Rather than just displaying the relationship in a graphical way, so-called contratrend indicators try to quantify the relationship between High, Low and Close prices in order to generate a clear trading signal7. The Stochastics, introduced by William Lane (1991), is a good example of such an indicator. It derives a trading signal using the following formula:
(1)
where Ct is today’s close, Htmax biggest high of a certain moving period, n, and Lt min is corresponding lowest low for the same period. Having established these values, %K generates a signal which can take on values between 0 and 100.
A common practice among technical analysts is to calculate Ht max and Ltmin over the last 14 periods and Ht max - Lt min denotes the so-called trading range or spread of a given period and can be interpreted as a basic measure of volatility. Crucio and Goodhard (1992) define trading range as “(...) the price range within which an asset has traded in the past and (which) can be characterised by the maximum and minimum of the series (of various length) of latest prices.” The term Ct - Lt min defines the upward potential of a given trading range.
The Stochastics thus weight the upward potential of a given period with the volatility of that period. %D represents a smoothed version of %K, where the smoothing factor used is normally 3 periods. The Stochastics can be traded in many different ways8. Since the actual trading techniques used are not of interest in this study the reader is referred to the literature on Technical Analysis. (e.g. Murphy 1986). For our purposes it is simple worth noting that the Stochastics is commonly interpreted as a so-called overbought-undersold indicator. The idea behind overbought-undersold indicators is closely linked to the concept of the trading range.
The boundaries of the trading range, given by the maximum and minimum of that period, represent temporary support and resistance levels9. For example, DeGrauwe and Decupere (1992) use 11 years of daily exchange rate data for USDDEM and USDJPY to show that certain price levels which coincide with round numbers, such as 1.500 for USDDEM or 100.00 for USDJPY, represent psychological barriers that might initiate buying or selling activity and hence act as substantial support and resistance levels10
Since the Stochastics measure the trading range over a moving period, it should be possible to capture the trading activity over time fairly well. The implication of the overbought / undersold indicators is once the exchange rate comes close to the extremes of the range, a reversion to the centre of the trading range is expected. Stochastic values between 70 and 100 are considered as indicating an overbought situation; that is, currency A has appreciated rather sharply against currency B and now a correction of this "exaggerated" price movement is expected.
Stochastic values below 30 are considered as undersold. Both regions have the implication of the expectation of a change in the direction of the price movement. Due to the set up of the Stochastics, values between 30 and 70 correspond to an exchange rate movement close to the middle of the range and therefore no change in the exchange rate is expected. When trading the Stochastics as an overbought-undersold indicator, the exchange rate can be seen as a form of mean-reverting process. However, the mean does not correspond to the absolute sample mean but to the average of the periodic extremes, thus taking the concept of temporary support and resistance levels into consideration.
By setting %K =50 in (1) and re-arranging yields:
Ht max -Lt min = 2(Ct - Lt min). (2)
Adding Lt min twice to both sides of the equation and re-arranging yields:
Ct = 0.5(Ht max + Lt min) = 0.5 Ht max + 0.5 Lt min,
or
Ct - 0.5 Ht min - 0.5 Lt min = 0, (3)
which translates into vector form as:
(1,-0.5,-0.5,0). (3')
The Stochastics thus establish a structural relationship between today’s Close and the Maximum and Minimum price of a moving period, measured as the highest High and lowest Low. This structural relationship represents a testable hypothesis and we demonstrate in the next section that it is possible to identify a long-run relationship in the exchange rate data that comes close to the empirical counterpart.
By incorporating this cointegrating relationship into short-run dynamic models we are then able to present out-of sample forecasts based on the dynamic representation of the exchange rate system. We take a good forecasting performance of our model as an indication that Technical Analysis methods can be thought of as capturing any latent Granger causality that exists in the data.
7 Since the trading algorithm of the Stochastics can be quantified, and its predictive power can be investigated using formal statistical method, the signals generated by the Stochastics qualify as Markov times and thus represent well defined forecasts in the sense of Neftci (1991).
8 A more complex way to trade Stochastics is to apply the same technique as described for a moving average cross-over (see e.g. Schulmeister 1987). The intersects between %K and %D are then consequently interpreted as buy and sell signals. A trading signals is considered most powerful, when is corresponds with the overbought-undersold indication of the Stochastics, i.e. when a sell signal occurs in the overbought region and a buy signal in the oversold area.
9 Edwards and Magee (1966, p.211) provide a definition of support and resistance that link support and resistance to supply and demand and thus selling and buying activity of speculative assets.
10 Many other ways to determine support and resistance levels can be found in the technical analysis literature. However, all have the common property that, once established, they coincide with local maxima and minima and thus confine the trading until enough buying or selling interest is gathered in order to break through the upper or lower boundary of the present trading range and then consequently establish a new trading range, where - in the case of a break-out through the top of the trading range - former top levels (resistance levels) will now become new bottom levels (support levels). (see Edwards and Megee, 1966, p.213)
Prof. Ronald MacDonald, Prof. Norbert Fiess
Next: Data Sources and Preliminary Statistics
Summary: Index