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In order to develop or refine our trading systems and algorithms, our traders often conduct experiments, tests, optimizations, and so on.  One of our traders tested several sell strategies and we are now sharing some of those findings.  R. Donchian, popularized the system in which a sale occurs if the 5-day moving average crosses below the 20-day moving average.  R.C. Allen popularized the system in which a sale occurs if the 9-day moving average crosses below the 18-day moving average.  Some traders feel they give up less of the gains they achieve if they use a shorter long moving average.  These people prefer to sell if the 5-day moving average crosses below the 10-day moving average.  Traders have used variations on these ideas (some touting the benefits of one variation and others touting the benefits of another).  A friend told me about the crossover of the 7-day and 13-day exponential moving averages.  Because that system appeared to have some merit, I included it in the tests for comparison purposes.  The strategies covered in this particular series of tests were as follows.  

 

1. Sell if the stock’s simple 9-day moving average crosses below its simple 18-day moving average,
    
2. Sell if the stock’s simple 10-day moving average crosses below its simple 18-day moving average,
    
3. Sell if the stock’s simple 10-day moving average crosses below its simple 19-day moving average,
    
4. Sell if the stock’s simple 9-day moving average crosses below its simple 19-day moving average,
    
5. Sell if the stock’s simple 9-day moving average crosses below its simple 20-day moving average,
    
6. Sell if the stock’s simple 10-day moving average crosses below its simple 20-day moving average,
    
7. Sell if the stock’s simple 4-day moving average crosses below its simple 18-day moving average,
    
8. Sell if the stock’s simple 5-day moving average crosses below its simple 18-day moving average,
    
9. Sell if the stock’s simple 4-day moving average crosses below its simple 20-day moving average,
    
10. Sell if the stock’s simple 5-day moving average crosses below its simple 20-day moving average,
     
11. Sell if the stock’s simple 5-day moving average crosses below its simple 9-day moving average,
     
12. Sell if the stock’s simple 4-day moving average crosses below its simple 9-day moving average,
     
13. Sell if the stock’s simple 4-day moving average crosses below its simple 10-day moving average, 
     
14. Sell if the stock’s simple 5-day moving average crosses below its simple 10-day moving average, 
     
15. Sell if the stock’s exponential 7-day moving average crosses below its exponential 13-day moving average,
     
16. Sell if the stock’s exponential 7-day moving average crosses below its exponential 14-day moving average.

We wanted to avoid "curve-fitting."  That is, we wanted to test these strategies over a wide range of stocks representing a variety of industries and market sectors.  Also, we wanted to test over a variety of market conditions.  Therefore, we tested the strategies on each of about 3000 stocks over a period of about 9 years (or over the period during which the stock has traded if it has traded for less than 9 years), factoring in commissions but not "slippage."  Slippage results when the sell order is for $30 but the price at which the sale is executed is $29.99.  In this case, the slippage would be one penny a share.  The same "buy" strategy was consistently used for each test.  The only variable was the rule for selling.  For each strategy, we totaled the returns on all stocks.  We performed a total of 47,312 tests.

The various sell systems are arranged below in order of their profitability.  The left column is the short moving average and the middle column is the long moving average.  The sell signals were generated when the short average crossed below the long average.  The right column is the total profitability for all stocks tested.  The key item of comparison is not the actual magnitude of gain for each sell system.  This would vary considerably with different "buy" and "sell" system combinations.  We were not testing for the profitability of any complete system, but for the relative merit of the various "sell" systems in isolation from their respective optimum "buy" disciplines.  As you can see from the table, selling when the 9-day moving average crossed below the 18-day moving average was not as profitable as selling when the 10-day moving average crossed below the 20-day moving average.  Donchian’s 5-day moving average cross of the 20-day average was also more profitable than the 9-day average cross of the 18-day average.  All tests were identical.  The only variable was the combination of moving averages selected.

This study supports the notion that a triple moving average system based on the 5-, 10-, and 20-day moving averages is likely to be more profitable than the similar 4-, 9-, 18-day moving average combination.  It has the additional advantage of enabling us to monitor the crossing of the 5-day moving average with the 20-day moving average.  The latter is Donchian’s system, and it is a strong system in its own right (the table above shows it is superior to the 9-day cross of the 18-day average.  It also gives earlier signals than either the 9-18 or the 10-20 combinations, though the 10-20 combination tends to generate higher average returns).  Therefore, including the 5-, 10-, and 20-day moving averages on our charts gives us an additional option.  We can use the 5-, 10-, and 20-day triple moving average system or we can use Donchian’s 5-, 20-day dual moving average system.  If the stock pattern does not look or "feel" right to us, the 5-day moving average cross will give us an earlier exit.  Otherwise, we can wait for the 10-20 crossover.  Either will likely give a more profitable signal than the 9-, 18-day combination.  The decision of which to use can be based on separate considerations related to stock behavior.

Copyright 2009, by Stock Disciplines, LLC. a.k.a. StockDisciplines.com