A Source of Bias in Filter Tests of Share Prices

READERS of this Journal have been kept well informed on research into the statistical nature of share prices.' One recent contribution by Eugene F. Fama and Marshall E. Blume (F and B) constitutes perhaps the most exhaustive analysis in the use of filter rules in determining the extent of the dependence in successive observations of changes in daily share prices.2 Statistical tests applied to share price series have frequently supported the random walk hypothesis by being unable to detect significant serial correlations or significant runs of price changes.3 Filter analysis approaches the problem somewhat differently.4 Can trading rules be formulated which exhibit significant profits? Briefly, filter rules are mechanical trading rules which determine the dates of buying and selling shares. The F and B rules work roughly as follows: an x percent filter rule initiates long (short) trading as soon as the price rises (falls) by x percent; as each day's closing price becomes available it is examined to see whether the position should be closed (and an opposite position immediately adopted) or held. In the latter case, it is also necessary to decide whether to change the reference point from which percentage changes are computed.5 In applying this rule to approximately five years of daily prices for each of the thirty securities which comprise the Dow-Jones Industrial Average, F and B computed the profitability in the form of a rate of return. Ignoring adjustments for dividends, commissions, etc., their rate of return calculation reduces to the following: if po is the price at which a transaction (long or short) is initiated, and pi the price at which it is concluded, then the rate of return of the transac-