Question

Consider the following bonds:

Bond A: 10% coupon, paid annually, matures in 3 years

Bond B: 8% coupon, paid annually, matures in 2 years

If Bond A is selling for $1,060 and Bond B is selling for $940, what is the yield to maturity on a portfolio consisting 30% of Bond A and 70% of Bond B?

A. 8.60%

B. 9.00%

C. 9.61%

D. 10.38%

Answer 1

Bond A

K = N

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

k=1

K =3

1060 =∑ [(10*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^3

k=1

YTM% = 7.69

Bond B

K = N

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

k=1

K =2

940 =∑ [(8*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^2

k=1

YTM% = 11.53

Weight of Bond A = 0.3

Weight of Bond B = 0.7

YTM of Portfolio = Weight of Bond A*YTM of Bond A+Weight of Bond B*YTM of Bond B

YTM of Portfolio = 7.69*0.3+11.53*0.7

YTM of Portfolio = 10.38