Test a Forecast Against a Volatility Estimate

[Fairman]

Test a Forecast Against a Volatility Estimate

A bank forecasts EUR/USD at 1.25 by the end of the year. The current rate is 1.10, and there are 12 months left. Implied volatility for the pair is 7 percent annualized. How plausible is the forecast?

Compute the required move. The natural log of 1.25 divided by 1.10 is 0.1278, a gain of about 13.6 percent.

Compare with the typical one-year range. With volatility of 7 percent, one standard deviation of the one-year return is about 7 percent. The required move is 0.1278 divided by 0.07, which is 1.83 standard deviations.

Estimate the probability. Under a simple model with no drift, the probability that the pair ends the year above that level is the upper-tail probability at 1.83 standard deviations, about 3.4 percent.

So the forecast describes an outcome that the options market assigns a probability of about 3 to 4 percent. That does not make it wrong. Forecasts often reflect views that differ from the market's. But it suggests that, if you want to trade it, your stop should reflect a low likelihood and a long wait.

Compute the cost of waiting. If you buy now and the pair drifts, the swap on a long, in a world where the dollar has the higher rate, costs maybe 2 percent a year.

Also consider what the forecaster is paid for: clients pay for views, and bold calls attract attention.

Use forecasts as one more scenario, not as the base case.

Exercise: convert any forecast you read into a number of standard deviations.