On January 15th, the one-day return to holding Swiss Francs from a Euro perspective was 16.9%. This is a high one-day return for any currency pair, but appears cataclysmic given the extremely low return volatility of the Swiss Franc from a Euro perspective in recent months. This one-day jump was a “239-sigma event” meaning that the magnitude of this return was 239 times the recent return volatility (using a 90-day historical estimate of volatility). In fact, in the period just before the sudden jump, the sample volatility of this exchange rate was even lower. Using a shorter 20-day volatility estimate, the sudden jump was a 400-sigma event.
It is interesting how closely the time-series behaviour of this exchange rate matches the predictions of Krugman’s 1991 model of a government-implemented exchange rate limit, in which traders credibly believe that the authorities will prevent the exchange rate from piercing the exchange rate limit. As the fundamentals for the exchange rate made the Swiss Franc greatly undervalued, the traded exchange rate settled down just near the government-imposed limit, with very low volatility. And then suddenly the credible promise became a non-promise.
Chalk one up for Krugman, in terms of the elegant fit between his theoretical model and this recent market experience. Several forex trading firms went bust, but they should have had better risk management systems.