The evaluation of exchange forecast performance

Because exchange forecasts are not free, MNCs must monitor their forecast performance to determine whether the forecasting procedure is satisfactory. Forecast performance can be evaluated by measuring the forecast error as follows:

where RSEis the root square error as a percentage of the realized value, FVis the forecasted value, and RV is the realized value. Average forecasting accuracy is usually measured by the root mean square error. The error is squared because a positive error is no better than a negative error. The RSE averages the squared errors over all forecasts. A forecasting model is more accurate than the forward rate if it has a smaller RSE than the forward rate.

In order to avoid a possible offsetting effect when we determine the mean forecast error, an absolute value (a squared error) is used to compute the forecast error. To clarify why the forecast error must have an absolute value, assume that the forecast error is 20 percent in the first quarter and -20 percent in the second quarter. If the absolute value is not used, the mean error over the two quarters is zero. The mean error of zero in this case, however, is misleading, because the forecast was not perfect in either quarter. If the absolute value is used here, the mean error over the quarters is 20 percent. Thus, the absolute value avoids such a distortion.

The forecasted value for the Canadian dollar is \$0.7300 and its realized value is \$0.7500. The forecasted value for the Mexican peso is \$0.1100 and its realized value is \$0.1000. What is the dollar difference between the forecasted value and the realized value for both the Canadian dollar and the Mexican peso? What is the forecast error for each of these two currencies?

The dollar difference between the forecasted value and the realized value is \$0.0200 for the Canadian dollar and \$0.0100 for the peso. This does not necessarily mean that the forecast of the peso is more accurate. When we consider the relative size of the difference, we can see that the Canadian dollar has been forecasted more accurately on a percentage basis. The forecast error of the Canadian dollar is computed as follows: