Nominal vs real

问题如下：

A risk manager at a foreign exchange dealer is assessing the relative level of real and nominal interest rates in the US and Canada. The exchange rate is currently at CAD 1.21 per USD 1, and the firm's economist forecasts an exchange rate of CAD 1.19 per USD 1 one year from now. The analyst notes that the annual risk-free rate of interest in the US is 0.85%, and the annual inflation rates for the US and Canada are 2.50% and 2.80% respectively. If purchasing power parity and covered interest parity both hold, what is the best estimate of the difference between the real interest rates in Canada and the US?

选项：

A.

0.30%

B.

1.36%

C.

1.69%

D.

1.91%

解释：

D is correct.

Two equations are needed to solve this question.

The first, as follows, is used to find the real interest rate in a single currency as a function of the nominal interest rate and the rate of inflation as follows:

The second equation describes the relationship between forward rates (F) and spot rates (S) assuming covered interest parity holds. R represents the risk-free rate in each currency.

where

S=1.21

F=1.19

R_us =0.85%

R_{infl, USD} =2.50%

R_infl,CAD =2.80%

Using the second formula:

(1 + R_CAD)^{^1} = F* (1 + R_USD)^{^1}/S = 0.9918

R_CAD = -0.82%

Using formula 1 above:

R_USD,real = −1.61%

R_CAD,real = −3.52%

Abs(R_USD,real − R_CAD,REAL) = 1.91%