Question

4. A newly-issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 8%. Find the holding period return for a one-year investment period if the bond is selling at a yield to maturity of 7% at the end of the year. a. Find the realized compound yield for a 2-year holding period, assuming that (i) you sell the bond after 2 years, (ii) the bond yield to maturity is 7% at the end of the second year and (i) the coupon received after one year can be reinvested for one year at a 3 percent interest rate. b.

Answer 1

a.

Bond's current selling price at the given YTM of 8% &

annual coupon of 5%*1000= $ 50 for no.of future periods/years till matutrity = 20

ie .PV of ordinary- coupon amt.-annuity for 20 yrs.+PV of the single Face-value amt. to be received at end of 20 yrs.

Current selling price=(50*(1-1.08^-20)/0.08)+(1000/1.08^20)

705.46

One-Year from now

No.of future periods/years till matutrity = 20-1=19

& YTM=7%

Selling price at the end of 1 year=(50*(1-1.07^-19)/0.07)+(1000/1.07^19)

793.29

So, $ holding period return for the one-year investment period=

(Coupon+Sale value at end of Yr.1)-Initial price at Yr. 0

(50+793.29)-705.46=

137.83

ie.137.83/705.46=

20%

b.2 Year holding period:
Cash flows on the bond
1st year coupon,reinvested at 3% for the 2nd year--50*1.03^1	51.5
2nd year coupon	50
Sale proceeds at end of yr.2 --n=20-2=18 & YTM=7%
(50*(1-1.07^-18)/0.07)+(1000/1.07^18)	798.82
Total at end yr. 2	900.32
Less:Value at Yr. 0(at investment)	705.46
Total realised $ return(900.32-705.46)	194.86
ie.194.86/705.46=
28%
Yield for a 2 year period
Or
((900.32/705.46)^(1/2))-1
12.97%
(annualised yield)