holding period. The second column lists the mean daily excess return of the strategy on a yearly basis, that is the mean daily return times the number of trading days in a year, which is set to 252. The third column lists the mean daily excess returns of the trading rules net of 0.1% transaction costs, with the t-ratios beneath these numbers. The t-test statistic tests whether the mean daily excess return is significantly different from zero under the assumption of iid returns. The fourth and fifth column list the number of days classified as a buy or sell day. The number of buy and sell trades is listed beneath these numbers. The sixth (seventh) column list the total number of days buy (sell) trades with a strictly positive excess return last, as a fraction of the total number of buy (sell) days. The fraction of buy and sell trades with a strictly positive excess return is listed beneath these numbers. The eight and ninth column list the mean daily return of the data series itself during buy and sell days. T-ratios to test whether the mean daily return during buy and sell days is significantly different from zero are listed beneath these numbers. In this way we can detect whether the data series itself rises during buy days and declines during sell days. The last column lists the differences between the mean daily buy and sell returns and the corresponding t-ratios, which test whether the mean daily buy return is significantly different from the mean daily sell return. These t-ratios are computed as
where
rB and
rS is the mean return of the data series during buy and sell days, and
SB and
SS is the standard error of the mean buy and sell return. This test statistic is not Student-t distributed. Satterthwhaite (1946) derived an approximation for the degrees of freedom, so that the critical values from the t-table can be used. If the number of observations is sufficiently large this test statistic will have a limiting standard normal distribution.
Notice that Brock et al. (1992) in fact do not use the correct t-test statistic, as derived in footnote 9, page 1738. To test whether the mean daily return of the DJIA during buy and sell periods is significantly different from the unconditional mean daily return it is assumed that returns are iid distributed and the following t-statistic is used:
where µ
k is the mean return during buy or sell periods,
Nk is the number of buy or sell days, µ is the mean market return, σ
2 is the variance of the daily returns and
N is
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