A comparison of trading rules to test the efficient market hypothesis



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The efficient market hypothesis is one of the widely accepted models for the behavior of stock prices. This hypothesis of stock price, behavior implies that any mechanical trading rule based on a series of past security prices will not perform better than a buy and hold investment strategy. This research tests the efficient market hypothesis by comparing the returns obtained using various trading rules with the results of the buy and hold investment strategy. The trading rules used in this study for comparison with the buy and hold investment strategy are (i) the five percent filter rule, (ii) the ten percent filter rule, and (iii) Zahorchak's trading rules. Filter rule trading decisions are based on changes of at least x percent (x = filter size) in a stock's price. A buy decision is triggered when a stock's price increases by at least x percent from its previous bottom. Conversely, a sell decision is triggered when the price of a stock declines by at least x percent from its previous top. Zahorchak's trading rules are based on the movement of market indices and individual stock prices. Here, five, fifteen and forty week moving averages of the Dow Jones Industrial Average and the fifteen week moving averages of the cumulative advance-decline line are used to time the primary trend of the market. The moving averages (five, fifteen and forty week) of the prices of individual stocks are then used to time, buy and sell decisions. For purposes of the present study, data were collected for weekly closings of market indices, the Federal Reserve Discount Rate, weekly closing prices and the volume of stock traded for twenty-two firms in five industries. The data span a four year period: January, 1973 to December, 1976. This period was selected because it covered periods of bull, bear and uncertain markets. Initially these data were used to compute the returns that would have been realized using the above described trading rules. In simulating the trading: (1) the investor's return was deemed to include both trading gains and dividends, (2) no short sales were allowed, and (3) idle funds were assumed to be placed in a savings account earning interest at five percent per annum, compounded daily. The representative transaction costs were obtained from a brokerage firm for the period studied and adjusted for odd-lot transactions. The results of the study indicate that, when transaction costs were excluded, both the filter rules and Zahorchak's trading rules realized higher returns than a buy and hold strategy. When the transaction costs were introduced, the buy and hold strategy performed significantly better than the filter rules. Zahorchak's trading rules, however, still resulted in somewhat higher returns than the buy and hold strategy, but the differences were not statistically significant at the ten percent level. To analyze further the differences between Zahorchak's trading rules and the buy and hold strategy, the stocks in the sample were divided into two groups: one group of stocks with Beta greater than one and the other with Beta less than or equal to one. The differences between the returns realized using Zahorchak's trading rules and the buy and hold strategy were compared in each of these groups. They were not found to be statistically significant. In the second stage of study, regression models were constructed to predict the stock prices one or more periods hence. The independent variables were lagged prices, moving averages of prices and various dummy variables reflecting Zahorchak's rules. Price changes and the level of market indices were also used as independent variables. The models were constructed for each of the twenty-two stocks. In each case, the previous price was a highly significant variable with the coefficient close to one, as predicted by the random walk model. However, in fourteen of the twenty-two stocks, one or more of the factors in Zahorchak's trading rules appeared as a significant variable. None of the variables consistently appeared in all of these fourteen stocks. In addition, the signs of the coefficients showed no consistent pattern when they did appear. The best performance was by the dummy variable signalling the movement of long term trend of the stock prices. This variable appeared in five of the twenty-two stocks with no sign reversals. Based on these results, the general relevancy of the factors in Zahorchak's trading rules for any randomly chosen stock cannot be substantiated.