Question

What is the percentage change in price for a zero coupon bond if the yield changes from 5% to 8%? The bond has a face value of $1,000 and it matures in 12 years. Use the price determined from the first yield, 5%, as the base in the percentage calculation.

Answer 1

Price when yield is @5% = Face value/(1+YTM)^years to maturity

Yield to maturity (YTM) = 5%

Years to maturity = 12 years

Face value = 1000

Price when yield is @5% = 1000/(1+0.05)^12

= 1000/1.7958

= 557

Price when yield is @8% = 1000/(1+0.08)^12

= 1000/2.5182

= 397

Percentage change in price of bond = price @5%- price @8%/price @5%

= 557-397/557

= 160/557

= 0.2872 or 28.72%

Percentage change in price of zero coupon bond = 28.72%