Question

You buy a bond with a face value of $100 at a price of 99.15. It has a YTM of 3.4% and a three-year maturity. Semiannual coupon payment. The second to the last coupon on the bond is worth $1.3145 at the end of your holding period. How much of the holding period return comes from coupons, how much comes from the reinvestment of coupons, how much comes from capital gains or losses and how much is due to the return of principal? (show your work for full credit)

Answer 1

Second to the last coupon worth = $1.3145

Which means it is received six months before maturity

YTM= 3.4% annually = 1.7 % for every six months

Coupon for that period = 1.3145/(1+ 0.017)= 1.3145/1.017=1.29

Since the bond has a three year maturity there are six coupons.

1.29 * 6 = 7.74 is the coupon received during holding period.

Amount from holding period = $7.74

Capital gain = 100 – 99.15 = $0.85

Amount from capital gain = $0.85

Also, amount from principal = price of bond = $99.15

Future value = price of bond * (1 + r)^t

YTM= 3.4% annually = 1.7 % for every six months

r = 0.017, t= 3*2 = 6

Future value = 99.15 * (1 + 0.017)^6 = $109.7

Reinvestment = Future value – price of bond - Capital gain – coupon from holding period

= 109.7 – 99.15 – 0.85 -7.74 =1.96

Amount from reinvestment= $1.96