Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bi

Question

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:              1R1 = 8%,  E(2r1) = 9%, E(3r1) = 9.4%, E(4r1) = 9.75% Using the unbiased expectations theory, calculate the current (long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities.

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:              1R1 = 8%,  E(2r1) = 9%, E(3r1) = 9.4%, E(4r1) = 9.75% Using the unbiased expectations theory, calculate the current (long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities.

Explanation / Answer

long term rates for year

1 = 8%

2 : 1.08*1.09 = (1+r)^2 => r = .085 = 8.5%

3 : 1.08*1.09*1.094 = (1+r)^3 => r = 0.088 = 8.8%

4 : 1.08*1.09*1.094*1.0975 = (1+r)^4 => r = 0.09 = 9%

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