Genetic programs, data-snooping, and technical analysis, страница 9

Note. r is the average monthly return, s_r is the standard error of r, t is Student’s t-statistic, and n  0 is the number of months in which r  0. Crude oil, unleaded, and heating oil have 156 monthly observations, all other commodities have 204 observations. * and ** denote rejection of the null hypothesis r  0 at the 5% and 1% levels, respectively. Out-of sample performance is measured using transactions costs of $50 per round turn. Trades/month refers to round-trips.

test of r  0, and the number of months with positive returns. Returns are reported as average gross monthly profit minus transactions costs divided by the exchange minimum initial margin.

In contrast to much of the previous research in commodity markets, these rules find little evidence of profitability for technical trading strategies. Of the 24 commodities studied only 2, CME Pork Bellies and CME S&P 500 futures, produced rules for which the trading returns were statistically positive at the 5% or greater level, which is only marginally above the 1.2 that would be expected with 24 tests at the 5% level. Examining the remainder of the commodities reveals no particular patterns in success or failure. Of the financial futures, two of the five returns are positive; only one is significant. Of the agricultural and foodstuffs futures, 7 of 13 have positive returns, with one significantly positive. Of the remaining six metals and energy futures, two are positive, but none is significant.

The fifth column reports the average number of round-turn trades per month for the rules generated. Treasury bonds, pork bellies, and silver produce rules with the highest frequency of trades, but still average only 1.2 round turns per month. Many of the generated rules average only one half-turn executed per month. This indicates that the $100 transactions cost used in rule training and selection was perhaps too successful in discouraging the evolution of oft-transacting rules.

The remaining two columns report the proportion of days on which the trading rules were correct, conditioned on holding long or short positions. If the prices and positions were generated randomly, these statistics would be expected to be near 50%, which nearly all are.

The results of the individual rules indicate little success in generating consistent profits from technical analysis in out-of-sample testing. While rules are generated that return statistically significant profits for two of the commodities, given that 24 commodities were tested, such results are not surprising. However, it should also be noted that these rules do not incorporate any sort of risk management techniques, such as stop-loss orders to prevent extended losses. In an actual trading environment, such additional rules would invariably be implemented, likely improving the out-of-sample results reported here.

To compare the results of a fund of technically traded futures, a portfolio of futures is created in which 30% of the assets are devoted to initial margin, as in Lukac et al. (1988a), and all of the assets are held in U.S. Treasury Bills. The return for such a portfolio is equal to the T-Bill rate plus 30% of the average of the individual commodity returns.

TABLE VI

Correlation of Futures Portfolio and Equity Index Returns