Question

Question: Consider the following $1,000 par value zero-coupon bonds:

Bond	Years until maturity	Yield to maturity
A	1	5%
B	2	6%
C	3	6.5%
D	4	7%

According to the expectations hypothesis, what is the market’s expectation of the one year interest rate three years from now?

Short answer

Answer

8.51%; a shift upward in next year’s curve

Step-by-step solution

Calculation of Forward rates and Price

Maturity (years)	YTM	Forward rates= (1+yn)n / (1 + yn-1)n-1	Price
1	5.00%		1000/(1+5%)=$952.38
2	6.00%	7.01%	1000/(1+6%)=$890.00
3	5.50%	7.51%	1000/(1+6.5%)=$827.85
4	7.00%	8.51%	1000/(1+7%)=$762.90

Calculation of next year’s price and yields

To obtain this, we discount each zero’s face value at the forward rates as derived above.

Therefore

Maturity years	Price
1	1000 / 1.0701 = $ 934.5
2	1000 / (1.0701 x 1.0751) = $ 869.24
3	1000 / (1.0701 x 1.0751 x 1.0851) = $ 801.04

Hence according to expectation hypothesis this year’s upward sloping yield curve implies a shift upward in next year’s curve.