A reality check on technical trading rule profits in the u,s, futures markets, страница 11

FIGURE 1

Performance of the best rule chosen from the full universe under the mean net return criterion: soybeans, 1985–2004. Economic and statistical performance of the best rule chosen from the full

universe of trading rules for soybean futures under the mean net return criterion over 1985–2004.

Each trading rule is indexed on the x-axis and two different lines track the performance of the best rule updated across all trading rules as the universe of trading rules expands. The dark thick line tracks the highest annual mean net return (measured on the left y-axis) up to a given point, while the light

thick line tracks the corresponding White’s Reality Check p-value (measured on the right g-axis) for the null hypothesis that the best rule among the trading rules considered up to a given point does not outperform the benchmark (in this case, mean zero profit). The scattered points plot annual mean net returns that each trading rule generates during the sample period.

Figures 1 and 2 provide further insights into the effects of data snooping. Figure 1 illustrates annual mean net return performance of each technical trading rule in soybean futures over 1985–2004. Each technical trading rule is indexed on the x-axis and two different lines track the performance of the best rule updated across all trading rules as the universe of trading rules expands. A dark thick line tracks the highest annual mean net return (measured on the left y-axis) up to a given point, while a light thick line tracks the corresponding White’s Reality Check p-value (measured on the right g-axis) for the null hypothesis that the best rule among the trading rules considered up to a given point does not outperform the benchmark. The scattered points plot annual mean net returns that each trading rule generates during the sample period and vertical clusters of the points indicate the performance of neighbor trading

FIGURE 2

Performance of the best rule chosen from the full universe under the mean net return criterion:

Eurodollar, 1985–2004. Economic and statistical performance of the best rule chosen from the full universe of trading rules for the Eurodollar futures under the mean net return criterion over 1985–2004.

Each trading rule is indexed on the x-axis and two different lines track the performance of the best rule updated across all trading rules as the universe of trading rules expands. The dark thick line tracks the highest annual mean net return (measured on the left y-axis) up to a given point, while the light thick

line tracks the corresponding White’s Reality Check p-value (measured on the right y-axis) for the null

hypothesis that the best rule among the trading rules considered up to a given point does not outperform the benchmark (in this case, mean zero profit). The scattered points plot annual mean net returns that each trading rule generates during the sample period.

rules in a similar group as parameters of a trading system are slightly altered. The maximum annual mean net return starts at around 54% with a Reality Check p-value of one and then gradually increases. The p-value, however, does not decrease noticeably until the first 6,000 trading rules have been considered because the best rule does not significantly outperform the benchmark. After 6,000 trading rules have been inspected, the best performance is improved to around 4% with a p-value of 0.97. Adding another 1,500 trading rules does not improve upon the best trading rule and the p-value remains almost unchanged. After about 7,500 trading rules have been considered, the best performance is improved to about 6%, and the p-value drops to 0.85. The p-value is kept at the same level until an additional 500 trading rules are evaluated but, after this, it quickly rises close to one as no more improvement over the previously best trading rule occurs. When the final trading rule is inspected, the p-value ultimately increases to 1.00. Since the order of trading rules is arbitrary, the sequence of the p-values may have a different shape but the final p-value is always the same. This result, therefore, strongly indicates that the best trading rule does not generate net profits greater than zero when over 9,000 trading rules are jointly considered.