Question

Suppose that the expectations hypothesis holds and that the current term structure of interest rates is...

Suppose that the expectations hypothesis holds and that the current term structure of interest rates is as follows:

• y1 = 5%

• y2 = 6%

• y3 = 7%

a. What is the expected value of the two-year spot rate realizing at year one, E(1y3)?

b. What is the expected price of a two-year zero-coupon bond with a face value of $100 trading at year one?

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Answer #1

a. What is the expected value of the two-year spot rate realizing at year one, E(1y3)?

(1 + year 1 rate) * (1 + E(1y3))^2 = (1 + 3 year rate)^3

(1 + 0.05) * (1 + E(1y3))^2 = (1 + 0.07)^3

1.05 * (1 + E(1y3))^2 = 1.225043

(1 + E(1y3))^2 = 1.225043/1.05

(1 + E(1y3))^2 = 1.1667076

1 + E(1y3) = 1.08014

E(1y3) = 8.01%

b. What is the expected price of a two-year zero-coupon bond with a face value of $100 trading at year one?

Price of Two year ZCB = Face Value / (1 + E(1y3))^2

Price of Two year ZCB = 100 / (1 + 8.01%)^2

Price of Two year ZCB = 100 / 1.1667076

Price of Two year ZCB = $85.71

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