FILTER RULES AND STOCK-MARKET TRADING NOTES TO TABLE 1-C where bri 3) is defined as This roundabout procedure for comput- [1+r11292y) g buy-and-hold returns is necessary to in- sure that the buy-and-hold returns cover exactly the same time periods and are com- where u=ri? if the correspond outed on exactly the same basis as the re ing filter transaction is long, and turns under the filter technique if the correspondi Finally, it should also be noted that the filter transaction is short. bR j) are results for the largest filters are probably not the returns reported for the buy- reliable since for these filters the number of and-hold policy(B)in Table 1 transactions is very small. Cf. Table 3 security and filter size, the annual re- policy. The reported returns are vari turns, adjusted for dividends but not for ously adjusted for dividends and for brokerage fees, under both the filter commissions technique and a simple buy-and-hold When commissions are taken into ac- policy. For each security and filter size, count the largest profits under the filter for the perio returns are computed only technique are those of the broker. Only tions are open under the filter rule, which General Foods, Procter Gamble, and requires that multiple buy-and-hold fig- Sears) have positive average returns per ures be reported for each security. The filter when commissions are included a act procedure used to compute the re-(col. [2J). When commissions are omitted, s is discussed in the note to Table 1. the returns from the filter technique(col. Table 1 presents only a small fraction [1]) are, of course, greatly improved but of the results of this study. For example, are still not as large as the returns from returns under the filter technique have simply buying and holding Comparison been computed in many different ways: of the profits before commissions under gross and net of brokerage fees, with and the filter technique(col. [1])and under a without dividends, etc. Since presenting buy-and-hold policy(col. [6]) indicates all the empirical work would require a that, even ignoring transactions costs, small book of tables, we shall be con- the filter technique is inferior to buy-and- strained to concentrate on summary ver- hold for all but two securities: Alcoa and sions of the results-summarized by Union Carbide security and by filter size. Table 1 pre- This last result is inconsistent with sents the most important of the basic re- some of Alexander's latest empirical work sults in full detail, however, and permits 2, Tables 1 and 2]. When commissions the reader to verify conclusions that will are omitted, alexander finds that the fil be drawn from the summary statistics. ter technique is typically superior to a A. ANALYSIS OF RESULTS BY SECURITY buy-and-hold policy, at least for the pe riod 1928-61 a bias in Alexander's com- Table 2 summarizes the filter results putations, however, tends to overstate by security. For each security the table the actual profitability of the filter tech- shows average returns per filter under nique relative to buy-and-hold. This bias both the filter rule and the buy-and-hold arises because using common price in