Question

(A) Suppose that the 6-month US Treasury bill rate is equal to 5.98%, and the forward rate on a 6-month Treasury bill 6 months from now is 7.88%. (Both are in yearly terms).

What is the 1-year bill rate? (Keep your answer to 4 decimal places, e.g 0.1234)

(B) Consider two 5-year bonds: one has an 6% coupon rate and sells for $98; the other has an 9% coupon rate and sells for $103. What is the price of a 5-year zero coupon bond? (Assume that coupons are paid annually, and the face values of all the bonds are $100.)

(Keep your answer to 2 decimal places, e.g. xx.12.)

Answer 1

A

Annualized Forward rate of 0.5 years 0.5 years from now =((1+1 Year rate)^1/(1+0.5 Year rate)^0.5)^1/0.5-1

7.88=((1+N2 rate)^1/(1+0.0598)^0.5)^1/0.5-1

N2 rate% = 6.9258

B

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

98 =∑ [(6*100/200)/(1 + YTM/200)^k]     +   100/(1 + YTM/200)^5x2

k=1

YTM% = 6.4746

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(0*100/200)/(1 + 6.4746/200)^k]     +   100/(1 + 6.4746/200)^5x2

k=1

Bond Price = 72.72