The sensitivity of the average will depend upon the time period chosen. Short periods will be highly sensitive, long periods less so. A sensitive moving average will capture every move and enter and exit a trend sooner. A long period will have fewer trades, but enter and exit a trend late. But even if our system is a winner, if the probability of a win is low, then the typical trader will have difficulty following it. Many losses will need to be absorbed before the big gain occurs, and it is tough for anyone to stay the course.
By way of example, consider the weekly close of the cash S&P index beginning in January 1970 through Dec. 10, 2010, a data set of 2,137 weeks. The index starts at 92.40 and ends at 1240, a net gain of 1,148 points. For any system to beat a buy and hold strategy, it must earn more than those 1,148 points. As observed in "S&P 500 Data: Three Ways to Profit" (February 2010), the S&P cash index had a high closing price of 1561.80 on Oct. 8, 2007, so our perfect "two-trade" system would buy in January 1970 at 92.40 and sell at 1,561.80. Then we would be short at 1,240. This hypothetically would yield 1,790.80 S&P points, buying at the low and selling at the high. The 1,148 serves as a benchmark and the 1,790.80 as an ideal target. We shall consider any system that produces 65% of our ideal, or 1,164 points of profit, as successful.
We’ll build a 15-week simple moving average and apply a simplistic filter to determine buy/sell points. Recent price action can be seen in "Weekly average" (below). We will go long the S&P when the weekly cash price closes above the moving average for the second consecutive week. We will reverse and short the index when price closes the week below the moving average on the second consecutive week.
Over the 41-year period, our rudimentary system traded 173 times, including its current open trade. It realized 606.94 S&P points, for an average gain of 3.508 points per trade, not including any slippage. The best gain was 503 points, and the worst loss was 181.37 points.
Although this is a winning system because it produces a positive expected value based on the 3,034 points realized on winning trades, it is not a good system. Only 46 of the 173 trades were winners, for a probability of 26.58%. A trader would have to withstand three losses for every four trades; that is enough to frustrate even the most die-hard trader. At that rate, a trader could expect long streaks of losing trades.
The system works well during trending periods, but is subject to numerous whipsaws during times where the S&P essentially is flat. The worst loss string is eight consecutive for a total loss of 613.95 points between Aug. 30, 1999, and Sept. 18, 2000, when the S&P was priced at about 1400. In 1991 and 1992, the system suffered 11 losses in a row, losing 128.34 points when the S&P traded around the 400 level. Ironically, we can conclude from our results that the S&P spent about 30 of the 40 years trading sideways.
Another problem is one of decision error. Because today’s moving average is a function of today’s close, we cannot know the accurate value until the close occurs, which makes it more difficult to execute a correct trade when the close is near the average. Our goals are to see if we can filter out the pesky whipsaw trades because these increase our cost of trading and reduce our probability of winning. As such, they simultaneously reduce the chance of an error trade based on computational issues.