[7] Slippage costs are incurred if the price moves unfavorably between signal generation and trade execution. These costs are estimated under the (realistic) assumption that in electronic futures exchanges orders are executed within 10 s. An analysis of the S&P 500 futures tick data shows that the mean of the price changes within this interval is 0.02% of contract value. I assume that the price moves always unfavorably when profitable trading signals are produced (40% of all trades), and that there is an equal chance that the price moves favorably or unfavorably in the case of unprofitable trading signals (hence, it is assumed that in 60% of all trades no slippage costs occur). Under these assumptions one arrives at estimated slippage costs of roughly 0.008% (0.02⁎0.4).
[8] This assumption is certainly unrealistic as regards trading stock index futures in the more distant past (when electronic exchanges did not exist yet), and it is even more unrealistic as regards trading the stocks comprised by the S&P 500 in the spot market. However, in order to keep the results comparable across markets and time periods the calculations operate with this assumption in all cases.
[9] When calculating these components, all those transactions are neglected which are only caused by switching futures contracts (these transactions are, however, taken into account when calculating the net rate of return), e.g., if a daily model opens a long position on June 2 (and, hence in the June contract), switches to the September contract on June 10, and closes the position on June 22, then DPP is calculated as 20 days.
[10] The t-statistic of the means of the single returns measures their statistical significance and, hence, estimates the probability of making an overall loss when following a specific trading rule. The t-statistic is therefore conceptually different from the Sharpe ratio which measures the univariate risk-return relation. As the number of observations goes to infinity, an estimated t-statistic will go to zero or to positive or negative infinity. By contrast, an estimated Sharpe ratio will converge to the true Sharpe ratio (I owe this clarification to one referee). However, in the context of the present study (with finite samples) the informational content of the t-statistic and the Sharpe ratio is equivalent. This is so because the t-statistic differs from the Sharpe ratio only by the factor pnffiffiffiffiffiffiffiffiffiffiffiffiffi− 1 (where n is the sample size) and by the risk-free rate.
[11] Two observations are in favor of the second hypothesis (Table 1). First, the profitability of technical stock trading based on daily data has primarily declined due to a decline in the ratio of the number of profitable positions to the number of unprofitable positions, namely from 0.78 (1960/71) to 0.51 (1992/2007). This decline
[12] Standard software for technical trading provides the user with the option to select the width of the preferred interval, usually ranging from 1 min to 1 h.
[13] Such a shift to using data of ever higher frequencies when applying (automated)
[14] fitability of technical trading from
The alternative explanation of the shift in the pro daily data to higher frequency data should not be considered a “special case” of the AMH. This is so because such a shift would by no means reflect a process by which markets become gradually more efficient. Traders would still base their decisions on the information contained in past prices. Such a behavior contradicts the assumption of rational expectations and—if profitable—the assumption of weak market efficiency.
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