Since the persisting profitability of our models could be explained by a risk premium, we go one step further and adjust the profits of the different trading rules for risk. Levich and Thomas (1993) show that the total return from following a trading strategy will overstate the true excess return, if a risk premium is present, especially if currencies exhibit prolonged trends. In order to derive the true excess return, we follow the methodology proposed by Sweeny (1986) and Levich and Thomas (1993), and estimate the risk premium as a constant over the sample period and equal to the returns from a Buy&Hold strategy. Adjusting the risk premium further for the fraction of days we are long in foreign currency (1-f) and short in foreign currency (f), the expected excess return of following a specific trading rule is calculated as: R* = (1-f) RP - f RP.
Levich and Thomas (1993) find that if the percentage of days Long and Short are in a 45-55% range and/ or the Risk Premium is close to zero, a constant risk premium has a negligible effect on the total return. While the estimated risk premium for USDDEM is small with only 0.0205 and not significant (t-value: 0.25), the risk premium for USDJPY is quite high with 0.1625 and borderline significant at the 10% level (t-value:1.60). The fraction of days Long and Short is close to 50% for our model forecast and for the Stochastics Crossover for both currencies.
The expected return of these two trading strategies is therefore close to zero and our earlier results are thus almost unaffected by including a risk premium. However, in the case of USDJPY, matters are quite different for the Stochastics 70/30 and the MA 10/20 model. The clear discrepancy between Long and Short positions demand an adjustment of the total return in these cases. The expected rate of return of the MA 10/20 is 0.036 (annualised: 4.14%), adjusting the annualised rate of return of 6.75% accordingly yields a far lower true rate of return of only 2.61%.
Since, according to Thomas and Levich, the trading models accumulate the risk premium over the fraction of days long and release the risk premium over the days short, the higher fraction of days short (61%) for the Stochastics 70/30 results therefore in an the expected negative rate of return of -0.049 (annualised: -5.2%). The effectively realised rate of return of 5.56% must be viewed within this context.
The expected negative return of the Stochastics 70/30 might actually be explained by a known weakpoint of the Stochastics. By construction, this indicator tends to give the wrong signals in a market situation with a pronounced trend. LeBeau and Lucas (1992) advise therefore not to use this indicator in such a market situation.
If the exchange rate exhibits a strong upward trend, as in the case of USDJPY in the out-of sample forecasting period, the Stochastics 70/30 will frequenlty wrongly indicate an overbought situation and thus a Short position. It is interesting to note that our model does not seem to share this weakpoint with the Stochastics. The reason for this is that the Stochastics derives a trading signal based on the assumption that the exchange rate exhibits mean reverting tendencies within the actual trading range, marked by Max and Min prices.
The Stochastic does not provide a point forecast of the Close series. Our modelling strategy differs in the respect that we incorporated the mean-reverting tendency of high freqeuncy exchange rates (ecm1) within a trading range (ecm2) into structural simultaneous equations for the Close, Max and Min series in order to derive a point forecast for the Close series and then, in a next step, to generate a trading signal.
Since Parkinson (1980) and Garman and Klass (1980) have shown that the efficiency of estimators of price volatility can be substantially increased if the classical Close priced based estimators are augmented with information embodied in High and Low prices, our results seem to suggest that the same holds for point forecasts.
Prof. Ronald MacDonald, Prof. Norbert Fiess
Next: Conclusion
Summary: Index