# P1.T3.22.17, Covered and uncovered interest rate parity

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Explain the purchasing power parity theorem and use this theorem to calculate the appreciation or depreciation of a foreign currency. Describe the relationship between nominal and real interest rates. Describe how a non-arbitrage assumption in the foreign exchange markets leads to the interest rate parity theorem and use this theorem to calculate forward foreign exchange rates. Distinguish between covered and uncovered interest rate parity conditions.

Questions:

22.17.1. Three months ago, the spot foreign exchange rate between the euro and the Canadian dollar was $1.40 EURCAD. Today it is markedly higher at$1.53 EURCAD. Each of the following developments, ceteris paribus, might reasonably explain this increase EXCEPT which is unlikely to be the explanation?

a. The inflation rate in the Eurozone suddenly increased but was unchanged in Canada
b. The money supply suddenly increased in Canada, but the money supply in the Eurozone is unchanged
c. Exports from the Eurozone to Canada (i.e., the imports to Canada from the Eurozone) suddenly increased
d. The risk-free interest rate in the Eurozone suddenly decreased, while the Canadian risk-free interest rate is unchanged

22.17.2. The current spot exchange rate between the euro (EUR) and quote currency YYY is 1.3000 EURYYY. The EUR risk-free rate is 4.0% and the YYY risk-free rate is 2.0%; each interest rate is per annum with annual compounding. According to covered interest rate parity (CIRP), which is nearest to the forward rate in nine months (T = 0.75 years) quoted in points?

a. -12,576
b. -188.0
c. +33.0
d. +291.0

22.17.3. The current spot exchange rate between the euro (EUR) and U.S. dollar (USD) is \$1.1500 EURUSD. The six-month (T = 0.5 years) EURUSD forward quote in points is 172.00. According to covered interest rate parity, which of the following is true about the approximate per annum (aka, annualized) interest rate differential between the risk-free rates in the two countries?

a. The EUR interest rate is approximately 0.9% per annum higher than the USD rate
b. The EUR interest rate is approximately 1.4% per annum higher than the USD rate
c. The USD interest rate is approximately 3.0% per annum higher than the EUR rate
d. The USD interest rate is approximately 6.2% per annum higher than the EUR rate