Question

Suppose the nominal policy interest rate in New Zealand is 1.5% (recall that this rate is called Official Cash Rate or OCR), it is risk-free. The expected inflation rate is 1.7%. Further suppose that the nominal interest rate at which New Zealand businesses can borrow is 4.7%, please call this rate the nominal borrowing rate.

a. Calculate the exact real policy interest rate and the approximate real policy interest rate.

b. Calculate the exact and approximate real borrowing rates?

c. How much is the risk premium in the borrowing rate? Use the nominal rates for this calculation.

d. Suppose that the risk premium arises entirely from the default risk, calculate the default probability of business loans, implied in the interest rates.

Answer 1

A.

Exact Real Policy Interest rate = (1+.015)/(1+.017) - 1 = -.197% or -.2%

Approximate Real Policy Interest rate = 1.5% - 1.7% = -.2%

B.

Exact real borrowing rate = (1+.047)/(1+.017) - 1 = 2.95%

Approximate real borrowing rate = 4.7% - 1.7% = 3%

C.

Risk premium = 4.7% - 1.5% = 3.2%

D.

Probability = =(1-1/(1+(0.032/1.015)))

Probability = .031