Question

1. You have just purchased a $1,000 bond with 7% annual coupon and maturity in 10 years.
   1. If the yield‐to‐maturity is 6%, how much did you pay for the bond?
   2. If, 1 year later and on the day after you receive the first coupon, the bond’s yield‐to‐maturity goes up to 8%, and you need cash and have to liquidate your investment. What will be your selling price?
   3. What will be your 1‐year holding period rate of return?

Answer 1

A) Current price = coupon/ (1+ YTM )1 + coupon/ (1+ YTM )2 + ....... + coupon/ (1+ YTM )10 + Bond price/(1+ YTM )10

= 70/(1.06)1 + .........+ 70/(1.06)10 + 1000/1.558

= 515 + 642

=1157

B) After 1 year price = coupon/ (1+ YTM )1 + ....... + coupon/ (1+ YTM )9 + Bond price/(1+ YTM )9

Here we will use new YTM

=70/(1.08)1 + .........+ 70/(1.08)9 + 1000/1.50

= 437 + 667

=1103

1 yr HPR = opening price + Coupon - closing price / opening price

1157 + 70 - 1103 / 1157

=10.71%