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'"jennergren and Korsvold [130) found 338.2 runs per stock over a period when uncorreiated returns would have led to 394.6.

One price pattern that has frequently been hypothesized for price movements is depicted in Figure 17.1. The argument behind this figure proceeds as follows. As long as no new information enters the market, the price fluctuates randomly within the two barriers around the "fair" price. If the actual price differs too much from the "fair" price, then "professionals" will step in and purchase or sell the security. This will keep the security price within the security price barriers. However, if new information comes into the market, then a new equilibrium price will be determined. If the news is very favorable, then the price should move up to a new equilibrium, well above the old price. Investors will know that this is occurring when the price breaks through the old barriers. If investors purchase at this point, they will benefit from the price increase to the new equilibrium level. Similarly, if bad news concerning the company is forthcoming, the stock will drop to a new equilibrium level. If investors sell the stock as it breaks the lower barrier, they will avoid much of the decline. If they sell the stock short as it breaks through the barrier, they will benefit from the decline. This argument is intuitively appealing; it is closely analogous to the idea of control charts and is put forth as an appropriate investment strategy by many who believe price series can be used to make superior profits. The strategy is called a filter rule. The filter rule is usually stated in the following way: Purchase the stock when it rises by X% from the previous low and hold it until it declines by Y% from the subsequent high. At this point, sell the stock short or hold cash.

Filter rules are a timing strategy. They show investors when they should be long in a security and when they should sell it short. The alternative to timing is to buy and hold the security. Thus, filter rules are analyzed by comparing them to a buy and hold strateWjjL,,.

The most extensive tests of filter rules were performed by Fama and Blume 178f. Table J7.5 reproduces their major results. The numbers under the letter F are the returns using the filter rule; the numbers under the letter B are returns from the buy and hold strategy. The only filter that showed a profit was a filter of 0.5%. However, Fama and Blume show

Figure 17,1 Security price and time.

11A number of tests of filter rules have analyzed returns during periods of market decline. During these periods, any rule that randomly caused the investor to sell a security and hold cash or go short should, on average, outperform a buy and hold strategy, at least before transaction costs are considered. The filter rule is purported to be a rule that utilizes past price behavior to lead to superior timing. It is important (if the rule is tested during periods of price decline) to determine that the rule outperforms a rule that randomly causes an investor to sell the security.

elsewhere in their article that the long purchases were profitable for filters of 1% and 1.5%. The average profits on each trade were very small, but, over long periods of time, they substantially outperformed buy and hold strategies. However, even with small transaction costs, these strategies are unprofitable. The profitability of these very small filter rules is consistent with a slight positive correlation of security price changes and is consistent with the evidence discussed earlier.

Jennergren and Korsvold [130] found some of the highest correlation coefficients of any investigators when they examined the lightly traded Norwegian and Swedish stocks. The relatively high correlations suggest that these securities are prime candidates for profitable filter rules. Jennergren examined filter rules for these securities. Norwegian and Swedish stocks cannot be sold short so that the alternative to holding securities long was to invest in a savings account. Some of the filter rules outperformed a buy and hold strategy. When taxes and transaction costs were considered, however, only the Queen (the only tax-exempt investor) had any prospects of making a profit.

We have examined one type of filter rule that purports to aid in timing decisions. We could test other types that suggest trades on the basis of alternative price patterns. Indeed, technical analysts are fond of talking about such things as head-and-shoulder patterns and Other esoteric perceived price phenomena. But there is no evidence that trading on the basis of any of these patterns can lead to an excess profit. Rather than review other timing models that are based on historic price movements, let us review a system put forth to select stocks based on past price performance.

Relative Strength One of the most popular ways of combining-past price information about securities in order to select stocks is relative strength. An example of a relative strength rule is the one suggested by Levy [154]. Define P.t as the average price over the last 27 weeks for stock j at time t. Further define P-t as the price of the stock at time t. Then, the relative strength of the stock is its current price relative to its average price, or PjtIPjr According to Levy the securities to select are the X% with the highest ratio and they should be purchased in equal dollar amounts. In subsequent periods if the relative strength of a security drops below the relative strength of K% of securities, sell and invest the proceeds m the top X% of the securities. Levy tested a number of values for X and K, with the most profitable being X = 5% and K = 70%.

Note that the relative strength rule causes funds to be invested in securities that have appreciated the most in the recent past. The most risky securities are usually those with the greatest variability of return. This suggests that the group of securities with greatest relative strength is likely to include a predominance of risky securities and the return earned from this investment must be adjusted for risk.

Also note that this rule does not involve the selection of a single security. Rather, it involves the selection of a set of securities. In testing the rule the relevant comparison is the rate of return on the securities that are selected by the relative strength rule adjusted for i isk compared to the rate of return on the full population of securities from which the selection was made.

When Jensen and Bennington [134] tested several relative strength rules (including the one used by Levy and discussed previously), they found that the return after transaction costs for the relative strength rule was no more than the return on the full population. Furthermore, after adjustment for risk, it was inferior to purchasing the full set of securities.

We are continually shown various forms of relative strength rules along with the tests that purport to demonstrate their superiority. Even with the simple rule discussed earlier,

Table 17.5 Comparisoi/ of Ratej; of Return, before Commissions, undesjfeeFilter Technique and under a Buy and Hold Policy

Filter size

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