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 a variety of moving average-based sell strategies and we are now sharing some of those findings. Richard 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 was highly recommended, it was included in the tests for comparison purposes.
The strategies covered in this particular series of tests were as follows and all involved simple moving averages except where otherwise noted.
Sell if the stock’s 9-day average crosses below its 18-day average,
Sell if the stock’s 10-day average crosses below its 18-day average,
Sell if the stock’s 10-day average crosses below its 19-day average,
Sell if the stock’s 9-day average crosses below its 19-day average,
Sell if the stock’s 9-day average crosses below its 20-day average,
Sell if the stock’s 10-day average crosses below its 20-day average,
Sell if the stock’s 4-day average crosses below its 18-day average,
Sell if the stock’s 5-day average crosses below its 18-day average,
Sell if the stock’s 4-day average crosses below its 20-day average,
Sell if the stock’s 5-day average crosses below its 20-day average,
Sell if the stock’s 5-day average crosses below its 9-day average,
Sell if the stock’s 4-day average crosses below its 9-day average,
Sell if the stock’s 4-day average crosses below its 10-day average,
Sell if the stock’s 5-day average crosses below its 10-day average,
Sell if the stock’s 7-day average crosses below its 13-day average (exponential),
Sell if the stock’s 7-day average crosses below its 14-day average (exponential).
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 idea behind this experiment was to find out which of these sell disciplines achieved the best results most of the time for most stocks. Remember that the profitability of a system that is applied to a single stock (even if this is repeated for 3000 stocks as in our test) does not paint the whole picture. Profitability per unit of time invested is a better way to compare systems. In designing this test, our stockdisciplines.com trader required that each system had to wait for a new buy signal in the particular stock being tested. In real life, a trader could jump to another stock immediately after a sale. Therefore the trader would have little or no “dead time” while waiting to make the next purchase. A system that is less profitable when trading a single stock but that exits a position earlier could therefore generate greater profits over a year by enabling a person to reinvest in a different security as soon as the first one is sold. On the other hand, it would be a poorer performer if it had to wait for the next buy signal on the same stock while another slower system was still holding and making money.
The various sell systems were arranged in order of their profitability. We set up a table in which the left column was the short moving average and the middle column was the long moving average. The sell signals were generated when the short average crossed below the long average. The right column was the total profitability for all stocks tested. However, the key item of comparison was 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. The main points can be briefly stated as follows. Any one of these systems may be the most profitable when trading a particular stock at a particular time. However, this experiment has shown to our satisfaction that selling when the 9-day moving average crossed below the 18-day moving average was generally 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 generally 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 for the selling system.
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. 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
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