MA trading rules make use of one or two moving averages. A special case is the single crossover MA trading rule using the price series itself and a MA of the price series. If the price crosses the MA upward (downward) this is considered as a buy (sell) signal. The double crossover MA trading rule on the other hand uses two moving averages, a slow one and a fast one. The slow MA represents the long run trend and the fast MA represents the short run trend. If the fast MA crosses the slow MA upward (downward) a buy (sell) signal is given. The signal generating model is given by6
|
|
| Post+1= 1, |
if MAtk > MAtn |
| Post+1= Post, |
if MAtk = MAtn |
| Post+1=-1, |
if MAtk < MAtn, |
|
where
k<
n and
Post+1=-1, 0, 1 means holding a short, neutral respectively long position in the market in period
t+1.
We call the single and double crossover MA rules described above, the basic MA trading rules. These basic MA rules can be extended with a %-band filter, a time delay filter, a fixed holding period and a stop-loss. The %-band filter and time delay filter are developed to reduce the number of false signals. In the case of the %-band filter, a band is introduced around the slow MA. If the price or fast MA crosses the slow MA with an amount greater than the band, a signal is generated; otherwise the position in the market is maintained. This strategy will not generate trading signals as long as the fast MA is within the band around the slow MA. The extended MA model with a b · 100% filter is given by
|
|
| Post+1= 1, |
if MAtk > (1+b)MAtn |
| Post+1= Post, |
if (1-b)MAtn ≤ MAtk ≤ (1+b)MAtn |
| Post+1=-1, |
if MAtk < (1-b)MAtn. |
|
According to the time delay filter a signal must hold for
d consecutive days before a trade is implemented. If within these
d days different signals are given, the position in the market will not be changed. A MA rule with a fixed holding period holds a long (short) position in the market for a fixed number of
f days after a buy (sell) signal is generated. After
f days the market position is liquidated and a neutral market position is held up to the next buy or sell signal. This strategy tests whether the market behaves different in a time period after the first crossing. All signals that are generated during the fixed holding period are ignored. The last extension is the stop-loss. The stop-loss is based on the popular phrase: ``
Let your profits run and cut your losses short.'' If a short (long) position is held in the market, the stop-loss will liquidate the position if the price rises
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