Question

A zero-coupon bond has a par value of $1,000 and a yield-to-maturity of 5%. You purchase the bond when it has exactly 17 years remaining until maturity. You hold the bond for 6 months and then sell it. If the bond's yield-to-maturity is 9% when you sell it, what is your percentage return over this 6-month holding period? When computing bond prices, use a semi-annual compounding period. Enter your answer as a decimal and show 4 decimal places. For example, if your answer is 6.25%, enter .0625.

Answer 1

Par/face Value of Zero-Coupon Bond = $1000

Calculating the Purchase price of Zero-Coupon Bond when there are exactly 17 years remaining until maturity:-

where, Semi-annual YTM = 5%/2 = 2.5%

n = no of periods = 17 years*2 = 34

Price = $431.91

So, the Purchase price of Zero-Coupon Bond is $431.91

- You hold the bond for 6 months and then sell it when YTM chnaged to 9%

Calculating the Selling price of Zero-Coupon Bond after holding for 6 months:-

where, Semi-annual YTM = 9%/2 = 4.5%

n = no of periods = (17 years - 0.5 years)*2 = 33

Price = $233.97

So, Selling price of Zero-Coupon Bond is $233.97

Now calculating the percentage return over this 6-month holding period:-

Percentage Return = (Selling Price - Buying Price)/Buying Price

Percentage Return = ($233.97 - $431.91)/$431.91

Percentage Return = -45.83%

Percentage Return over this 6-month holding period is 0.4583

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