Question

Suppose we observe the following rates: ₁R₁ = 12 percent, ₁R₂ = 15 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now, E(₂r₁)?

13.5 percent

14.2 percent

15.6 percent

18.0 percent

Answer 1

Based on unbiased expectations theory, short term rates are indicator of long term rates.

(1 + 2 Year Rate)² = (1 + 1 Year Rate) * (1 + 1 Year Rate 1 Year later)

(1 + 15%)² = (1 + 12%) * (1 + 1 Year Rate 1 Year later)

1.3225 = 1.12 *  (1 + 1 Year Rate 1 Year later)

1.1808 =  (1 + 1 Year Rate 1 Year later)

1 Year Rate 1 Year later = 0.1808 = 18.08% (Option 4)