Question

If you have 1-year rate is 8%, 2-year rate is 9%, and 3-year rate is 10%. Assume that the pure expectations theory for the term structure of interest rates holds, no liquidity or maturity premium exists. What is implied 1 year rate 2 year from now?

a. 9%
b. 10%
c. 11%
d. 12%

Answer 1

Answer:

1 year rate 2 year from now = 12%  (Approx)

Explanation:

Given:

1-year rate = 8%

2-year rate = 9%

3-year rate = 10%

Computation:

According to Pure Expectations Hypothesis,

(1 + 3-year rate)³ = (1 + 2-year rate)² (1 + 1 year rate 2 year from now)

(1.10)³ = (1 + 1.09)²(1 + 1 year rate 2 year from now)

1.331 = 1.1881 (1 + 1 year rate 2 year from now)

(1 + 1 year rate 2 year from now)  = 1.12

1 year rate 2 year from now = 0.12

1 year rate 2 year from now = 12%  (Approx)