Exhibit 7.1 also shows the inflation rate that occurred over the subsequent three-
month period. The inflation rate is measured by the consumer price index (CPI) in the
United States. The third line in Exhibit 7.1 shows the real interest rate, defined con-
ventionally as follows:
Real $ Interest Rate $LIBOR – $ CPI Inflation rateThe real interest rate is an ex-postmeasure of the real rate of return earned by in-
vestors from investing $LIBOR for each three-month period, given the inflation that
subsequently occurred over that period.
Exhibit 7.2 shows the three-month LIBORs in three major currencies—dollar,
yen, and pound sterling—during the period 1992–2001. It is evident from the graph
that these key rates have fluctuated considerably in all three currencies.
The volatility of short-term interest rates is closely related to the volatility of for-
eign exchange rates. Exhibit 7.3 shows the foreign exchange rates against the U.S.
dollar of key currencies, the yen, the euro, and the pound sterling, over the period
1999–2001.
The historical volatility of a financial variable is normally measured by the stan-
dard deviation of the observations of the logarithm of the variable, stated on an an-
nualized basis. The standard deviation of the quarterly observations of $LIBOR
7 • 4 INTEREST RATE AND FOREIGN EXCHANGE RISK MANAGEMENT PRODUCTSExhibit 7.2. Short Term Interest Rates in Major Currencies.
Exhibit 7.3. Foreign Exchange Rate.