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2.2 Technical Trading Rules
In this paper, technical analysis we adopt can be categorized into two groups, the first group is the technical analysis without the information of the market volatility, and the second one, in contrast, consolidates the market volatility to form the new moving average system. Each group of rules is explained below.
2.2.1 Static Trading Rules
For the first group, we consider five types of trading rules: filter, moving average, support and resistance (trading range break), channel breakout, and momentum strategies. These five types of rules are very popular among the practitioners on financial markets and have already drawn a lot of discussion in the literature. For the parameter values of each type of rules, we select a fairly large variety that has been applied in Sullivan et al. (1999), Hsu and Kuan (2005), and Qi and Wu (2006).
Technical trading rules, even having different mechanisms or forms, are to identify a trend reversal at a relatively early stage and then ride on that trend until there exists evidence showing that the trend has reversed. A filter rule generates a buy (sell) signal when today’s closing price rises (falls) by x % above (below) its most recent low (high). The moving average rule uses n-period previous prices, including today’s price, to calculate an average value. It generates a buy (sell) signal when the n-period shorter moving average moves above (below) the m-period longer moving average.
The support and resistance (trading range break) rule involves buying (selling) when the closing price rises above (falls below) the maximum (minimum) price over the previous n pe-riods. The channel breakout rule is quite similar to the support and resistance rule. It uses the maximum and minimum price over the previous n periods to construct the channel with one limitation that is the difference between the maximum and minimum price should be within x. The channel breakout rule involves buying (selling) when the closing price moves above (below) the channel.
The momentum strategy we adopt is the momentum strategy in volume. The momentum
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strategy in volume has been widely analyzed in the literature. Momentum strategy’s signals are determined by the oscillator and the overbought/oversold level k. It generates a buy (sell) signal as the oscillator crosses the overbought (oversold) level from below (above).
2.2.2 Dynamic Trading Rule
VMA rule In 1992, Chande proposed a variant of the moving average system, the VMA rule. The main reason that Chande proposed this rule is that the existing technical trading rules are static and not responsive enough to the changing nature of markets. Static trading rules, by the definition, are the rules that do not change the length of the historical data used for forecast future price movement. For example, an n-length simple moving average strategy means that market practitioners at each time use fixed n-length of the historical data to calculate one moving average value, and then make trading decisions based on these calculations.
The market is dynamically evolving with continuous changes; therefore, static trading rules with fixed length of data used in detecting the emergence of new trends may not work all the time. For instance, consider two simple moving averages, a shorter moving average and a longer moving average. If the market is trending, making big moves in up or down direction, the shorter moving average will response more quickly than the longer one since it gives more weight to latest data and then may generate signal earlier. If the market, on the other hand, is ranging on which price trades in a narrow range without any trend, the shorter moving average will tend to produce numerous false trading signals due to its’ great proportion of more recent data, but the longer moving average desensitizes small erratic price movement and will generate fewer or no false signals.
Due to the continuous changes in the market, Chande introduces a trading rule that can adapt itself to the market condition becoming a shorter moving average as the market is trending and automatically changing into a longer one when the market is ranging. He constructs the VMA rule by revising the exponential moving average as follows:
EMAt= αPt+ (1 − α)EMAt−1, (1)
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α = 2
N + 1, (2)
Here, EMAtis the exponential moving average value at time t, α is the numerical constant, N is the effective length of historical data used to calculate the exponential moving average value, Pt is the closing price at time t. Equation (1) is the traditional exponential moving average in which α is referred as the smoothing parameter describing the weight that the exponential moving average gives to the more recent data. As the smoothing parameter α increases (N decreases), the exponential moving average adopts less length of historical data and has a greater proportion of the latest data; therefore, it will trace the market price more closely. In contrast, as α decreases (N increases), more length of historical data is considered, greater weight is given to the more distant data and the gap between the exponential moving average and the current price will increase.
Since α is a constant and fixed term, it does not adjust to the changing nature of market in advance. Therefore, Chande improves the smoothing parameter of the exponential moving average from constant to continuously variable by tying it to a market-related variable as below:
VMAt= α∗tPt+ (1 − α∗t)VMAt−1, (3)
α∗t = αVRt, (4)
VRt= σtn
σreft , (5)
In Equation (3), VMAt is the variable moving average at time t, and the smoothing parameter here is α∗t, which is variable, consists of the constant term α and the market variable VRt. VRt is the market volatility ratio viewed as a market variable and is formed by σnt and σreft . σtnis the standard deviation of closing prices over past n periods at time t, σtref is the reference standard deviation of closing prices over some period of time longer than n at time t.
The value of the market volatility The most important part in the VMA rule is the market volatility ratio, VRt. It is constructed in order to detect the market condition: the price action
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is heating up or cooling down. It acts as the automatically adjusting device for choosing more suitable effective length of the historical data. The key idea of Chande’s VRtis that if the market is active with the trend, making big moves in up or down direction, the market price will change largely. Whether the market price changes largely or not might be measured by the standard deviation of closing prices, and a reference standard deviation is needed to tell us whether the observed standard deviation is too high or too low. Thus Chande attempts to use the ratio of σtn to σtref as the proxy of the market condition.
The information of the market volatility makes the VMA a more responsive and smarter indicator than the exponential and the simple moving average. Consider the following three situations. First, if σtn is greater than σreft , that is VRt > 1, it implies that the market price over the past n periods changes more largely than before because traders over the past n periods adjust rapidly to new information. Since VRt > 1, the VMA will take a larger bite of the new data Ptand the effective length of the average decreases. Then the VMA will generate an earlier signal under the moving average crossover decision model. In the second situation in which σtn is smaller than σtref (VRt < 1), market price over the past n periods moves in a narrow range due to no influential or new information on the market. When VRt < 1, the VMA takes a smaller bite out of the new data, and the effective length of the average increases. Thus the VMA will generate fewer false signals. In other words, the VMA will automatically become a shorter moving average or change into a longer one based on whether the market is active or not. Third, the VMA will become the exponential moving average when VRt = 1 and the effective length of moving average will be determined only by the constant term, α.
The trading strategies in the VMA For the trading strategies in the VMA, Chande mentions that all the conventional strategies with the moving average system can be extended in the VMA.
The most popular trading strategies is the moving average crossover decision model as follows:
1
1For the parameter values of the VMA, the settings in Chande (1992) and Chande (1994) are adopted. We also consider the suggestions of some professional traders from the websites of professional trading companies.
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Buy when current price (shorter VMA) moves above the VMA (longer VMA).
Sell when current price (shorter VMA) moves below the VMA (longer VMA).