Question

A 7% coupon bond has a par value of $1,000 and a yield-to-maturity of 5%. You purchase the bond when it has exactly 7 years remaining until maturity. You hold the bond for 6 months, collect the coupon payment, and then sell the bond immediately. If the bond's yield-to-maturity is 9% when you sell it, what is your percentage return over this 6-month holding period? Enter your answer as a decimal and show 4 decimal places. For example, if your answer is 6.25%, enter .0625.

Answer 1

Purchase Price

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 5% /2 = 0.025

And n is the no of Compounding periods 7 years * 2 = 14

Coupon 7% / 2 = 0.035

=

= 1116.90912172

Sale Value

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 9% /2 = 0.045

And n is the no of Compounding periods = 14 - 1 = 13 periods

Coupon 7% / 2 = 0.035

=

= 903.171475768

6 month holding returns = Capital Gain + Coupon / Purchase Price

= ((903.171475768 - 1116.90912172) + 35) / 1116.90912172

= (-213.73764596 + 35) / 1116.90912172

= -178.73764596 / 1116.90912172

= -16%

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