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The results using this system were disappointing (see Figure 1). Over the 1976-1984 test period, six of the 16 parameter sets tested for the weekly version of the crossover stochastic system actually lost money. The best parameter set registered only a 27.7 percent average gain, with a Sharpe Ratio of 0.65 and a Gain to Retracement Ratio of 2.19. (For a definition of this measure, see "Alternative to Sharpe Ratio Better Measure of Performance," Futures magazine, March 1985).

The daily version of the system did somewhat better (Figure 2). Sixteen of the 22 parameter sets tested were profitable, but in most cases, the gains were mediocre. The best performing parameter set registered a 36.3 percent average annual gain, with a Sharpe Ratio of 0.88 and a Gain to Retracement Ratio of 4.26.

Even the much maligned crossover moving average system

performed significantly better than the stochastic crossover

system described.

While the performance of the best parameter set tested was respectable, it must be emphasized that it was derived on the basis of hindsight. A trader using the type of stochastic system described would likely have experienced far less favorable results since it is unlikely that he would have picked the optimum parameter set.

It should be pointed out that the parameter sets which performed the best used much slower moving averages of the stochastic than suggested by popular literature (i.e.,3-day moving average, and 3-day moving average of the 3-day moving average). While this particular combination was not tested, the performance of similar parameter sets which were tested suggests that the use of fast moving averages in a stochastic crossover system would be a consistent money drain (the opposite of the proverbial money machine). Unfortunately, one cannot get rich trading the reverse system, since in each case (i.e., trading or fading the system), performance is decimated by the extreme burden of transaction costs. (Of course "Disneyland simulations," which do not include transaction costs, might show such systems as being viable. Any trader using actual money would know better.)

The average trader should not automatically assume the value of stochastics before rigorously testing their past performance....

Finally, it should be noted that even the much maligned crossover moving average system performed significantly better than the stochastic crossover system described above (Figure 3). For example, a 10/30-day crossover combination witnessed a 32.5 percent average gain during the test period, with a Sharpe Ratio of 0.85 and a Gain to Retracement Ratio of 3.94. Although these performance figures are slightly below those scored by the best performing parameter set tested in the stochastic crossover system, it should be emphasized that the 10/30 combination is not the optimum parameter set for the crossover moving average system. Overall, a wide scattering of parameter sets for a straightforward crossover system would perform better than the parameter sets of the stochastic crossover system. For comparison purposes, tables are included summarizing the performance of the daily crossover stochastic system, weekly crossover stochastic system, and 1:3 moving average crossover combinations (e.g., 3/9, 4/12, etc.). Each table indicates the portfolio performance for a range of parameter sets for each system.

Conclusion

The test described above suggests that the generally perceived value of the stochastic as a technical indicator may be overstated. It appears particularly doubtful whether fast stochastic moving averages can be useful as a sole input for trading decisions. Nevertheless, all we have proven is that a particular systemusing a stochastic measure provides poor to mediocre results. Obviously, one can never prove that a given technical indicator is useless, since there are an infinite number of ways an indicator could be used. Certainly, some more creative individuals might be able to construct a methodology which successfully uses the stochastic as a trading tool. However, the average trader should not automatically assume the value of stochastics before rigorously testing their past performance for the given application.

Jack D. Schwager is Director of Research and Managed Trading for Paine Webber, and author of A Complete Guide to the Futures Markets, John Wiley & Sons, 1984. Norman Strahm is the Managed Trading Strategist for Paine Webber Futures Department.