A reality check on technical trading rule profits in the u,s, futures markets, страница 12

Figure 2 presents another interesting finding. As in Figure 1, it plots annual mean net returns of each technical trading rules along with a sequence of Reality Check p-values in the Eurodollar over 1985–2004. After the first 600 trading rules are inspected, the p-value drops to around 0.54, and then repeatedly increases and decreases whenever different classes of trading rules are introduced, with an overall decreasing trend. A superior trading rule is evaluated around trading rule number 5,000 and the p-value quickly falls from around 0.30 to around 0.01. The p-value then slowly increases to around 0.02 because no improvements occur in annual mean net returns as the universe of trading rules expands. However, as another superior trading rule is introduced around trading rule number 7,000, the p-value completely drops to zero. Because the performance of the superior trading rule is so strong, adding 2,000 more trading rules does not change the p-value of zero. For the Eurodollar futures, therefore, the null hypothesis that the annual mean net return of the best rule is no greater than zero is rejected.^[6]

To assess the effect of transaction costs on the performance of technical trading rules, each trading rule is re-simulated by applying lower transaction costs of $50 to each of the three sample periods. As explained above, such lower commissions (around $12.50 per round turn) might be available either to traders through discount brokers or for high volume trades and electronic trades. Results show that for each market in each sample period, annual mean net returns are moderately increased and thus data-snooping-adjusted p-values are slightly improved. These improvements, however, do not greatly alter the previous findings because the number of markets showing statistical significance of technical trading profits, measured by the data-snooping-adjusted p-value, is similar to that under transaction costs of $100. Over the full sample period of 1985–2004, as shown in Table IV, annual mean net returns of the best rules are statistically significant only for the Eurodollar (1.26%) and the yen (9.62%) with Reality Check p-values of 0.00 and 0.02, respectively. Interestingly, in each sample period, the best trading rules identified with $100 transaction costs remain the same even with $50 transaction costs for all but a few markets. Hence, lowering transaction costs has little effect on the selection and performance of the best trading rules. For the Sharpe ratio criterion, the same

TABLE IV

Performance of the Best Technical Trading Rules under Mean Net Return

Criterion with $50 Transaction Costs, 1985–2004