Question

Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

₁R ₁ = 5 percent,
E( ₂r ₁) = 7 percent,
E( ₃r ₁) = 7.5 percent
E( ₄r ₁) = 7.85 percent

Using the unbiased expectations theory, calculate the current (long-term) rates for one-year and two-year-maturity Treasury securities.

		one-year: 5.00 percent,two-year: 5.50 percent
		one-year: 5.00 percent, two-year: 6.00 percent
		one-year: 5.50 percent, two-year: 6.15 percent
		one-year: 5.50 percent, two-year: 5.75 percent

Answer 1

Current 1 year maturity Treasury security = 5% (as mentioned in question)

Using unbiased expectations theory,

(1 + 2 Yr Rate)² = (1 + 1 Yr Rate) * (1 + 1 Yr Rate 1 Yr Later)

(1 + 2 Yr Rate)² = (1 + 5%) * (1 + 7%)

(1 + 2 Yr Rate)² = 1.1235

1 + 2 Yr Rate = 0.059953

2 Yr Rate = 0.059953 = 6.00%

Hence correct option is 2nd.