The probability of making an overall loss when blindly following a technical trading model is estimated by testing the mean of the single rates of return against zero (only if it is negative does the trading rule produce an overall loss).[10]
In the next two sections I report how the 2580 models would have performed in the S&P 500 market, first based on daily data and then based on 30 minute-data.
3. The performance of technical trading systems based on daily stock prices
Table 1 classifies all models according to their performance as measured by the t-statistic into five groups and quantifies the components of profitability for each of them. When trading in the S&P 500 spot market between 1960 and 2007, 8.6% of all models achieve a tstatistic greater than 3 and the average gross rate of return per year over these models amounts to 8.3%. The t-statistic of 25.8% of all models lies between 1.0 and 3.0, 31.1% generate a t-statistic between 0.0 and 1.0 and 34.4% of all models are unprofitable (t-statisticb0.0).
As regards the pattern of profitability, the following observations can be made. First, the number of profitable positions is always smaller than the numberof unprofitablepositions. Second, the average returnperday duringprofitablepositions is lower thanthe averagereturn (loss)during unprofitable positions (the average slope of price movements during the-relatively longer lasting-profitable positions is flatter than during the short lasting unprofitable positions). Third, the average duration of profitable positions is several times greater than that of unprofitable positions. This pattern characterizes technical trading in general (Schulmeister, 1988, 2002, 2008a,b): The profits from the exploitation of relatively few persistent price trends exceed the losses from many small price fluctuations (“cut losses short and let profits run”).
Table 1 shows alsothe performance of the 2580 trading systems over 5 subperiods since 1960. It turns out that the average gross rate of return has almost continuously declined in the S&P 500 spot market from 8.6% (1960/71)to2.0%(1972/82),−0.0%(1983/91)andfinallyto−5.1%(1992/ 2000) and −0.8% (2001/07), respectively. A similar result is reported by Sullivan, Timmermann, and White (1999), and—for currency markets— by Olson (2004), Neely et al. (2008) and Schulmeister (2008a, b).
The 2580 trading systems are also unprofitable on average when trading S&P 500 futures based on daily data between 1983 and 2007— they produce an average rate of return of 3.7% per year (Table 2). This performance is worse than in the S&P 500 spot market over the same period (GRR: −2.1%). This difference is mainly duetothestrongincrease in stock prices between 1983 and 2000. Under this condition technical models hold long positions for a longer time span as compared to short positions. At the same time the return from holding a long position in stock index futures is lower than from holding stocks in the spot market if the rate of interest exceeds the dividend yield (as has been the case).
The pattern of profitability (i.e., the relations between its components) is the same in the S&P 500 futures and spot market. As in the spot market the best performing models are those which specialize on the exploitation of short-term stock price trends (Tables 1 and 2).
This pattern implies that “underlying” price trends occur in the stock index futures markets more frequently than could be expected under a random walk. However, this non-randomness cannot be profitably exploited by technical models due to the too frequent “jumps” of daily futures prices causing low ratios between the number of profitable and unprofitable positions as well as between the average return per day during profitable and unprofitable positions.
Уважаемый посетитель!
Чтобы распечатать файл, скачайте его (в формате Word).
Ссылка на скачивание - внизу страницы.