GA/GP have found their way into futures markets as well. Wang (2000) applies GP to the S&P 500 futures market. Based on daily data and technical indica-tors such as moving averages, trading range breaks, volume etc. ranging from 1985-1998, the author picks GP-evolved trading rules based on 2-year
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ing periods and applies them out-of-sample. The benchmark is a buy-and-hold strategy which consists of a long position in 2 S&P 500 futures contracts all the time. In contrast to this, the GP-based rules were designed to yield five different signals: long 2 contracts, long 1 contract, neutral (i. e. zero investment), short 1 contract, short 2 contracts (short-selling is assumed to be feasible, at least for institutional investors). Basically, Wang (2000) finds that GP-performance in the S&P 500 futures market is inconsistent. While some generated rules beat the benchmark, their overall power is limited often resulting in slightly negative excess returns when taking transaction costs into account. Overall performance seems to be better when markets are volatile whereas the GP-rules reportedly have difficulties in picking up sustained upward trends. Interestingly, although being unable to beat the benchmark, the GP-rules often converge to the buy-and-hold benchmark, i. e. 2 contracts long. The author notes that U.S. equity returns in the twentieth century (and therefore the higly-correlated futures mar-kets) have been the highest of all countries making it difficult for GP to beat buy-and-hold.
In spirit of Allen and Karjalainen (1999), Karjalainen (2002) investigates the performance of a GP trading system for the S&P 500 futures market. The data range from 1982-1993. Inputs were moving averages, maximum/minimum of past prices, lagged prices etc.. The benchmark was once more a buy-and-hold strategy, i. e. a rolled over long position in a single S&P 500 futures contract.
It turned out that the GP-based trading rules slightly outperform the bench-mark for the 1988-1993 out-of-sample period. Further analysis showed that a portfolio of trading rules results in a superior annualized Sharpe ratio which is in-line with the findings in Allen and Karjalainen (1999) for the equity market.
Therefore, GP-based timing strategies apparently reduce volatility by a signifi-cant amount while roughly matching buy-and-hold.
Tsang and Lajbcygier (2002) also explore evolutionary trading in futures. As a special feature, they make use of a standard GA and a Split Search GA17.
17Basically, the idea is to start the GA search using two different input sets of variables for
the starting solutions, one using variables from class x, the other using variables from class y. Solutions from the two separated evolutionary processes are allowed to eventually cross over in analogy to two slightly different species (say two different kinds of giant lizards on the
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Basically, the data consist of daily highs and lows plus opening and closing prices for eight commodities between 1988 and 1998. The authors use a rolling-time frame of one year in-sample training followed by subsequent one year out-of-sample application throughout the entire data sample. The input data for GA consists of the classic filter rule (buy or sell contract when prices have de-creased/increased by more than x%) and a moving average filter rule which translates the classic filter rule concept to a smoothed time-series creating so-called percentage envelopes or volatility bands. Fitness of the trading rules is measured using the Sharpe ratio, benchmark strategy was buy-and-hold (only one contract long/short at any one time). The authors report that the Split Search GA and the standard GA only marginally beat the benchmark and that the results are not statistically significant. After changing the fitness measure to incorporate a take-profit mechanism plus the number of winning trades, the results improve but still lack statistical significance. Finally, the authors note that the difference in performance between the split island GA and the standard GA was almost statistically significant. In defense of their study, they point out that the primary goal was to show how GA performance can be improved by using modified GA and fitness functions that do not solely focus on total prof-itability.
Apart from the S&P 500, Bauer (1994) also looks at the U.S. government and corporate bond market. The approach is basically the same as already discussed in the section on equity markets. This time, the variables with the highest corre-lation with the spread between the long maturity Treasury bonds and the short maturity T-bills are the 1-month change in U.S. stock prices, economic growth momentum indicators, changes in unemployment levels and 3-month changes in consumer installment debt. The alternative investment to going long in Trea-sury bonds is going long in TreaTrea-sury bills. In addition, a switching strategy between corporate- and Treasury bonds is considered using basically the same input variables. For the Treasury bonds/Treasury bills case study, the author reports an average return of the portfolio of GA-trading rules of 10.51% vs.
14.35% for buy-and-hold for the 1989-1991 out-of-sample period clearly
miss-Galapagos islands) living on two separate islands that sometimes, by crossing the water in between, manage to mate.