Returns on Filter Rule Strategies

Results of Study

The only filter rule that beats the returns from the buy and hold strategy is the 0.5% rule, but it does so before transactions costs. This strategy creates 12,514 trades during the period which generate enough transactions costs to wipe out the principal invested by the investor.

While this test is dated, it also illustrates a basic problem with strategies that require frequent short term trading. Even though these strategies may earn excess returns prior to transactions costs, adjusting for these costs can wipe out the excess returns.

Relative Strength Rules

A variant on the filter rule is the relative strength measure, which relates recent prices on stocks or other investments to either average prices over a specified period, say over six months, or to the price at the beginning of the period.

Stocks which score high on the relative strength measure are considered good investments.

This investment strategy is also based upon the assumption of price momentum.

Runs Tests

A runs test is a non-parametric variation on the serial correlation, and it is based upon a count of the number of runs, i.e., sequences of price increases or decreases, in the price changes. Thus, the following price changes, where U is an increase and D a decrease would result in the following runs:

UUU DD U DDD UU DD U D UU DD U DD UUU DD UU D UU D

There were 18 runs in this price series of 33 periods.

The actual number of runs in the price series is compared against the number that can be expected in a series of this length, assuming that price changes are random.

There are statistical tables that summarize the expected number of runs, assuming randomness, in a series of any length.

• If the actual number of runs is greater than the expected number, there is evidence of negative correlation in price changes.

• If it is lower, there is evidence of positive correlation.

Studies of Price Runs

A study of price changes in the Dow 30 stocks, assuming daily, fourday, nine-day and sixteen day return intervals provided the following results -

Based upon these results, there is evidence of positive correlation in daily returns but no evidence of deviations from normality for longer return intervals.

Long strings of positive and negative changes are, by themselves, insufficient evidence that markets are not random, since such behavior is consistent with price changes following a random walk. It is the recurrence of these strings that can be viewed as evidence against randomness in price behavior.

Prof. Aswath Damodaran