The quantitative approaches try to isolate trends from nondirectional movements using statistical transformations of past prices. Consequently, these models produce clearly defined buy and sell signals, which can be accurately tested. The most common quantitative trading systems are moving average models, momentum models and the so-called relative strength index. These types of models are tested in the study.
Thefirst type of model consists of a (unweighted) short-term moving average (MASj) and a long-term moving average (MALk) of past prices. Thelengthj of MAS usually varies between 1 day (in this case theoriginal price series serves as the shortest possible MAS) and 10 days, the length k of MAL usually lies between 10 and 30 days (if one uses 30-minutesdata, then MAL would lie between 10 and 30 intervals of 30 min).
The basic trading rule of average models is as follows (signal generation 1/SG1):
Buy (go long) when the short-term (faster) moving average crosses the long-term (slower) moving average from below and sell (go short) when the converse occurs. Or equivalently: Open a long position when the difference (MASj−MALk) becomes positive, otherwise open a short position. If one expresses this difference as percentage of MALk one gets the moving average oscillator:
MAOðj; kÞt = hMASj;t − MALk;t= MALk;tiT100 ð1Þ
This type of representation facilitates a (graphical) comparison of the signal generation between moving average models and momentum models. Another way to express the basic trading rule (SG1) is then: Hold a long position when MAO is positive, hold a short position when MAO is negative.
The second type of model works with the relative difference (rate of change in %) between the current price and that i days ago:
The basic trading rule of momentum models is as follows (signal generation 1/SG1):
Buy (go long) when the momentum M(i) turns from negative into positive and sell (go short) in the opposite case. Or equivalently: Hold a long position when M is positive, hold a short position when M is negative.
The variables MAO(j,k) or M(i) are called “oscillators” because they fluctuate around zero.
The basic trading rule (SG 1) of moving average models and momentum models is trend-following since MAO(j,k)t and M(i)t, respectively, are positive (negative) only if an upward (downward) price movement has persisted for some days (or some 30-minutesintervals). When and how often MAO(j,k)t and M(i)t, respectively, cross the zero line depends not only on the persistence of the most recent prices movements but also on the lengths of the moving averages and the time span i in the case of momentum models, respectively.
The modifications of the basic version of moving average and momentum models use a band with varying width around zero combined with different rules of opening a long, short or neutral position (see, e.g., Kaufman, 1987, chapters 5 and 6). These rules—termed SG 2 to SG 6 in this study—are either trend-following or contrarian.
According to signal generation 2 one opens a long (short) position whenever the oscillator crosses the upper (lower) bound from below (above). When the model holds a long (short) position and the oscillator crosses the zero line from above (below), then the model switches to a neutral position. Fig. 1 clarifies the meaning of this rule by comparing it to SG 1.
Rule SG 2 is “more” trend-following than SG 1 since it opens a long or short position at a later stage of a price trend. At the same time SG 2 is more “cautious” than SG 1 since it always holds a neutral position between switching from long to short and vice versa.
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