Many traders use concrete trading rules, called systems, to make trading decisions. The performance of a system depends on both the merits of the system itself and market conditions under which it is used. A system might perform well historically only because it is well suited to specific market conditions during the test period. For example, the buy-and-hold strategy works extremely well when the price is going up; swing trading works well when the price is in a range.

A system might achieve good performance simply through random trading. However, such a system should not be traded because in the long run random trading has poor performance. The procedure described in this paper tests whether a system can be distinguished from random trading. It is called the Random Signals Test because it is a hypothesis test based on randomly generated trading signals.

A system should only be traded if its performance is so high that the null hypothesis of random trading is rejected. The hypothesis test is based on a performance measure that describes trader preferences. An example of such a performance measure is Rate of Return. First, we construct the probability distribution of a performance measure under the null hypothesis of random trading.

The distribution is constructed through randomly issued trading signals. Then, based on this distribution, we find the appropriate critical value. If a system’s performance is greater than this critical value, we reject the null hypothesis of random trading.

The Random Signals Test controls for price behavior during the test period and so the results of the test are not influenced by it. We control for price behavior by comparing a system’s performance to the performance of random trading on the same price data. The test also controls for the trade characteristics of the system being tested. The trade characteristics of random trading are set equal to those of the system being tested.

For example, if the system being tested trades a variable number of contracts, so should random trading. We do this so that performance is the only potential distinguishing factor between the system being tested and random trading.

 

Prof. Alex Strashny

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