Consider the following spot interest rates for maturities of one, two, three, an

Question

Consider the following spot interest rates for maturities of one, two, three, and four years.

r1 = 4.3% r2 = 4.9% r3 = 5.6% r4 = 6.4%

Assuming a constant real interest rate of 2 percent, what are the approximate expected inflation rates for the next four years? Use the Fisher hypothesis and the unbiased expectations theory

Explanation / Answer

2F1 = [(1+1R2)^2/(1+1R1)] – 1 2F1 = (1+0.049)^2)/(1+0.043) – 1 2F1 = (1.049)^2/(1.043) –> 1.100401/1.043 = 1.55035 2F1 = 1.055035 – 1 = .055035 Year 2 = 5.503% 3F1 = [(1+1R3)^3/(1+1R2)^2] – 1 3F1 = (1+0.056)^3/(1+0.049)^2 3F1 = (1.056)^3/(1.049)^2 –> 1.177584/1.100401 = 1.07014 3F1 = 1.07014 - 1 = .07014 Year 3 = 7.0% 4F1 = [(1+1R4)^4/(1+1R3)^3] – 1 4F1 = (1.064)^4/(1.056)^3 –> 1.281641/1.177584 = 1.088365 4F1 = 1.088365 – 1 = .088365 Year 4 = 8.8%

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