2580 models. However, the riskiness of technical trading rises when traders engage in what can be called “model mining”. If a trader searches for the “optimal” system out of a great number of different models on the basis of their past performance, then he might suffer substantial losses out of sample if its abnormal profitability in sample occurred mainly by chance (see Section 5).
The closepositive correlation between the gross rate of returns of the models and the t-statistic of the means of their single returns implies that the return-risk-relation (risk in the sense of the probability of making an overall loss) rises with the overall profitability of the models (Fig. 4).
The second source of risk of technical stock trading concerns the fact that every technical model produces sequences of (mostly) unprofitable positions which accumulate substantial losses over the short run. These losses might prevent a trader from stickingto a certain rule over the long run (the occurrence of “whipsaws”-price oscillations around a more or less constant level—is the most important single reason for why technical models produce nearly always substantially more single losses than single profits—see Tables 1 to 3 and Fig. 5).
When trading S&P 500 futures based on 30-minutes-data, the momentum models and the RSIN models (GRR: 8.1% and 9.5%, respectively), perform better than the moving average models (GRR: 6.8%— Table 3). The contrarian rules SG 4 to SG 6 are almost twice as profitable than the trend-following rules SG 1 to SG 3 (average GRR: 9.1% and 6.8%, respectively). Due to the frequent transactions involved in trading based on intraday data the net rate of return is roughly 41/2 percentage points lower than the gross return. This difference is greater in the case of contrarian trading rules as compared to trend-following rules since the former “specialize” on the exploitation of very short-term price runs and, hence, generate more transactions than trend-following systems.
Over the entire period between 1983 and 2007 almost all of the 2580 technical models are profitable, 97.3% of them produce a positive gross rate of return (Table 3).
Table 4 classifies all models according to the t-statistic into 5 groups. 29.3% of the models achieve a t-statistic greater than 3.0, their average gross (net) rate of return amounts to 12.5% (5.7%) per year. 29.6% of the models achieve a t-statistic between 2.0 and 3.0, they produce a gross (net) rate of return of 7.3% (3.0%) per year. Hence, 58.9% of the trading systemsproduceagrossrateofreturnsignificantlygreaterthanzeroover the entire sample period of 25 years. This result can hardly be reconciled with the hypothesis of (weak) efficiency in the S&P 500 futures markets given the great number of different models investigated.
The characteristic patternof profitabilityof technical tradingsystems is as follows (Tables 1 to 4):
• The number of profitable positions (NPP) is lower than the number of unprofitable positions (NPL).
• The average return per day during profitable positions (DRP) is smaller (in absolute terms) than the average return per day during unprofitable positions (DRL).
• The duration of profitable positions (DPP) is several times greater than the duration of unprofitable positions (DPL).
TheFigs. 5,6and7showthedistributionof the2580technicalmodels by the ratios of the three profitability components, i.e., by the ratios NPP/ NPL, DRP/DRL, and DPP/DPL (the means of these ratios describe the characteristic profitability pattern of technical trading systems).
Profitable positions occur on average 35% less frequently than unprofitable positions. Fig. 5 shows that cases where the number of profitable trades exceeds the number of unprofitable trades almost never occur. Also the daily return during profitable positions almost never exceeds the return during unprofitable positions. On average the former is by 33% lower than the latter (Fig. 6).
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