Assume Spot rates right now are as follows. 6-months 0.75% 18-months 1.25% 12-mo

Question

Assume Spot rates right now are as follows.

6-months 0.75% 18-months 1.25%
12-months 1.00% 24-months 1.50%

A newly issued 2-year bond pays a coupon rate of 1.5% (assume semiannual payments - use the convention (1+r/2)t where r is the simple annual interest rate and t refers to the number of semiannual periods) and has a par value of $1,000.

Assume the expectations hypothesis holds. What is the expected price of this bond 6 months from today, just before it makes its first interest payment? In other words, what price would you pay for the bond if you buy it immediately before the first coupon payment arrives?

Explanation / Answer

Face Value=1000

Coupon=1.5%*1000/2=7.5

rate for 6 months 6 months from now=1.005^2/1.00375-1=0.6252%

rate for 1 year 6 months from now=(1.00625^3/1.00375)^0.5-1=0.75%

rate for 18 months 6 months from now=(1.0075^4/1.00375)^(1/3)-1=0.8753%

Price 6 months later=7.5+7.5/1.003126+7.5/1.00375^2+1007.5/1.0043765^3=1016.808

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