Question

What is the price of a 2-year Treasury note with a 4.6% coupon rate and semiannual coupon payments if the annualized theoretical spot rates for 6-month, 12-month, 1.5-year, and 2-year maturities are 2.1%, 3.1%, 4.27%, and 5.42%, respectively? Express in % of par, round to 0.001. E.g., if your answer is 102.3785, record it as 102.379.

Answer 1

Given annualized spot rates are:

r0.5 = 2.1%

r1 = 3.1%

r1.5 = 4.27%

r2 = 5.42%

For a 2 year bond,

coupon rate = 4.6% paid semiannually,

Let par value be FV = $100

so, semiannual coupon payment C = (4.6%/2) of 100 = $2.3

So, price of the bond is calculated using formula

Price = C/(1+r0.5/2) + C/(1+r1/2)^2 + C/(1+r1.5/2)^3 + (C+FV)/(1+r2/2)^4

=> Price = 2.3/(1+0.021/2) + 2.3/(1+0.031/2)^2 + 2.3/(1+0.0427/2)^3 + 102.3/(1+0.0542/2)^4

=> Price = $98.59

So, price of the bond is 98.59% of the par value.