0.003063 -0.8704 82.85a 43.08a 895.86a

Table 5.2 continued.

Data set N Yearly Mean Std.Dev. Skew. Kurt. t-ratio Sharpe Max.loss Q20 Adj Q20 Q20 r2

UK FTSE100 4042 0.0679 0.000261 0.011301 -0.822 14.148 1.47 0.005322 -0.4307 35.65b 17.41 1338.35a

Ireland ISEQ 3250 0.0221 0.000087 0.011081 -0.484 8.459 0.45 -0.008499 -0.3997 21.93 17.89 332.65a

Egypt CMA 1695 0.1205 0.000451 0.007462 0.214 14.211 2.49b 0.036029 -0.3609 196.80a 117.79a 42.62a

Israel TA100 2996 0.0676 0.00026 0.016554 -0.6 9.001 0.86 0.005322 -0.5359 137.64a 91.70a 263.49a

Table 5.3: 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 index 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. The results are computed for an US-based trader who applies the technical trading rule set to the local main stock market indices recomputed in US Dollars. The daily interest rate on 1-month US certificates of deposits is used to compute the Sharpe and excess Sharpe ratio in columns 5 and 6.

Data set Strategy parameters r r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

World MSCI [ MA: 1, 2, 0.000, 0, 0, 0.000] 0.5152 0.3980 0.1461 0.1349 -0.1868 2215 0.748 0.859 1.4453

Argentina Merval [ FR: 0.010, 0, 50, ] 0.2691 0.5789 0.0266 0.0648 -0.6139 61 0.656 0.854 1.4492

Brazil Bovespa [ MA: 1, 5, 0.000, 0, 0, 0.025] 0.4663 0.5036 0.0425 0.0528 -0.5389 455 0.686 0.809 1.1355

Canada TSX Composite [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.3988 0.3347 0.0879 0.0894 -0.4481 1241 0.737 0.850 1.0806

Chile IPSA [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.6768 0.8065 0.1046 0.1396 -0.3578 659 0.707 0.842 1.4096

Mexico IPC [ MA: 1, 2, 0.001, 0, 0, 0.000] 1.1004 0.9829 0.1026 0.1004 -0.3558 556 0.710 0.820 1.5576

Peru Lima General [ MA: 1, 2, 0.001, 0, 0, 0.000] 1.2380 1.0112 0.1447 0.1281 -0.3233 814 0.720 0.846 1.4390

US S&P500 [ FR: 0.005, 0, 0 ] 0.2310 0.1156 0.0434 0.0284 -0.3795 1409 0.725 0.822 1.2534

US DJIA [ MA: 1, 2 0.000, 0, 0, 0.000] 0.2060 0.0791 0.0351 0.0157 -0.4630 2667 0.695 0.795 1.2852

US Nasdaq100 [ MA: 1, 2 0.001, 0, 0, 0.000] 0.3972 0.2543 0.0480 0.0362 -0.8507 1821 0.717 0.821 1.1472

US NYSE Composite [ MA: 1, 2 0.000, 0, 0, 0.000] 0.2630 0.1486 0.0561 0.0410 -0.2849 2543 0.712 0.815 1.3261

US Russel2000 [ MA: 1, 2 0.001, 0, 0, 0.000] 0.5653 0.4423 0.1273 0.1134 -0.2872 989 0.762 0.874 1.1298

US Wilshire5000 [ MA: 1, 2 0.000, 0, 0, 0.000] 0.3202 0.2010 0.0711 0.0539 -0.5005 2115 0.722 0.825 1.2656

Venezuela Industrial [ MA: 1, 2 0.000, 0, 0, 0.000] 1.2107 1.3313 0.0835 0.0963 -0.4630 857 0.704 0.823 1.5636

Australia ASX All Ordinaries [ MA: 1, 2, 0.000, 0, 0, 0.000] 0.2837 0.2470 0.0506 0.0576 -0.4159 1855 0.699 0.814 1.1426

China Shanghai Composite [ FR: 0.005, 2, 0 ] 0.5693 0.3764 0.0558 0.0389 -0.4502 266 0.711 0.824 1.2988

Hong Kong Hang Seng [ MA: 1, 5, 0.000, 0, 0, 0.000] 0.6507 0.5112 0.0870 0.0788 -0.3691 870 0.721 0.858 1.3489

India BSE30 [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.6566 0.7110 0.0775 0.0950 -0.4509 867 0.713 0.844 1.0448

Indonesia Jakarta Composite [ FR: 0.005, 0, 0 ] 1.2643 1.5135 0.0884 0.1109 -0.7013 739 0.747 0.878 0.8928

Table 5.3 continued.

Data set Strategy parameters r r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

Japan Nikkei225 [ MA: 5, 10, 0.000, 4, 0, 0.000] 0.1563 0.1776 0.0184 0.0350 -0.6483 296 0.703 0.802 1.1137

Malaysia KLSE Composite [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.9261 0.8537 0.0988 0.1016 -0.5149 1457 0.725 0.845 1.4378

New Zealand NZSE30 [ MA: 1, 2, 0.000, 0, 0, 0.000] 0.1580 0.1535 0.0269 0.0397 -0.4712 1315 0.687 0.806 1.3303

Pakistan Karachi100 [ FR: 0.005, 0, 0 ] 0.5733 0.6473 0.0676 0.0874 -0.3842 672 0.710 0.841 1.0956

Philippines PSE Composite [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.9814 1.0536 0.1027 0.1214 -0.3457 1348 0.714 0.830 1.4767

Singapore Straits Times [ MA: 1, 2, 0.000, 0, 0, 0.000] 0.7293 0.6537 0.1005 0.1020 -0.4133 1757 0.714 0.833 1.6259

South-Korea Kospi200 [ FR: 0.005, 0, 0 ] 0.8663 0.9385 0.0660 0.0786 -0.4491 710 0.725 0.845 1.3776

Sri Lanka CSE All Share [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.6559 0.7839 0.1287 0.1766 -0.2126 409 0.731 0.868 1.7512

Thailand SET [ MA: 1, 5, 0.000, 0, 0, 0.025] 0.6785 0.9181 0.0718 0.1053 -0.6064 525 0.710 0.844 1.1477

Taiwan TSE Composite [ MA: 1, 10, 0.000, 0, 0, 0.000] 0.3018 0.3928 0.0410 0.0658 -0.3560 242 0.682 0.856 1.4028

Austria ATX [ FR: 0.025, 0, 25 ] 0.1616 0.1582 0.0335 0.0472 -0.2883 151 0.689 0.824 1.0489

Belgium Bel20 [ SR: 10, 0.000, 0, 50, 0.000 ] 0.1525 0.0902 0.0282 0.0237 -0.2711 96 0.740 0.872 1.0449

Czech Republic PX50 [ FR: 0.005, 0, 0 ] 0.5962 0.6293 0.0900 0.1087 -0.3120 477 0.730 0.857 1.2415

Denmark KFX [ FR: 0.005, 0, 5 ] 0.2166 0.1470 0.0401 0.0349 -0.2979 642 0.646 0.701 1.0276

Finland HEX General [ SR: 25, 0.000, 4, 0, 0.000 ] 0.4692 0.2238 0.0524 0.0265 -0.4667 52 0.769 0.866 0.9368

France CAC40 [ MA: 1, 2, 0.000, 0, 0, 0.000] 0.2094 0.1391 0.0344 0.0289 -0.4030 1383 0.694 0.803 1.2673

Germany DAX30 [ MA: 1, 2, 0.000, 0, 10, 0.000] 0.2130 0.1227 0.0326 0.0223 -0.3935 303 0.680 0.821 1.0603

Greece ASE General [ FR: 0.005, 0, 0 ] 0.9309 0.7898 0.0962 0.0901 -0.4239 595 0.726 0.836 1.3280

Italy MIB30 [ MA: 1, 2, 0.000, 0, 50, 0.000] 0.3026 0.2161 0.0473 0.0414 -0.4097 45 0.711 0.854 1.2225

Netherlands AEX [ MA: 5, 25, 0.000, 0, 50, 0.000] 0.1572 0.0657 0.0264 0.0166 -0.5858 124 0.758 0.843 1.0739

Norway OSE All Share [ SR: 5, 0.000, 0, 0, 0.000 ] 0.3418 0.3435 0.0625 0.0771 -0.1751 144 0.757 0.860 1.2095

Portugal PSI General [ MA: 1, 5, 0.000, 0, 0, 0.025] 0.4210 0.3336 0.0817 0.0758 -0.3514 394 0.695 0.844 1.2825

Russia Moscow Times [ FR: 0.005, 0, 0 ] 2.6707 1.9746 0.1142 0.0950 -0.6517 590 0.741 0.859 1.1977

Slovakia SAX16 [ MA: 25, 200, 0.050, 0, 0, 0.000] 0.0857 0.2175 0.0095 0.0512 -0.4280 4 0.750 0.904 1.4098

Spain IGBM [ FR: 0.005, 0, 0 ] 0.2441 0.1473 0.0404 0.0286 -0.3333 793 0.702 0.809 1.2348

Sweden OMX [ FR: 0.010, 0, 0 ] 0.3569 0.2406 0.0466 0.0358 -0.5876 540 0.713 0.827 1.1050

Switzerland SMI [ MA: 1, 5, 0.000, 0, 50, 0.000] 0.2360 0.1127 0.0407 0.0219 -0.5320 111 0.694 0.855 0.8339

Turkey ISE100 [ FR: 0.005, 0, 0 ] 1.3096 1.1419 0.0673 0.0643 -0.8882 1307 0.719 0.832 1.1805

UK FTSE100 [ FR: 0.005, 0, 0 ] 0.1635 0.0895 0.0269 0.0216 -0.3811 1242 0.702 0.814 1.1872

Ireland ISEQ [ MA: 1, 25, 0.000, 0, 50, 0.000] 0.1608 0.1357 0.0284 0.0369 -0.4451 99 0.717 0.832 0.9301

Egypt CMA [ MA: 1, 2, 0.001, 0, 0, 0.000] 0.5158 0.3528 0.1423 0.1063 -0.2460 420 0.698 0.861 1.4805

Israel TA100 [ MA: 2, 5, 0.000, 0, 0, 0.050] 0.2567 0.1771 0.0354 0.0301 -0.4236 612 0.722 0.830 1.1227

Table 5.4: Statistics best strategy: mean return criterion, 0.25% costs. Columns as in table 5.3.

Data set Strategy parameters r r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

World MSCI [ MA: 1, 200, 0.025, 0, 0, 0.000] 0.1492 0.0604 0.0332 0.0221 -0.2591 19 0.842 0.955 1.0955

Argentina Merval [ FR: 0.010, 0, 50 ] 0.2456 0.5501 0.0240 0.0623 -0.6142 61 0.639 0.850 1.4653

Brazil Bovespa [ SR: 20, 0.001, 0, 0, 0.000 ] 0.3899 0.4257 0.0413 0.0517 -0.5308 41 0.659 0.855 1.3801

Canada TSX Composite [ MA: 1, 25, 0.005, 0, 0, 0.000] 0.1578 0.1049 0.0327 0.0342 -0.3146 176 0.341 0.656 1.0849

Chile IPSA [ FR: 0.020, 0, 0 ] 0.2694 0.3680 0.0431 0.0782 -0.4024 188 0.277 0.506 0.9045

Mexico IPC [ MA: 1, 5, 0.000, 0, 0, 0.050] 0.5489 0.4629 0.0606 0.0585 -0.3213 321 0.227 0.384 0.8530

Peru Lima General [ FR: 0.010, 0, 0 ] 0.7477 0.5709 0.0957 0.0793 -0.4778 420 0.224 0.346 1.0951

US S&P500 [ MA: 1, 200, 0.050, 0, 0, 0.000] 0.1617 0.0529 0.0268 0.0118 -0.3268 11 1.000 1.000 NA

US DJIA [ SR: 50, 0.025, 0, 0, 0.000 ] 0.1533 0.0321 0.0311 0.0117 -0.2942 5 0.800 0.969 1.1554

US Nasdaq100 [ MA: 1, 100, 0.025, 0, 0, 0.000] 0.2163 0.0920 0.0286 0.0168 -0.5527 51 0.627 0.875 1.1226

US NYSE Composite [ MA: 2, 5, 0.025, 0, 0, 0.000] 0.1405 0.0373 0.0271 0.0120 -0.2683 11 0.727 0.964 0.7816

US Russel2000 [ SR: 5, 0.010, 0, 0, 0.000 ] 0.2219 0.1261 0.0529 0.0390 -0.3048 88 0.511 0.874 0.6334

US Wilshire5000 [ FR: 0.120, 2, 0 ] 0.1438 0.0406 0.0241 0.0070 -0.5276 14 0.643 0.917 0.8450

Venezuela Industrial [ FR: 0.005, 0, 0 ] 0.4879 0.5696 0.0395 0.0523 -0.6257 581 0.210 0.316 0.7833

Australia ASX All Ordinaries [ FR: 0.020, 0, 50 ] 0.1586 0.1257 0.0245 0.0315 -0.4966 129 0.682 0.729 1.1199

China Shanghai Composite [ FR: 0.005, 3, 0 ] 0.4222 0.2478 0.0424 0.0256 -0.3520 146 0.295 0.567 1.2350

Hong Kong Hang Seng [ MA: 1, 5, 0.005, 0, 0, 0.000] 0.3228 0.2112 0.0434 0.0352 -0.5703 560 0.236 0.442 1.0851

India BSE30 [ SR: 5, 0.000, 0, 50, 0.000 ] 0.1711 0.2099 0.0203 0.0379 -0.6945 83 0.554 0.660 1.0689

Indonesia Jakarta Composite [ FR: 0.005, 0, 0 ] 0.7656 0.9602 0.0594 0.0819 -0.7517 739 0.235 0.395 0.7857

Japan Nikkei225 [ SR: 100, 0.025, 0, 0, 0.000 ] 0.1041 0.1246 0.0140 0.0307 -0.3604 7 1.000 1.000 NA

Malaysia KLSE Composite [ FR: 0.010, 0, 0 ] 0.4358 0.3821 0.0496 0.0524 -0.5651 760 0.249 0.421 0.9173

New Zealand NZSE30 [ MA: 10, 25, 0.050, 0, 0, 0.000] 0.1077 0.1036 0.0161 0.0290 -0.4231 4 1.000 1.000 NA

Pakistan Karachi100 [ SR: 5, 0.010, 0, 0, 0.000 ] 0.3336 0.3967 0.0421 0.0619 -0.4130 128 0.406 0.623 1.0918

Philippines PSE Composite [ FR: 0.010, 0, 0 ] 0.4644 0.5180 0.0535 0.0723 -0.4586 760 0.224 0.372 1.0759

Singapore Straits Times [ FR: 0.025, 0, 0 ] 0.2639 0.2089 0.0374 0.0389 -0.5301 312 0.282 0.521 0.7085

South-Korea Kospi200 [ MA: 1, 25, 0.000, 0, 0, 0.000] 0.3863 0.4403 0.0402 0.0528 -0.5323 164 0.262 0.660 1.3717

Sri Lanka CSE All Share [ FR: 0.015, 0, 0 ] 0.3138 0.4158 0.0621 0.1102 -0.2045 133 0.338 0.564 1.1930

Thailand SET [ SR: 25, 0.000, 0, 0, 0.000 ] 0.3706 0.5666 0.0482 0.0819 -0.4167 41 0.659 0.866 1.4849

Taiwan TSE Composite [ MA: 1, 25, 0.000, 0, 0, 0.075] 0.1783 0.2611 0.0224 0.0473 -0.5332 151 0.245 0.608 0.9980

Austria ATX [ FR: 0.025, 0, 25 ] 0.1209 0.1179 0.0224 0.0362 -0.2883 151 0.464 0.503 1.1183

Belgium Bel20 [ SR: 10, 0.000, 0, 50, 0.000 ] 0.1292 0.0684 0.0224 0.0180 -0.2831 96 0.708 0.830 1.0036

Czech Republic PX50 [ FR: 0.030, 0, 0 ] 0.2908 0.3181 0.0445 0.0634 -0.4742 124 0.331 0.611 0.8085

Denmark KFX [ SR: 150, 0.025, 0, 0, 0.000 ] 0.1107 0.0474 0.0213 0.0161 -0.3159 3 1.000 1.000 NA

Finland HEX General [ SR: 25, 0.000, 4, 0, 0.000 ] 0.4302 0.1916 0.0482 0.0224 -0.4821 52 0.500 0.750 1.1126

Table 5.4 continued.

Data set Strategy parameters r r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

France CAC40 [ FR: 0.300, 4, 0 ] 0.1111 0.0468 0.0129 0.0075 -0.4289 2 1.000 1.000 NA

Germany DAX30 [ FR: 0.180, 3, 0 ] 0.1550 0.0693 0.0218 0.0116 -0.3575 9 0.889 0.967 0.7431

Greece ASE General [ FR: 0.020, 0, 0 ] 0.4924 0.3839 0.0567 0.0507 -0.5695 255 0.212 0.330 0.9890

Italy MIB30 [ MA: 1, 2, 0.000, 0, 50, 0.000] 0.2771 0.1928 0.0430 0.0372 -0.4299 45 0.644 0.781 1.2051

Netherlands AEX [ SR: 25, 0.050, 0, 0, 0.000 ] 0.1440 0.0538 0.0233 0.0136 -0.3882 4 0.750 0.949 0.9584

Norway OSE All Share [ FR: 0.040, 3, 0 ] 0.2513 0.2534 0.0415 0.0562 -0.3115 52 0.519 0.768 0.9366

Portugal PSI General [ FR: 0.080, 3, 0 ] 0.3020 0.2224 0.0565 0.0507 -0.2312 20 0.650 0.906 1.1021

Russia Moscow Times [ MA: 1, 5, 0.000, 0, 0, 0.000] 1.9105 1.3593 0.0947 0.0755 -0.7254 366 0.249 0.433 0.8564

Slovakia SAX16 [ MA: 25, 200, 0.050, 0, 0, 0.000] 0.0839 0.2159 0.0090 0.0508 -0.4328 4 0.750 0.904 1.4098

Spain IGBM [ FR: 0.040, 0, 50 ] 0.2021 0.1089 0.0365 0.0249 -0.4048 69 0.696 0.725 0.9860

Sweden OMX [ MA: 25, 200, 0.050, 0, 0, 0.000] 0.2768 0.1677 0.0451 0.0344 -0.3288 4 1.000 1.000 NA

Switzerland SMI [ MA: 1, 5, 0.000, 0, 50, 0.000] 0.2094 0.0890 0.0353 0.0166 -0.5344 111 0.640 0.775 0.8875

Turkey ISE100 [ SR: 15, 0.000, 0, 0, 0.000 ] 0.7537 0.6267 0.0531 0.0501 -0.7020 113 0.522 0.746 1.2321

UK FTSE100 [ MA: 10, 25, 0.050, 0, 0, 0.000] 0.1152 0.0445 0.0133 0.0081 -0.5638 4 1.000 1.000 NA

Ireland ISEQ [ MA: 1, 25, 0.000, 0, 50, 0.000] 0.1384 0.1140 0.0231 0.0316 -0.4578 99 0.687 0.778 0.8604

Egypt CMA [ FR: 0.015, 0, 0 ] 0.3421 0.1983 0.0931 0.0573 -0.3240 99 0.263 0.543 1.0064

Israel TA100 [ MA: 10, 200, 0.001, 0, 0, 0.000] 0.2048 0.1288 0.0254 0.0201 -0.3815 21 0.619 0.887 1.4522

Table 5.5: 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 index listed in the first column. The results are computed for an US-based trader who applies the technical trading rule set to the local main stock market indices recomputed in US Dollars. Column 2 shows the parameters of the best strategy. 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 (here the daily interest rate on 1-month US certificates of deposits is used in the computations). 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. Results are only shown for those indices 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 r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

Brazil Bovespa [ SR: 20, 0.001, 0, 0, 0.000 ] 0.4294 0.4657 0.0454 0.0558 -0.5075 41 0.829 0.916 1.3860

US DJIA [ FR: 0.005, 0, 0 ] 0.2014 0.0750 0.0357 0.0163 -0.3194 1459 0.714 0.815 1.2992

US Wilshire5000 [ FR: 0.005, 0, 0 ] 0.3188 0.1997 0.0722 0.0550 -0.2372 1039 0.736 0.840 1.2514

Belgium Bel20 [ MA: 2, 5, 0.000, 0, 10, 0.000] 0.1522 0.0899 0.0283 0.0239 -0.4269 393 0.634 0.717 1.0197

Table 5.5 continued.

0% costs per trade

Data set Strategy parameters r r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

Finland HEX General [ SR: 200, 0.000, 4, 0, 0.000 ] 0.3828 0.1518 0.0544 0.0285 -0.3823 3 1.000 1.000 NA

Netherlands AEX [ FR: 0.045, 0, 50 ] 0.1557 0.0643 0.0317 0.0220 -0.3998 113 0.735 0.884 1.0743

Portugal PSI General [ MA: 1, 2, 0.025, 0, 0, 0.000] 0.2202 0.1452 0.0835 0.0776 -0.1735 4 1.000 1.000 NA

Russia Moscow Times [ MA: 1, 5, 0.000, 0, 0, 0.000] 2.6618 1.9674 0.1168 0.0976 -0.7031 366 0.754 0.878 1.2155

Spain IGBM [ FR: 0.045, 0, 50 ] 0.2230 0.1279 0.0434 0.0317 -0.3896 73 0.712 0.809 1.0747

UK FTSE100 [ MA: 1, 25, 0.000, 0, 10, 0.000] 0.1457 0.0729 0.0269 0.0216 -0.3111 343 0.665 0.678 0.9716

0.25% costs per trade

Data set Strategy parameters r r^e S S^e ML # tr. %tr.>0 %d > 0 SDR

World MSCI [ MA: 1, 10, 0.050, 0, 0, 0.000] 0.1252 0.0383 0.0345 0.0234 -0.2156 5 0.800 0.969 1.1816

US S&P500 [ SR: 50, 0.025, 0, 0, 0.000 ] 0.1466 0.0392 0.0289 0.0139 -0.2767 5 0.800 0.969 1.0532

US Nasdaq100 [ SR: 100, 0.025, 0, 0, 0.000 ] 0.2117 0.0878 0.0331 0.0213 -0.4633 5 0.800 0.919 1.3541

US Wilshire5000 [ FR: 0.100, 0, 50 ] 0.1357 0.0333 0.0338 0.0167 -0.2969 30 0.700 0.885 0.7503

Australia ASX All Ordinaries [ MA: 5, 10, 0.000, 0, 25, 0.000] 0.1439 0.1114 0.0268 0.0338 -0.3663 227 0.546 0.591 1.1789

Hong Kong Hang Seng [ MA: 1, 10, 0.000, 0, 0, 0.100] 0.3179 0.2067 0.0440 0.0358 -0.4383 526 0.202 0.443 1.0970

India BSE30 [ MA: 2, 100, 0.010, 0, 0, 0.000] 0.1596 0.1980 0.0214 0.0390 -0.5671 29 0.655 0.918 0.9743

Japan Nikkei225 [ SR: 100, 0.050, 0, 0, 0.000 ] 0.0781 0.0981 0.0165 0.0332 -0.1883 2 1.000 1.000 NA

Malaysia KLSE Composite [ MA: 5, 50, 0.001, 0, 0, 0.000] 0.3780 0.3264 0.0573 0.0602 -0.3697 87 0.552 0.885 1.6523

New Zealand NZSE30 [ MA: 2, 10, 0.050, 0, 0, 0.000] 0.1021 0.0981 0.0207 0.0336 -0.4231 4 1.000 1.000 NA

Singapore Straits Times [ SR: 15, 0.010, 0, 0, 0.000 ] 0.2570 0.2023 0.0430 0.0445 -0.5026 76 0.618 0.847 1.1832

Czech Republic PX50 [ MA: 1, 25, 0.010, 0, 0, 0.000] 0.2763 0.3033 0.0460 0.0649 -0.4318 61 0.426 0.776 1.1062

Finland HEX General [ SR: 200, 0.000, 4, 0, 0.000 ] 0.3815 0.1511 0.0542 0.0283 -0.3823 3 1.000 1.000 NA

France CAC40 [ MA: 10, 25, 0.000, 0, 50, 0.000] 0.1057 0.0417 0.0148 0.0094 -0.5647 86 0.674 0.816 0.9545

Germany DAX30 [ MA: 5, 50, 0.000, 0, 50, 0.000] 0.1354 0.0512 0.0242 0.0140 -0.4855 62 0.710 0.794 0.9216

Netherlands AEX [ FR: 0.045, 0, 50 ] 0.1358 0.0461 0.0258 0.0161 -0.4028 113 0.717 0.860 1.0887

Norway OSE All Share [ MA: 1, 2, 0.000, 4, 0, 0.000] 0.2392 0.2413 0.0450 0.0598 -0.3157 48 0.583 0.839 1.2401

Portugal PSI General [ MA: 1, 2, 0.025, 0, 0, 0.000] 0.2181 0.1436 0.0823 0.0766 -0.1777 4 0.750 0.999 NA

Russia Moscow Times [ SR: 10, 0.001, 0, 0, 0.000 ] 1.6640 1.1596 0.0957 0.0765 -0.4612 83 0.422 0.700 1.1650

Spain IGBM [ FR: 0.045, 0, 50 ] 0.2006 0.1075 0.0383 0.0266 -0.3927 73 0.671 0.764 1.0464

UK FTSE100 [ SR: 100, 0.025, 0, 0, 0.000 ] 0.1067 0.0365 0.0224 0.0171 -0.2905 4 1.000 1.000 NA

Egypt CMA [ SR: 25, 0.010, 0, 0, 0.000 ] 0.3285 0.1861 0.1138 0.0780 -0.1512 11 0.818 0.946 1.0548

Table 5.6: 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 index 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 index listed in the first column. The row labeled ``Average 3'' at the bottom of the table shows for trading case 3 the average over the results as shown in the table for each transaction costs case. The rows labeled ``Average 1'' and ``Average 2'' show the average over the results for the two other trading cases 1 and 2.

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%

World MSCI 0.3980 0.2201 0.0604 0.0562 0.0519 0.0500 0.1349 0.0779 0.0234 0.0229 0.0223 0.0218

Argentina Merval 0.5789 0.5673 0.5501 0.5218 0.4939 0.4665 0.0648 0.0638 0.0623 0.0597 0.0572 0.0546

Brazil Bovespa 0.5036 0.4496 0.4257 0.3867 0.3487 0.3132 0.0558 0.0541 0.0517 0.0475 0.0434 0.0393

Canada TSX Composite 0.3347 0.1817 0.1049 0.0494 0.0474 0.0453 0.0894 0.0518 0.0342 0.0236 0.0231 0.0226

Chile IPSA 0.8065 0.5672 0.3680 0.2518 0.2085 0.1666 0.1396 0.1074 0.0782 0.0619 0.0527 0.0435

Mexico IPC 0.9829 0.7003 0.4629 0.3220 0.2928 0.2643 0.1004 0.0824 0.0585 0.0451 0.0413 0.0375

Peru Lima General 1.0112 0.7629 0.5709 0.3279 0.2788 0.2504 0.1281 0.1023 0.0793 0.0535 0.0486 0.0436

US S&P500 0.1156 0.0543 0.0529 0.0506 0.0484 0.0461 0.0284 0.0141 0.0139 0.0136 0.0133 0.0130

US DJIA 0.0791 0.0394 0.0321 0.0313 0.0306 0.0298 0.0163 0.0119 0.0117 0.0114 0.0111 0.0108

US Nasdaq100 0.2543 0.1076 0.0920 0.0869 0.0859 0.0850 0.0362 0.0215 0.0213 0.0211 0.0208 0.0206

US NYSE Composite 0.1486 0.0386 0.0373 0.0350 0.0327 0.0305 0.0410 0.0125 0.0120 0.0111 0.0103 0.0094

US Russel2000 0.4423 0.2773 0.1261 0.0916 0.0721 0.0602 0.1134 0.0736 0.0390 0.0306 0.0255 0.0224

US Wilshire5000 0.2010 0.0813 0.0406 0.0371 0.0363 0.0356 0.0550 0.0211 0.0167 0.0149 0.0130 0.0121

Venezuela Industrial 1.3313 0.9638 0.5696 0.1866 0.1059 0.1063 0.0963 0.0768 0.0523 0.0204 0.0129 0.0129

Australia ASX All Ordinaries 0.2470 0.1393 0.1257 0.1032 0.0811 0.0594 0.0576 0.0408 0.0338 0.0264 0.0239 0.0236

China Shanghai Composite 0.3764 0.3190 0.2478 0.1440 0.1258 0.1078 0.0389 0.0333 0.0256 0.0186 0.0160 0.0134

Hong Kong Hang Seng 0.5112 0.3756 0.2112 0.1142 0.0934 0.0734 0.0788 0.0602 0.0358 0.0250 0.0211 0.0188

India BSE30 0.7110 0.4822 0.2099 0.1845 0.1658 0.1500 0.0950 0.0706 0.0390 0.0362 0.0334 0.0306

Indonesia Jakarta Composite 1.5135 1.2757 0.9602 0.6410 0.5394 0.4962 0.1109 0.0993 0.0819 0.0754 0.0715 0.0675

Japan Nikkei225 0.1776 0.1351 0.1246 0.1229 0.1211 0.1194 0.0350 0.0333 0.0332 0.0331 0.0329 0.0327

Malaysia KLSE Composite 0.8537 0.6284 0.3821 0.3049 0.2774 0.2682 0.1016 0.0799 0.0602 0.0549 0.0497 0.0460

New Zealand NZSE30 0.1535 0.1052 0.1036 0.1020 0.1004 0.0988 0.0397 0.0339 0.0336 0.0330 0.0324 0.0319

Pakistan Karachi100 0.6473 0.4944 0.3967 0.3145 0.2778 0.2420 0.0874 0.0741 0.0619 0.0533 0.0481 0.0428

Philippines PSE Composite 1.0536 0.7989 0.5180 0.3372 0.3025 0.2687 0.1214 0.0994 0.0723 0.0586 0.0533 0.0481

Singapore Straits Times 0.6537 0.3933 0.2089 0.1779 0.1621 0.1465 0.1020 0.0719 0.0445 0.0394 0.0361 0.0328

South-Korea Kospi200 0.9385 0.6940 0.4403 0.3241 0.3092 0.3064 0.0786 0.0630 0.0528 0.0465 0.0461 0.0457

Sri Lanka CSE All Share 0.7839 0.6097 0.4158 0.2913 0.2321 0.2111 0.1766 0.1469 0.1102 0.0844 0.0735 0.0685

Table 5.6 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%

Thailand SET 0.9181 0.7545 0.5666 0.5360 0.5058 0.4762 0.1053 0.0916 0.0819 0.0783 0.0747 0.0711

Taiwan TSE Composite 0.3928 0.3280 0.2611 0.2243 0.2206 0.2168 0.0658 0.0573 0.0473 0.0428 0.0421 0.0415

Austria ATX 0.1582 0.1419 0.1179 0.0789 0.0515 0.0414 0.0472 0.0428 0.0362 0.0251 0.0170 0.0140

Belgium Bel20 0.0902 0.0814 0.0684 0.0504 0.0494 0.0488 0.0239 0.0214 0.0180 0.0156 0.0151 0.0146

Czech Republic PX50 0.6293 0.4446 0.3181 0.2626 0.2325 0.2030 0.1087 0.0825 0.0649 0.0581 0.0523 0.0466

Denmark KFX 0.1470 0.0805 0.0474 0.0468 0.0463 0.0457 0.0349 0.0192 0.0161 0.0159 0.0157 0.0156

Finland HEX General 0.2238 0.2108 0.1916 0.1747 0.1656 0.1565 0.0285 0.0284 0.0283 0.0282 0.0281 0.0280

France CAC40 0.1391 0.0595 0.0468 0.0461 0.0455 0.0449 0.0289 0.0123 0.0094 0.0074 0.0073 0.0072

Germany DAX30 0.1227 0.0861 0.0693 0.0653 0.0613 0.0574 0.0223 0.0164 0.0140 0.0138 0.0136 0.0135

Greece ASE General 0.7898 0.5638 0.3839 0.1966 0.1939 0.1912 0.0901 0.0694 0.0507 0.0308 0.0282 0.0265

Italy MIB30 0.2161 0.2067 0.1928 0.1839 0.1805 0.1771 0.0414 0.0397 0.0372 0.0329 0.0325 0.0322

Netherlands AEX 0.0657 0.0576 0.0538 0.0530 0.0523 0.0515 0.0220 0.0196 0.0161 0.0134 0.0132 0.0130

Norway OSE All Share 0.3435 0.2873 0.2534 0.1987 0.1582 0.1349 0.0771 0.0665 0.0598 0.0522 0.0458 0.0393

Portugal PSI General 0.3336 0.2633 0.2224 0.2068 0.1915 0.1762 0.0776 0.0772 0.0766 0.0755 0.0745 0.0734

Russia Moscow Times 1.9746 1.7075 1.3593 1.0428 0.9321 0.8271 0.0976 0.0887 0.0765 0.0706 0.0647 0.0587

Slovakia SAX16 0.2175 0.2168 0.2159 0.2143 0.2126 0.2110 0.0512 0.0510 0.0508 0.0504 0.0501 0.0497

Spain IGBM 0.1473 0.1201 0.1089 0.0904 0.0722 0.0542 0.0317 0.0297 0.0266 0.0216 0.0165 0.0116

Sweden OMX 0.2406 0.1690 0.1677 0.1656 0.1634 0.1613 0.0358 0.0346 0.0344 0.0340 0.0336 0.0332

Switzerland SMI 0.1127 0.1031 0.0890 0.0657 0.0616 0.0596 0.0219 0.0197 0.0166 0.0112 0.0092 0.0091

Turkey ISE100 1.1419 0.8497 0.6267 0.5642 0.5040 0.4459 0.0643 0.0540 0.0501 0.0459 0.0417 0.0375

UK FTSE100 0.0895 0.0544 0.0445 0.0433 0.0422 0.0411 0.0216 0.0173 0.0171 0.0168 0.0164 0.0160

Ireland ISEQ 0.1357 0.1269 0.1140 0.0926 0.0716 0.0629 0.0369 0.0348 0.0316 0.0263 0.0228 0.0205

Egypt CMA 0.3528 0.2564 0.1983 0.1801 0.1773 0.1745 0.1063 0.0800 0.0780 0.0746 0.0712 0.0676

Israel TA100 0.1771 0.1341 0.1288 0.1198 0.1109 0.1021 0.0301 0.0210 0.0201 0.0187 0.0174 0.0164

Average 3 0.4914 0.3709 0.2725 0.2089 0.1875 0.1722 0.0672 0.0535 0.0435 0.0372 0.0343 0.0320

Average 1 0.5391 0.3935 0.2759 0.1984 0.1656 0.1470 0.0801 0.0599 0.0462 0.0379 0.0339 0.0315

Average 2 0.5764 0.4238 0.2994 0.2142 0.1862 0.1710 0.0769 0.0578 0.0451 0.0376 0.0342 0.0317

Table 5.7: Estimation results CAPM. Coefficient estimates of the Sharpe-Lintner CAPM: r_tⁱ-r_t^f=a + b (r_t^Local-r_t^f) + e_t. That is, the return in US Dollars of the best recursive optimizing and testing procedure, when selection in the optimizing period is done by the mean return criterion (Panel A) or by the Sharpe ratio criterion (Panel B), in excess of the US risk-free interest rate is regressed against a constant and the return of the local main stock market index in US Dollars in excess of the US risk-free interest rate. Estimation results for the 0 and 0.10% 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

World MSCI 0.001342a 0.850c 0.000223b 0.913 0.001342a 0.850c 0.000188b 0.506a

Argentina Merval 0.001297a 0.509a 0.001148b 0.508a 0.001297a 0.509a 0.001148b 0.508a

Brazil Bovespa 0.001558a 0.749a 0.001163b 0.546a 0.001386a 0.547a 0.001163b 0.546a

Canada TSX Composite 0.001144a 0.878 0.000193 1.087 0.001144a 0.878 0.000157 0.322a

Chile IPSA 0.002290a 0.878c 0.000715b 0.640a 0.002290a 0.878c 0.000715b 0.640a

Mexico IPC 0.002716a 0.849b 0.001140b 0.714a 0.002716a 0.849b 0.001140b 0.714a

Peru Lima General 0.002781a 0.973 0.001146a 0.913 0.002781a 0.973 0.001101a 0.853c

US S&P500 0.000454a 0.875 0.000199c 0.975 0.000454a 0.875 0.000202c 0.662a

US DJIA 0.000315b 0.94 0.000201c 0.616a 0.000316b 0.859 0.000201c 0.616a

US Nasdaq100 0.000930a 0.860a 0.000407b 0.627a 0.000930a 0.860a 0.000407b 0.627a

US NYSE Composite 0.000567a 0.876 0.000169 0.770b 0.000567a 0.876 0.000169 0.770b

US Russel2000 0.001471a 0.873a 0.000386b 0.726a 0.001471a 0.873a 0.000380b 0.609a

US Wilshire5000 0.000752a 0.849c 0.000111 1.206a 0.000753a 0.821b 0.000161c 0.721a

Venezuela Industrial 0.003238a 0.691 0.000598 0.801 0.003238a 0.691 0.000588 0.778

Australia ASX All Ordinaries 0.000861a 0.832 0.000378c 0.87 0.000861a 0.832 0.000378c 0.87

China Shanghai Composite 0.001238a 1.127 0.000565 0.932 0.001238a 1.127 0.000565 0.932

Hong Kong Hang Seng 0.001691a 0.655a 0.000412 1.126 0.001691a 0.655a 0.000428b 0.641a

India BSE30 0.002126a 0.98 0.000641c 0.891 0.002126a 0.98 0.000576c 0.715a

Indonesia Jakarta Composite 0.003589a 0.882 0.001850a 0.808b 0.003589a 0.882 0.001384a 0.392a

Japan Nikkei225 0.000592b 0.793a 0.000295c 0.397a 0.000592b 0.793a 0.000134 0.130a

Malaysia KLSE Composite 0.002452a 0.925 0.001033a 0.651a 0.002452a 0.925 0.000997a 0.564a

New Zealand NZSE30 0.000542a 0.855b 0.000367c 0.886 0.000542a 0.855b 0.000275 0.414a

Pakistan Karachi100 0.001950a 0.925 0.001005a 0.791b 0.001950a 0.925 0.001005a 0.791b

Philippines PSE Composite 0.002842a 0.958 0.001052a 0.697a 0.002842a 0.958 0.001052a 0.697a

Singapore Straits Times 0.001990a 0.844c 0.000648a 0.633a 0.001990a 0.844c 0.000648a 0.633a

Table 5.7 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

South-Korea Kospi200 0.002608a 0.929 0.000986b 0.622a 0.002608a 0.929 0.000897b 0.457a

Sri Lanka CSE All Share 0.002336a 1.078 0.001062a 1.103 0.002336a 1.078 0.001062a 1.103

Thailand SET 0.002512a 0.893c 0.001469a 0.666a 0.002512a 0.893c 0.001469a 0.666a

Taiwan TSE Composite 0.001197a 0.700a 0.000640c 0.663a 0.001197a 0.700a 0.000640c 0.663a

Austria ATX 0.000540a 0.727a 0.000256 0.723a 0.000540a 0.727a 0.000256 0.723a

Belgium Bel20 0.000348b 0.882 0.000204 0.824b 0.000343c 0.916 0.000203 0.710a

Czech Republic PX50 0.001914a 0.897b 0.000856b 0.756a 0.001914a 0.897b 0.000856b 0.756a

Denmark KFX 0.000550a 0.978 0.000205 0.565a 0.000550a 0.978 0.000205 0.565a

Finland HEX General 0.000906b 0.805b 0.000712b 0.865c 0.000696a 0.754a 0.000691a 0.754a

France CAC40 0.000521b 0.921c 0.000152 1.404a 0.000521b 0.921c 0.000152 1.404a

Germany DAX30 0.000462b 0.949 0.000237 1.086 0.000462b 0.949 0.000251 0.782a

Greece ASE General 0.002340a 0.896c 0.000722b 1.062 0.002340a 0.896c 0.000673c 0.771a

Italy MIB30 0.000815b 0.764a 0.000658b 0.966 0.000815b 0.764a 0.000664c 0.763a

Netherlands AEX 0.000287c 0.729a 0.000231 0.794a 0.000307b 0.526a 0.000231 0.794a

Norway OSE All Share 0.001125a 0.782b 0.000704b 0.927 0.001125a 0.782b 0.000580b 0.554a

Portugal PSI General 0.001151a 0.831b 0.000751a 0.936 0.000585a 0.288a 0.000574a 0.286a

Russia Moscow Times 0.004420a 0.877c 0.003003a 0.755a 0.004426a 0.851c 0.003003a 0.755a

Slovakia SAX16 0.000461c 0.507a 0.000448c 0.507a 0.000461c 0.507a 0.000448c 0.507a

Spain IGBM 0.000560b 0.924c 0.000365c 0.832b 0.000516b 0.764a 0.000373c 0.764a

Sweden OMX 0.000878a 0.943 0.000637b 0.760a 0.000878a 0.943 0.000637b 0.760a

Switzerland SMI 0.000450b 0.89 0.000281 0.887 0.000450b 0.89 0.000281 0.887

Turkey ISE100 0.003030a 0.921c 0.001810a 0.685a 0.003030a 0.921c 0.001810a 0.685a

UK FTSE100 0.000348b 0.879c 0.000156 1.221a 0.000287b 0.872 0.000175 0.407a

Ireland ISEQ 0.000502a 0.958 0.000350b 0.957 0.000502a 0.958 0.000350b 0.957

Egypt CMA 0.001202a 1.003 0.000674a 0.939 0.001202a 1.003 0.000721a 0.721a

Israel TA100 0.000667b 0.806a 0.000439c 1.067 0.000667b 0.806a 0.000439c 1.067

Table 5.8: Testing for predictive ability. Nominal (p_n), White's (2000) Reality Check (p_W) and Hansen's (2001) Superior Predictive Ability test (p_H) 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 0.25% costs per trade. The results are computed for an US-based trader who applies the technical trading rule set to the local main stock market indices recomputed in US Dollars.

Panel A Panel B

selection criterion Mean return Sharpe ratio

costs per trade 0% 0.25% 0% 0.25%

Data set p_n p_W p_H p_n p_W p_H p_n p_W p_H p_n p_W p_H

World MSCI 0 0 0 0 0.96 0.37 0 0 0 0.04 0.98 0.33

Argentina Merval 0 1 0.88 0 1 0.91 0 0.11 0.08 0 0.12 0.08

Brazil Bovespa 0 1 0.85 0 1 0.95 0 0.39 0.11 0 0.52 0.11

Canada TSX Composite 0 0 0 0 0.81 0.14 0 0 0 0 0.59 0.21

Chile IPSA 0 0.36 0 0 0.6 0.38 0 0 0 0 0.22 0.01

Mexico IPC 0 1 0.01 0 1 0.8 0 0.04 0 0 0.81 0.08

Peru Lima General 0 0 0 0 0.01 0 0 0 0 0 0.02 0

US S&P500 0 0.97 0.08 0 1 0.87 0 1 0.1 0.02 1 0.46

US DJIA 0 1 0.66 0.01 1 0.99 0 1 0.61 0.02 1 0.52

US Nasdaq100 0 1 0.44 0 1 1 0 0.86 0.02 0 1 0.3

US NYSE Composite 0 0.28 0.02 0 1 0.98 0 0.45 0.04 0.03 1 0.64

US Russel2000 0 0 0 0 0.94 0.02 0 0 0 0 0.86 0.04

US Wilshire5000 0 0.02 0 0.01 1 0.78 0 0.04 0 0 1 0.48

Venezuela Industrial 0 1 0.04 0 1 0.94 0 0 0 0 0.38 0.09

Australia ASX All Ordinaries 0 0.94 0.06 0 1 0.98 0 0.03 0.01 0 0.75 0.11

China Shanghai Composite 0 0.5 0.03 0 0.98 0.12 0 0.82 0.07 0 1 0.26

Hong Kong Hang Seng 0 0 0 0 0.83 0.81 0 0 0 0 0.58 0.06

India BSE30 0 1 0 0 1 0.79 0 0 0 0 0.88 0.18

Indonesia Jakarta Composite 0 1 0 0 1 0.11 0 0 0 0 0.02 0

Japan Nikkei225 0 0.97 0.57 0 1 0.8 0 0.63 0.08 0 0.7 0.08

Malaysia KLSE Composite 0 1 0 0 1 0.21 0 0 0 0 0.03 0.01

New Zealand NZSE30 0 0.99 0.68 0 1 0.92 0 0.78 0.24 0 0.96 0.29

Pakistan Karachi100 0 1 0 0 1 0.18 0 0.04 0 0 0.2 0.06

Philippines PSE Composite 0 0.92 0 0 0.93 0.08 0 0 0 0 0.02 0

Singapore Straits Times 0 0.99 0 0 1 0.82 0 0 0 0 0.22 0.03

South-Korea Kospi200 0 1 0.08 0 1 0.92 0 0.04 0 0 0.49 0.06

Table 5.8 continued.

Panel A Panel B

Selection criterion Mean return Sharpe ratio

costs per trade 0% 0.25% 0% 0.25%

Data set p_n p_W p_H p_n p_W p_H p_n p_W p_H p_n p_W p_H

Sri Lanka CSE All Share 0 0 0 0 0.05 0 0 0 0 0 0.05 0

Thailand SET 0 1 0.1 0 1 0.47 0 0 0 0 0.02 0

Taiwan TSE Composite 0 1 0.62 0 1 0.88 0 0.27 0.03 0 0.86 0.26

Austria ATX 0 0.98 0.86 0 1 0.95 0 0.42 0.03 0 0.91 0.13

Belgium Bel20 0 1 0.91 0 1 0.92 0 1 0.56 0 1 0.57

Czech Republic PX50 0 0.24 0.24 0 0.93 0.83 0 0.05 0 0 0.65 0.25

Denmark KFX 0 0.95 0.1 0 1 0.9 0 0.91 0.04 0 1 0.54

Finland HEX General 0 1 0.94 0 1 0.96 0 1 0.48 0 1 0.4

France CAC40 0 1 0.43 0 1 1 0 1 0.18 0 1 0.97

Germany DAX30 0 1 0.96 0 1 1 0 1 0.72 0 1 0.91

Greece ASE General 0 0.89 0.06 0 0.96 0.64 0 0 0 0 0.5 0.02

Italy MIB30 0 0.99 0.73 0 1 0.8 0 0.98 0.14 0 1 0.1

Netherlands AEX 0 1 1 0 1 0.96 0 1 0.45 0 1 0.48

Norway OSE All Share 0 0.12 0 0 0.65 0.07 0 0.08 0.01 0 0.41 0.1

Portugal PSI General 0 0.98 0.1 0 1 0.37 0 0.28 0.02 0 0.27 0.02

Russia Moscow Times 0 1 0.12 0 1 0.24 0 0.18 0 0 0.53 0.01

Slovakia SAX16 0 1 0.56 0 1 0.53 0 0.51 0.22 0 0.51 0.18

Spain IGBM 0 1 0.3 0 1 0.36 0 1 0.24 0 1 0.29

Sweden OMX 0 1 0.6 0 1 0.85 0 1 0.24 0 1 0.2

Switzerland SMI 0 1 0.39 0 1 0.27 0 1 0.28 0 1 0.32

Turkey ISE100 0 1 0.13 0 1 0.62 0 0.02 0 0 0.1 0.01

UK FTSE100 0 1 0.64 0 1 0.91 0 1 0.55 0 1 0.47

Ireland ISEQ 0 0.77 0.45 0 0.94 0.67 0 0.7 0.21 0 0.89 0.25

Egypt CMA 0 0.02 0 0 0.51 0 0 0.05 0 0 0.34 0

Israel TA100 0 1 0.83 0 1 0.96 0 0.99 0.29 0 1 0.55

Table 5.13: Statistics best out-of-sample testing procedure: mean return criterion, 0.25% costs. Statistics of the best recursively optimizing and testing procedure applied to the local main stock market indices listed in the first column in the case of 0.25% costs per trade. The best strategy in the optimizing period is selected on the basis of the mean return criterion. Column 2 shows the sample period. Column 3 shows the parameters: [length optimizing period, length testing period]. Columns 4 and 5 show the mean return and excess mean return on a yearly basis in %/100 terms. Columns 6 and 7 show the Sharpe and excess Sharpe ratio. Column 8 shows the largest cumulative loss in %/100 terms. Columns 9, 10 and 11 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. The results are computed for an US-based trader who applies the technical trading rule set to the local main stock market indices recomputed in US Dollars.

Data set Period Parameters r r^e S S^e ML # tr %tr>0 %d>0 SDR

World MSCI 12/21/82 - 6/28/02 [ 252, 63 ] 0.50 0.1113 0.0493 0.0368 -0.2368 736 0.308 0.582 0.9429

Argentina Merval 7/19/95 - 6/28/02 [ 252, 21 ] 0.0095 0.2099 -0.0044 0.0350 -0.6802 211 0.308 0.518 0.9341

Brazil Bovespa 9/25/96 - 6/28/02 [ 5, 1 ] 0.2457 0.3229 0.0208 0.0383 -0.5796 594 0.279 0.356 0.7282

Canada TSX Composite 12/21/87 - 6/28/02 [ 252, 126 ] 0.1715 0.1262 0.0331 0.0355 -0.4191 443 0.307 0.693 1.0272

Chile IPSA 12/20/95 - 6/28/02 [ 252, 1 ] 0.3501 0.4332 0.0615 0.1017 -0.2851 300 0.253 0.488 1.1244

Mexico IPC 1/16/98 - 6/28/02 [ 252, 63 ] 0.5145 0.4800 0.0500 0.0521 -0.4411 300 0.197 0.377 1.0408

Peru Lima General 6/16/93 - 6/28/02 [ 252, 10 ] 0.4885 0.4786 0.0730 0.0827 -0.5448 383 0.261 0.517 1.0024

US S&P500 12/21/82 - 6/28/02 [ 126, 42 ] 0.0593 -0.0436 0.0003 -0.0157 -0.3877 426 0.392 0.565 1.0668

US DJIA 12/21/82 - 6/28/02 [ 252, 42 ] 0.1048 -0.0111 0.0124 -0.0076 -0.3744 358 0.466 0.678 1.1000

US Nasdaq100 12/19/84 - 6/28/02 [ 252, 126 ] 0.0811 -0.0524 0.0037 -0.0123 -0.9658 393 0.344 0.602 1.0298

US NYSE Composite 12/21/82 - 6/28/02 [ 126, 63 ] 0.0770 -0.0222 0.0059 -0.0105 -0.3294 390 0.405 0.604 0.8420

US Russel2000 12/20/89 - 6/28/02 [ 21, 1 ] 0.2418 0.1581 0.0541 0.0401 -0.3691 784 0.337 0.472 0.7052

US Wilshire5000 12/18/85 - 6/28/02 [ 63, 10 ] 0.0384 -0.0512 -0.0044 -0.0182 -0.6333 485 0.363 0.536 1.0589

Venezuela Industrial 12/19/95 - 6/28/02 [ 252, 5 ] 0.5495 0.5769 0.0437 0.0543 -0.4984 442 0.210 0.363 1.1968

Australia ASX 3/07/88 - 6/28/02 [ 252, 10 ] 0.1542 0.1105 0.0250 0.0276 -0.3613 293 0.433 0.667 0.9447

China Shanghai Composite 12/22/95 - 6/28/02 [ 21, 5 ] 0.3531 0.1818 0.0405 0.0159 -0.4810 252 0.329 0.506 1.1991

Hong Kong Hang Seng 12/21/87 - 6/28/02 [ 5, 1 ] 0.2936 0.1831 0.0394 0.0266 -0.5788 1409 0.310 0.379 0.7703

India BSE30 12/17/93 - 6/28/02 [ 10, 1 ] 0.1976 0.2544 0.0259 0.0506 -0.4002 698 0.269 0.344 0.8968

Indonesia Jakarta Composite 12/19/90 - 6/28/02 [ 5, 1 ] 0.7264 0.8291 0.0539 0.0760 -0.7819 958 0.310 0.398 0.7512

Japan Nikkei225 12/21/87 - 6/28/02 [ 252, 10 ] -0.0516 -0.0057 -0.0208 0.0029 -0.7133 294 0.381 0.623 0.9086

Malaysia KLSE Composite 12/02/86 - 6/28/02 [ 5, 1 ] 0.5185 0.4750 0.0584 0.0601 -0.6204 1378 0.319 0.399 0.9771

New Zealand NZSE30 12/17/92 - 6/28/02 [ 126, 5 ] 0.0380 0.0294 -0.0015 0.0099 -0.5436 272 0.338 0.502 0.9380

Pakistan Karachi100 2/03/94 - 6/28/02 [ 21, 1 ] 0.2568 0.3585 0.0297 0.0624 -0.4138 521 0.274 0.410 1.0583

Philippines PSE Composite 12/20/88 - 6/28/02 [ 5, 1 ] 0.6073 0.6445 0.0694 0.0880 -0.4182 1220 0.293 0.361 1.0754

Singapore Straits Times 3/17/88 - 6/28/02 [ 10, 1 ] 0.3079 0.2523 0.0489 0.0476 -0.4661 1169 0.297 0.382 0.8930

South-Korea Kospi200 11/17/94 - 6/28/02 [ 42, 1 ] 0.3682 0.4553 0.0308 0.0507 -0.7459 459 0.264 0.431 0.9370

Sri Lanka CSE All Share 9/24/96 - 6/28/02 [ 252, 21 ] 0.4593 0.5117 0.0853 0.1226 -0.1444 222 0.311 0.628 1.2987

Table 5.13 continued.

Data set Period Parameters r r^e S S^e ML # tr %tr>0 %d>0 SDR

Thailand SET 12/23/93 - 6/28/02 [ 21, 1 ] 0.2291 0.4190 0.0224 0.0693 -0.7942 566 0.261 0.346 1.1670

Taiwan TSE Composite 7/17/96 - 6/28/02 [ 10, 5 ] 0.0399 0.1286 -0.0012 0.0284 -0.5981 240 0.300 0.486 0.9699

Austria ATX 5/26/93 - 6/28/02 [ 252, 126 ] 0.0617 0.0409 0.0047 0.0131 -0.4850 148 0.439 0.641 1.1216

Belgium Bel20 12/19/91 - 6/28/02 [ 126, 63 ] 0.0637 0.0044 0.0051 -0.0006 -0.5859 226 0.407 0.544 0.8259

Czech Republic PX50 11/26/96 - 6/28/02 [ 252, 1 ] 0.2286 0.2823 0.0314 0.0583 -0.4457 226 0.230 0.511 1.0208

Denmark KFX 11/20/91 - 6/28/02 [ 252, 63 ] 0.0027 -0.0592 -0.0099 -0.0160 -0.5036 170 0.435 0.619 0.9315

Finland HEX General 3/18/94 - 6/28/02 [ 21, 10 ] 0.2873 0.1521 0.0287 0.0140 -0.5073 291 0.357 0.503 0.9817

France CAC40 7/21/92 - 6/28/02 [ 126, 42 ] 0.0063 -0.0440 -0.0082 -0.0102 -0.5954 181 0.403 0.625 0.9856

Germany DAX30 10/20/92 - 6/28/02 [ 42, 21 ] 0.0500 -0.0338 0.0013 -0.0094 -0.6310 243 0.366 0.599 0.9495

Greece ASE General 3/27/96 - 6/28/02 [ 10, 1 ] 0.5593 0.4880 0.0622 0.0577 -0.3888 529 0.299 0.357 0.8994

Italy MIB30 10/02/96 - 6/28/02 [ 126, 10 ] 0.1264 0.0654 0.0149 0.0115 -0.4792 147 0.333 0.522 0.9747

Netherlands AEX 12/21/87 - 6/28/02 [ 126, 63 ] 0.0703 -0.0377 0.0043 -0.0129 -0.5241 315 0.416 0.658 0.8524

Norway OSE All Share 12/17/97 - 6/28/02 [ 63, 5 ] 0.1624 0.1925 0.0238 0.0463 -0.2813 135 0.311 0.569 0.9697

Portugal PSI General 9/18/96 - 6/28/02 [ 126, 5 ] 0.2733 0.2292 0.0481 0.0490 -0.3297 189 0.349 0.541 0.9301

Russia Moscow Times 8/19/96 - 6/28/02 [ 5, 1 ] 1.2044 1.0412 0.0674 0.0555 -0.7146 550 0.305 0.384 0.8085

Slovakia SAX16 9/26/95 - 6/28/02 [ 126, 63 ] 0.0244 0.1274 -0.0041 0.0353 -0.5690 86 0.465 0.625 0.9164

Spain IGBM 12/06/93 - 6/28/02 [ 63, 42 ] 0.1420 0.0604 0.0177 0.0076 -0.7088 201 0.363 0.551 1.0715

Sweden OMX 11/18/94 - 6/28/02 [ 42, 10 ] 0.0504 -0.0158 0.0005 -0.0037 -0.5889 247 0.332 0.503 1.0641

Switzerland SMI 6/19/90 - 6/28/02 [ 126, 21 ] 0.0933 -0.0047 0.0101 -0.0059 -0.5295 297 0.360 0.591 0.8487

Turkey ISE100 12/20/89 - 6/28/02 [ 10, 1 ] 0.4749 0.5022 0.0288 0.0371 -0.8799 1055 0.283 0.380 0.8919

UK FTSE100 12/21/87 - 6/28/02 [ 252, 63 ] 0.0224 -0.0337 -0.0073 -0.0091 -0.6128 264 0.432 0.585 1.0021

Ireland ISEQ 1/02/91 - 6/28/02 [ 21, 5 ] 0.0704 0.0217 0.0067 0.0051 -0.3324 429 0.298 0.452 0.9366

Egypt CMA 12/18/96 - 6/28/02 [ 252, 1 ] 0.3819 0.2974 0.0989 0.0808 -0.1773 156 0.301 0.588 1.1224

Israel TA100 12/24/91 - 6/28/02 [ 252, 21 ] 0.1428 0.0975 0.0168 0.0163 -0.6316 366 0.276 0.558 0.9378

Table 5.14: Statistics best out-of-sample testing procedure: Sharpe ratio criterion, 0.25% costs. Statistics of the best recursively optimizing and testing procedure applied to the local main stock market indices listed in the first column in the case of 0.25% costs per trade. The best strategy in the optimizing period is selected on the basis of the Sharpe ratio criterion. Column 2 shows the sample period. Column 3 shows the parameters: [length optimizing period, length testing period]. Columns 4 and 5 show the mean return and excess mean return on a yearly basis in %/100 terms. Columns 6 and 7 show the Sharpe and excess Sharpe ratio. Column 8 shows the largest cumulative loss in %/100 terms. Columns 9, 10 and 11 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. The results are computed for an US-based trader who applies the technical trading rule set to the local main stock market indices recomputed in US Dollars.

Data set Period Parameters r r^e S S^e ML # tr %tr>0 %d>0 SDR

World MSCI 12/21/82 - 6/28/02 [ 252, 63 ] 0.1772 0.0935 0.0470 0.0345 -0.3409 600 0.355 0.623 0.9476

Argentina Merval 7/19/95 - 6/28/02 [ 252, 5 ] -0.0183 0.1821 -0.0079 0.0315 -0.7451 231 0.255 0.463 0.8697

Brazil Bovespa 9/25/96 - 6/28/02 [ 126, 1 ] 0.1213 0.1985 0.0091 0.0266 -0.6559 223 0.309 0.503 0.9222

Canada TSX Composite 12/21/87 - 6/28/02 [ 252, 21 ] 0.1266 0.0813 0.0240 0.0264 -0.4496 356 0.371 0.622 0.8949

Chile IPSA 12/20/95 - 6/28/02 [ 63, 1 ] 0.3566 0.4397 0.0685 0.1087 -0.2042 293 0.331 0.539 0.9860

Mexico IPC 1/16/98 - 6/28/02 [ 252, 63 ] 0.3561 0.3216 0.0363 0.0384 -0.5057 252 0.183 0.493 1.0082

Peru Lima General 6/16/93 - 6/28/02 [ 252, 126 ] 0.4452 0.4353 0.0673 0.0770 -0.6088 368 0.277 0.486 0.9316

US S&P500 12/21/82 - 6/28/02 [ 252, 63 ] 0.0733 -0.0296 0.0044 -0.0116 -0.4291 349 0.430 0.605 1.0756

US DJIA 12/21/82 - 6/28/02 [ 126, 63 ] 0.1019 -0.0140 0.0124 -0.0076 -0.4244 374 0.468 0.577 1.0549

US Nasdaq100 12/19/84 - 6/28/02 [ 63, 21 ] 0.1778 0.0443 0.0202 0.0042 -0.7823 549 0.344 0.491 1.1590

US NYSE Composite 12/21/82 - 6/28/02 [ 252, 63 ] 0.0585 -0.0407 0.0001 -0.0163 -0.4517 344 0.430 0.596 0.7990

US Russel2000 12/20/89 - 6/28/02 [ 63, 1 ] 0.2231 0.1394 0.0537 0.0397 -0.3659 573 0.339 0.562 0.7307

US Wilshire5000 12/18/85 - 6/28/02 [ 63, 10 ] 0.0561 -0.0335 0.0011 -0.0127 -0.6567 509 0.411 0.548 0.9887

Venezuela Industrial 12/19/95 - 6/28/02 [ 252, 5 ] 0.3535 0.3809 0.0267 0.0373 -0.5929 388 0.247 0.388 1.0575

Australia ASX 3/07/88 - 6/28/02 [ 252, 5 ] 0.1473 0.1036 0.0257 0.0283 -0.3421 339 0.381 0.624 1.0518

China Shanghai Composite 12/22/95 - 6/28/02 [ 126, 5 ] 0.5150 0.3437 0.0704 0.0458 -0.3331 157 0.427 0.648 1.0809

Hong Kong Hang Seng 12/21/87 - 6/28/02 [ 5, 1 ] 0.2352 0.1247 0.0341 0.0213 -0.5250 1547 0.337 0.375 0.7756

India BSE30 12/17/93 - 6/28/02 [ 21, 1 ] 0.1838 0.2406 0.0255 0.0502 -0.4230 622 0.265 0.362 0.8613

Indonesia Jakarta Composite 12/19/90 - 6/28/02 [ 5, 1 ] 0.5526 0.6553 0.0484 0.0705 -0.6310 1081 0.337 0.371 0.8210

Japan Nikkei225 12/21/87 - 6/28/02 [ 126, 63 ] -0.0165 0.0294 -0.0131 0.0106 -0.6752 229 0.415 0.608 1.0573

Malaysia KLSE Composite 12/02/86 - 6/28/02 [ 5, 1 ] 0.4141 0.3706 0.0510 0.0527 -0.4796 1568 0.349 0.376 0.9594

New Zealand NZSE30 12/17/92 - 6/28/02 [ 21, 5 ] 0.0885 0.0799 0.0113 0.0227 -0.4270 388 0.322 0.424 0.9576

Pakistan Karachi100 2/03/94 - 6/28/02 [ 42, 1 ] 0.1390 0.2407 0.0143 0.0470 -0.5913 521 0.313 0.418 0.9061

Philippines PSE Composite 12/20/88 - 6/28/02 [ 5, 1 ] 0.4247 0.4619 0.0547 0.0733 -0.3502 1334 0.301 0.337 1.0882

Singapore Straits Times 3/17/88 - 6/28/02 [ 63, 1 ] 0.2326 0.1770 0.0378 0.0365 -0.3679 791 0.291 0.470 1.0758

South-Korea Kospi200 11/17/94 - 6/28/02 [ 21, 1 ] 0.2399 0.3270 0.0200 0.0399 -0.6106 589 0.299 0.387 0.9735

Sri Lanka CSE All Share 9/24/96 - 6/28/02 [ 252, 21 ] 0.4948 0.5472 0.0943 0.1316 -0.1606 200 0.320 0.596 1.5490

Table 5.14 continued.

Data set Period Parameters r r^e S S^e ML # tr %tr>0 %d>0 SDR

Thailand SET 12/23/93 - 6/28/02 [ 63, 5 ] 0.1703 0.3602 0.0161 0.0630 -0.7485 312 0.301 0.467 1.1553

Taiwan TSE Composite 7/17/96 - 6/28/02 [ 21, 10 ] 0.0382 0.1269 -0.0017 0.0279 -0.6458 194 0.330 0.491 0.9601

Austria ATX 5/26/93 - 6/28/02 [ 126, 1 ] 0.0498 0.0290 0.0013 0.0097 -0.4206 347 0.323 0.530 1.0148

Belgium Bel20 12/19/91 - 6/28/02 [ 252, 63 ] 0.0695 0.0102 0.0076 0.0019 -0.5068 196 0.408 0.597 0.9877

Czech Republic PX50 11/26/96 - 6/28/02 [ 252, 10 ] 0.2726 0.3263 0.0372 0.0641 -0.5573 177 0.288 0.610 0.9209

Denmark KFX 11/20/91 - 6/28/02 [ 21, 10 ] 0.0106 -0.0513 -0.0084 -0.0145 -0.4764 381 0.333 0.456 0.8865

Finland HEX General 3/18/94 - 6/28/02 [ 42, 10 ] 0.3293 0.1941 0.0364 0.0217 -0.4799 245 0.359 0.517 1.0787

France CAC40 7/21/92 - 6/28/02 [ 252, 63 ] -0.0012 -0.0515 -0.0097 -0.0117 -0.6428 210 0.414 0.593 0.9638

Germany DAX30 10/20/92 - 6/28/02 [ 126, 63 ] -0.0305 -0.1143 -0.0169 -0.0276 -0.6148 154 0.474 0.679 0.9333

Greece ASE General 3/27/96 - 6/28/02 [ 42, 1 ] 0.3930 0.3217 0.0475 0.0430 -0.5344 395 0.278 0.429 0.9537

Italy MIB30 10/02/96 - 6/28/02 [ 21, 5 ] 0.1522 0.0912 0.0198 0.0164 -0.4994 209 0.340 0.475 1.0810

Netherlands AEX 12/21/87 - 6/28/02 [ 252, 10 ] 0.0844 -0.0236 0.0086 -0.0086 -0.4538 302 0.434 0.617 0.8951

Norway OSE All Share 12/17/97 - 6/28/02 [ 252, 42 ] 0.2266 0.2567 0.0391 0.0616 -0.2573 60 0.450 0.735 0.9775

Portugal PSI General 9/18/96 - 6/28/02 [ 63, 5 ] 0.2626 0.2185 0.0551 0.0560 -0.3628 227 0.344 0.520 1.0275

Russia Moscow Times 8/19/96 - 6/28/02 [ 126, 63 ] 1.1498 0.9866 0.0742 0.0623 -0.6347 149 0.456 0.668 1.1245

Slovakia SAX16 9/26/95 - 6/28/02 [ 126, 63 ] 0.0735 0.1765 0.0054 0.0447 -0.5512 84 0.500 0.699 1.0657

Spain IGBM 12/06/93 - 6/28/02 [ 63, 5 ] 0.0201 -0.0615 -0.0061 -0.0162 -0.6451 310 0.326 0.460 1.0523

Sweden OMX 11/18/94 - 6/28/02 [ 63, 1 ] 0.0864 0.0202 0.0075 0.0033 -0.5023 420 0.317 0.458 0.9048

Switzerland SMI 6/19/90 - 6/28/02 [ 252, 10 ] 0.1002 0.0022 0.0136 -0.0024 -0.3344 282 0.418 0.526 0.8583

Turkey ISE100 12/20/89 - 6/28/02 [ 252, 1 ] 0.5291 0.5564 0.0329 0.0412 -0.7598 445 0.335 0.573 1.0130

UK FTSE100 12/21/87 - 6/28/02 [ 63, 10 ] 0.0435 -0.0126 -0.0020 -0.0038 -0.5442 452 0.316 0.484 1.0903

Ireland ISEQ 1/02/91 - 6/28/02 [ 63, 42 ] 0.0402 -0.0085 -0.0010 -0.0026 -0.6260 228 0.399 0.601 0.9129

Egypt CMA 12/18/96 - 6/28/02 [ 126, 10 ] 0.3100 0.2255 0.0898 0.0717 -0.3523 149 0.342 0.622 1.3125

Israel TA100 12/24/91 - 6/28/02 [ 252, 126 ] 0.1146 0.0693 0.0133 0.0128 -0.5281 278 0.313 0.574 1.0276

Table 5.15: 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, 0.50, 0.75 and 1% 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 index. The results are computed for an US-based trader who applies the technical trading rule set to the local main stock market indices recomputed in US Dollars.

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%

World MSCI 0.3919 0.2675 0.1113 -0.0068 -0.0013 -0.0071 0.1155 0.0693 0.0345 0.0027 -0.0055 -0.0166

Argentina Merval 0.4352 0.3242 0.2099 0.1261 0.0750 0.0488 0.0559 0.0445 0.0315 0.0343 0.0329 0.0270

Brazil Bovespa 0.4400 0.4362 0.3229 0.2278 0.0671 0.0380 0.0492 0.0413 0.0266 0.0262 0.0168 0.0184

Canada TSX Composite 0.3056 0.1908 0.1262 0.0343 -0.0125 0.0030 0.0681 0.0483 0.0264 0.0149 0.0048 -0.0008

Chile IPSA 0.6686 0.5342 0.4332 0.3034 0.2695 0.1649 0.1308 0.1091 0.1087 0.0861 0.0653 0.0544

Mexico IPC 0.6690 0.5766 0.4800 0.3090 0.1214 0.0703 0.0808 0.0625 0.0384 0.0151 0.0010 -0.0061

Peru Lima General 0.6644 0.5859 0.4786 0.4118 0.2540 0.1739 0.1044 0.0977 0.0770 0.0607 0.0458 0.0373

US S&P500 0.0372 -0.0151 -0.0436 -0.0842 -0.0604 -0.0833 0.0118 -0.0011 -0.0116 -0.0146 -0.0165 -0.0171

US DJIA 0.0493 -0.0015 -0.0111 -0.0415 -0.0526 -0.0679 0.0032 -0.0052 -0.0076 -0.0214 -0.0263 -0.0238

US Nasdaq100 0.1531 0.0452 -0.0524 -0.1164 -0.1287 -0.1380 0.0259 0.0080 0.0042 -0.0095 -0.0099 -0.0119

US NYSE Composite 0.1030 0.0121 -0.0222 -0.0447 -0.0717 -0.0540 0.0352 -0.0043 -0.0163 -0.0241 -0.0279 -0.0258

US Russel2000 0.4399 0.3460 0.1581 0.0333 -0.0093 -0.0358 0.0978 0.0733 0.0397 0.0161 0.0071 -0.0015

US Wilshire5000 0.1353 0.0421 -0.0512 -0.0846 -0.0468 -0.0467 0.0446 0.0120 -0.0127 -0.0284 -0.0312 -0.0398

Venezuela Industrial 0.8696 0.8050 0.5769 0.2384 0.0692 0.0242 0.0653 0.0568 0.0373 0.0280 0.0159 0.0088

Australia ASX All Ordinaries 0.1558 0.1242 0.1105 0.0508 0.0364 0.0171 0.0444 0.0335 0.0283 0.0164 0.0091 0.0068

China Shanghai Composite 0.2973 0.2659 0.1818 0.0918 0.0652 0.1339 0.0465 0.0456 0.0458 0.0341 0.0233 0.0185

Hong Kong Hang Seng 0.3698 0.3260 0.1831 0.0554 0.0593 0.0520 0.0563 0.0458 0.0213 0.0032 -0.0036 -0.0013

India BSE30 0.4842 0.3855 0.2544 0.1347 0.0557 -0.0093 0.0810 0.0687 0.0502 0.0241 0.0076 -0.0033

Indonesia Jakarta Composite 1.1893 0.9802 0.8291 0.6649 0.5068 0.4426 0.0884 0.0834 0.0705 0.0551 0.0409 0.0309

Japan Nikkei225 0.0541 0.0282 -0.0057 -0.0361 -0.0211 -0.0436 0.0163 0.0116 0.0106 0.0041 0.0009 -0.0045

Malaysia KLSE Composite 0.7683 0.6175 0.4750 0.2818 0.1799 0.0864 0.0757 0.0692 0.0527 0.0257 0.0182 0.0146

New Zealand NZSE30 0.0986 0.0711 0.0294 -0.0184 -0.0875 -0.0878 0.0438 0.0339 0.0227 -0.0092 -0.0173 -0.0168

Pakistan Karachi100 0.4970 0.4012 0.3585 0.2602 0.2245 0.2112 0.0704 0.0629 0.0470 0.0372 0.0358 0.0355

Philippines PSE Composite 0.8376 0.8145 0.6445 0.4390 0.3094 0.1979 0.0987 0.0892 0.0733 0.0488 0.0314 0.0286

Singapore Straits Times 0.4749 0.4138 0.2523 0.1106 0.0232 0.0266 0.0719 0.0568 0.0365 0.0154 0.0053 0.0084

South-Korea Kospi200 0.5053 0.5061 0.4553 0.3071 0.1777 0.1224 0.0610 0.0482 0.0399 0.0326 0.0301 0.0256

SriLanka CSE All Share 0.7466 0.6436 0.5117 0.3879 0.3617 0.2747 0.1669 0.1494 0.1316 0.0978 0.0787 0.0647

Table 5.15 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%

Thailand SET 0.5727 0.5007 0.4190 0.2913 0.2737 0.2951 0.0817 0.0710 0.0630 0.0586 0.0544 0.0476

Taiwan TSE Composite 0.2485 0.1528 0.1286 0.0690 0.0229 0.0111 0.0469 0.0431 0.0279 0.0161 0.0103 0.0112

Austria ATX 0.0530 0.0321 0.0409 0.0067 -0.0310 -0.0303 0.0276 0.0217 0.0097 -0.0075 -0.0131 -0.0137

Belgium Bel20 0.0671 0.0185 0.0044 -0.0622 -0.1210 -0.1306 0.0161 0.0068 0.0019 -0.0103 -0.0222 -0.0218

Czech Republic PX50 0.5005 0.5041 0.2823 0.2161 0.1508 0.1239 0.0963 0.0834 0.0641 0.0420 0.0313 0.0366

Denmark KFX 0.0998 0.0334 -0.0592 -0.0728 -0.0505 -0.0570 0.0186 0.0073 -0.0145 -0.0308 -0.0260 -0.0235

Finland HEX General 0.2917 0.1997 0.1521 0.0556 0.0446 0.0052 0.0288 0.0252 0.0217 0.0118 0.0095 0.0061

France CAC40 0.0204 -0.0452 -0.0440 -0.0402 -0.0620 -0.0928 0.0106 -0.0131 -0.0117 -0.0065 -0.0127 -0.0126

Germany DAX30 -0.0264 -0.0424 -0.0338 -0.0737 -0.0753 -0.0669 -0.0081 -0.0201 -0.0276 -0.0292 -0.0174 -0.0304

Greece ASE General 0.7763 0.6760 0.4880 0.2301 0.1079 0.0316 0.0718 0.0594 0.0430 0.0286 0.0101 0.0068

Italy MIB30 0.1368 0.1417 0.0654 0.0089 -0.0375 -0.0614 0.0378 0.0265 0.0164 0.0112 -0.0006 0.0060

Netherlands AEX 0.0149 -0.0056 -0.0377 -0.0532 -0.0608 -0.0678 0.0045 0.0017 -0.0086 -0.0118 -0.0252 -0.0325

Norway OSE All Share 0.2836 0.2749 0.1925 0.1707 0.1466 0.1277 0.0640 0.0591 0.0616 0.0580 0.0510 0.0552

Portugal PSI General 0.5386 0.3880 0.2292 0.1413 0.0663 0.0704 0.0808 0.0675 0.0560 0.0286 0.0177 0.0054

Russia MoscowTimes 1.7811 1.5672 1.0412 0.8313 0.4889 0.3705 0.0660 0.0631 0.0623 0.0536 0.0473 0.0359

Slovakia SAX16 0.2256 0.2392 0.1274 0.1179 0.1520 0.1414 0.0405 0.0456 0.0447 0.0322 0.0337 0.0246

Spain IGBM 0.0835 0.0281 0.0604 -0.0139 -0.0389 -0.0458 0.0313 -0.0013 -0.0162 -0.0264 -0.0260 -0.0305

Sweden OMX 0.0960 0.0476 -0.0158 -0.0231 -0.0655 -0.1019 0.0249 0.0205 0.0033 -0.0174 -0.0179 -0.0193

Switzerland SMI 0.0600 0.0171 -0.0047 -0.0069 -0.0351 -0.0400 0.0111 -0.0012 -0.0024 -0.0157 -0.0205 -0.0165

Turkey ISE100 0.7669 0.6091 0.5022 0.2757 0.1597 0.1328 0.0388 0.0396 0.0412 0.0327 0.0180 0.0113

UK FTSE100 0.0498 0.0221 -0.0337 -0.0466 -0.0422 -0.0318 0.0129 0.0055 -0.0038 -0.0037 -0.0114 -0.0081

Ireland ISEQ 0.0794 0.0430 0.0217 -0.0085 -0.0234 -0.0176 0.0151 0.0044 -0.0026 -0.0108 -0.0136 -0.0175

Egypt CMA 0.3987 0.3330 0.2974 0.2645 0.2545 0.1954 0.1016 0.0852 0.0717 0.0662 0.0405 0.0457

Israel TA100 0.2759 0.1419 0.0975 0.0088 0.0053 0.0023 0.0441 0.0274 0.0128 -0.0026 -0.0106 -0.0096

Average: out-of-sample 0.3772 0.3060 0.2141 0.1240 0.0705 0.0447 0.0544 0.0419 0.0298 0.0164 0.0086 0.0052

Average: in sample 0.4870 0.3684 0.2737 0.2186 0.1958 0.1798 0.0689 0.0546 0.0441 0.0387 0.0358 0.0335

Table 5.16: Estimation results CAPM for best out-of-sample testing procedure. Coefficient estimates of the Sharpe-Lintner CAPM: r_tⁱ-r_t^f=a + b (r_t^Local-r_t^f) + e_t. That is, the return in US Dollars of the best recursive optimizing and testing procedure, when selection in the optimizing period is done by the mean return criterion (Panel A) or by the Sharpe ratio criterion (Panel B), in excess of the US risk-free interest rate is regressed against a constant and the return of the local stock market index in US Dollars in excess of the US 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

World MSCI 0.001241a 0.849c -2.02E-05 0.969 0.001129a 0.802b 6.60E-05 0.711a

Argentina Merval 0.001469a 0.771a 0.000367 0.784b 0.001075b 0.614a 0.000638 0.757a

Brazil Bovespa 0.001412b 0.735a 0.000748 0.750a 0.001273b 0.615a 0.000561 0.594a

Canada TSX Composite 0.001016a 0.942 0.000127 1.028 0.000752a 0.777a 0.000159 0.809a

Chile IPSA 0.002085a 0.833b 0.001028a 0.800b 0.001870a 0.791a 0.001057a 0.707a

Mexico IPC 0.002000a 0.949 0.001054c 0.871 0.002285a 0.904 0.000454 0.994

Peru Lima General 0.001995a 0.911 0.001347a 0.923 0.001916a 0.919 0.001045a 0.868c

US S&P500 0.000144 0.902 -0.000324b 1.03 0.000213c 0.838 -0.00012 0.87

US DJIA 0.000202 0.851 -0.0001 0.774c 0.000114 0.693a -0.0002 0.847

US Nasdaq100 0.000465c 1.135c -0.000476c 1.154b 0.000653a 0.712a -0.00012 0.942

US NYSE Composite 0.000388a 0.783b -0.00015 0.918 0.000406a 0.734a -0.0002 0.753b

US Russel2000 0.001361a 0.939 0.000129 0.935 0.001155a 0.689a 0.000247 0.744a

US Wilshire5000 0.000495a 0.771a -0.000325b 1.031 0.000525a 0.715a -0.000284b 0.823b

Venezuela Industrial 0.002564a 1.075 0.000791 0.702b 0.002230a 0.925 0.000989b 1.093

Australia ASX All Ordinaries 0.000547a 1.027 0.000185 1.107c 0.000573a 0.865b 0.000206 0.905

China Shanghai Composite 0.001014b 0.735a 0.000304 0.983 0.001125a 0.684a 0.000896b 0.686a

Hong Kong Hang Seng 0.001162a 0.842b 0.00023 0.764b 0.001067a 0.702a 0.00013 0.653a

India BSE30 0.001566a 0.808a 0.000459 0.830a 0.001368a 0.777a 0.000462 1.159b

Indonesia Jakarta Composite 0.003274a 0.873 0.002154a 0.921 0.002661a 0.825b 0.001540a 0.791b

Japan Nikkei225 0.000134 0.774a -0.00024 0.782a 0.000155 0.763a -6.91E-05 0.894c

Malaysia KLSE Composite 0.002191a 0.952 0.000950a 0.947 0.001708a 0.871 0.000603b 0.846

New Zealand NZSE30 0.000357c 0.872a -7.91E-05 0.932 0.000548a 0.710a -0.00019 0.883c

Pakistan Karachi100 0.001712a 0.929 0.000809b 0.661a 0.001423a 0.888c 0.000763c 1.058

Philippines PSE Composite 0.002450a 0.912c 0.001467a 0.942 0.002065a 0.860b 0.000944a 0.799a

Singapore Straits Times 0.001476a 0.906 0.000398c 0.868c 0.001138a 0.785a 0.000269 0.775a

Table 5.16 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

South-Korea Kospi200 0.001701a 0.914 0.001054c 0.820a 0.001809a 0.826a 0.000759 0.668a

Sri Lanka CSE All Share 0.002353a 1.12 0.001397a 1.091 0.002399a 1.098 0.001095a 0.876

Thailand SET 0.002001a 0.886 0.001126b 0.915 0.001858a 0.879 0.001066b 0.759b

Taiwan TSE Composite 0.000866b 0.814a 0.00016 0.744a 0.000749b 0.718a 0.000143 0.754a

Austria ATX 0.000197 0.939 4.53E-06 0.754a 0.000337c 0.801a -0.00014 0.795a

Belgium Bel20 0.000242 1.019 -0.00024 0.986 0.000247 0.897 -0.00011 0.824a

Czech Republic PX50 0.001658a 0.927 0.000793b 0.939 0.001788a 0.953 0.000685c 0.941

Denmark KFX 0.000362c 0.966 -0.00028 1.015 0.000291 0.851a -0.000463b 1.014

Finland HEX General 0.000971b 0.794a 0.00024 0.835b 0.000838b 0.710a 0.000434 0.796a

France CAC40 7.79E-05 0.927c -0.00016 1.075 0.000166 0.830a -0.0001 1.012

Germany DAX30 -7.69E-05 0.882b -0.00026 0.897 -7.90E-05 0.811a -0.000462b 0.894

Greece ASE General 0.002186a 0.787a 0.000787c 0.861b 0.001652a 0.769a 0.000734 0.777a

Italy MIB30 0.000482 0.849b 3.00E-05 0.886 0.000725b 0.870c 0.000224 0.908

Netherlands AEX 2.99E-05 1.082 -0.00019 0.925 0.000148 0.812a -0.0001 0.923

Norway OSE All Share 0.000966a 0.829c 0.000587 0.812c 0.000882b 0.783b 0.000819b 0.796c

Portugal PSI General 0.001649a 0.923 0.0005 0.883 0.001133a 0.756a 0.000404 0.711a

Russia Moscow Times 0.003745a 0.877 0.002219a 0.832b 0.002736a 0.763a 0.002280a 0.672a

Slovakia SAX16 0.000806b 0.852 0.000495 1 0.000462 0.705a 0.000458 0.987

Spain IGBM 0.000297 0.941 -4.26E-05 0.974 0.000507b 0.800a -0.000427c 1.006

Sweden OMX 0.000349 0.926 -8.57E-05 0.932 0.000503c 0.741a -0.00031 0.743a

Switzerland SMI 0.000219 0.952 -7.53E-06 0.902 0.000243 0.838a -0.00016 0.853a

Turkey ISE100 0.002297a 0.94 0.000980c 0.942 0.001732a 0.984 0.001393b 0.895c

UK FTSE100 0.000179 0.891b -0.00019 1.026 0.00018 0.943 -5.44E-05 1.041

Ireland ISEQ 0.000295 0.913 -3.42E-05 0.908 0.000213 0.814a -0.00015 0.947

Egypt CMA 0.001220a 1.167 0.000863a 1.018 0.000990a 0.932 0.000740a 0.936

Israel TA100 0.000925a 0.943 3.77E-05 1.005 0.000879a 0.877c -5.67E-05 0.907

Table 5.18: Summary of the results found in Chapters 3, 4 and 5. The table shows for different transaction costs cases the fraction of data series analyzed for which (1) at the 10% significance level a significantly positive estimate of a is found in the CAPMs (3.5), (4.1) and (5.1), if the best strategy is selected in sample, (2) White's (2000) RC p-value is smaller than 0.10, (3) Hansen's (2001) SPA-test p-value is smaller than 0.10, (4) at the 10% significance level a significantly positive estimate of a is found in the CAPMs (3.5), (4.1) and (5.1), if the best recursive out-of-sample testing procedure is applied. Panel A shows the results for the mean return selection criterion and Panel B shows the results for the Sharpe ratio selection criterion. In Chapters 3 and 5 the results are in US Dollars and in Chapter 4 the results are in Dutch Guilders. For entries marked with X no results are computed.

Panel A Panel B

selection criterion Mean return Sharpe ratio

costs per trade 0% 0.10% 0.25% 0.50% 0.75% 1% 0% 0.10% 0.25% 0.50% 0.75% 1%

Chapter 3 DJIA and stocks listed in the DJIA: 1973-2001 (35 data series)

(1) in-sample CAPM: a>0 0.83 0.49 0.29 0.2 0.2 0.23 0.83 0.51 0.37 0.26 0.26 0.26

(2) p_W < 0.10 0 0 0 0 0 0 0.11 0 0 0 0 0

(3) p_H < 0.10 0.23 0 0 0 0 0 0.46 0.09 0 0 0 0

(4) out-of-sample CAPM: a>0 0.34 0.09 0.03 0 X X 0.4 0.2 0.17 0.03 X X

Chapter 4 AEX-index and stocks listed in the AEX-index: 1983-2002 (51 data series)

(1) in-sample CAPM: a>0 0.73 0.73 0.63 0.61 0.51 0.47 0.76 0.75 0.69 0.63 0.57 0.49

(2) p_W < 0.10 0.04 0 0 0 0 0 0.20 0.08 0.08 0.08 0.04 0.04

(3) p_H < 0.10 0.27 0.04 0.04 0.04 0.02 0.02 0.59 0.33 0.25 0.29 0.29 0.29

(4) out-of-sample CAPM: a>0 0.61 0.41 0.20 0.08 0.06 0.04 0.65 0.47 0.22 0.04 0.04 0.04

Chapter 5 Local main stock market indices: 1981-2002 (51 data series)

(1) in-sample CAPM: a>0 1 0.88 0.86 0.73 0.63 0.53 1 0.88 0.82 0.73 0.65 0.55

(2) p_W < 0.10 0.16 0.12 0.04 0 0 0 0.47 0.33 0.14 0.06 0.06 0.02

(3) p_H < 0.10 0.53 0.29 0.12 0.04 0.02 0.02 0.69 0.55 0.45 0.31 0.29 0.25

(4) out-of-sample CAPM: a>0 0.61 0.47 0.35 0.14 0.08 0.02 0.65 0.47 0.33 0.16 0.04 0.04

1: Morgan Stanley Capital International. MSCI indices are the most widely used benchmarks by global portfolio managers.
2: At the moment of writing the stock markets are reaching new lows.
3: See section 3.2, page ??, for an explanation. Separate ACFs of the returns are computed for each stock market index, but not presented here to save space. The tables are available upon request from the author.
4: These results are not presented here to save space.
5: Computations are also done for the 0.10, 0.50, 0.75 and 1% costs per trade cases but the results are not presented here to save space. The results are available upon request from the author.

Gerwin Griffioen's Technical Analysis Pages

Chapter 5 Technical Trading Rule Performance in Local Main Stock Market Indices

5.1 Introduction

5.2 Data and summary statistics

5.3 Empirical results

5.3.1 Results for the mean return criterion

Technical trading rule performance

CAPM

Data snooping

5.3.2 Results for the Sharpe ratio criterion

Technical trading rule performance

CAPM

Data snooping

5.4 A recursive out-of-sample forecasting approach

5.5 Conclusion

5.6 Comparing the US, Dutch and Other Stock Markets

Appendix

A. Tables

Chapter 5
Technical Trading Rule Performance in Local Main Stock Market Indices

5.6 Comparing the US, Dutch and
Other Stock Markets