Question

5. “A low-coupon security is more price-volatile [in response to a given change in yield that a high-coupon security.” True or false, or what? Explain carefully.

Answer 1

True a low coupon security is more price volatile than high coupon rate.
Considering maturity and par value to be same lower coupon rate will fluctuate more as compared to

Numerical Explanation is as follows
Let us take two bond with bond A at lower coupon rate and Bond B at higher coupon rate.

Let par value of Bond A =1000
Assuming 10% YTM
Coupon = 6%*1000 = 60
PV of Bond at 10% YTM = 60*(1-(1+10%)^-10)/10%+1000/(1+10%)^10 =754.22
PV of Bond at 10.5% YTM =60*(1-(1+10.5%)^-10)/10.5%+1000/(1+10.5%)^10 =729.34

Percentage Fall in price =(754.22-729.34)/729.34 = 3.41%

For Bond B
Assuming 10% YTM
Coupon = 10%*1000 = 100
PV of Bond at 10% YTM = 100*(1-(1+10%)^-10)/10%+1000/(1+10%)^10 =1000
PV of Bond at 10.5% YTM =100*(1-(1+10.5%)^-10)/10.5%+1000/(1+10.5%)^10 =969.31

Percentage fall in price =(1000-969.31)/1000 =3.01%

With increase in YTM there is a higher fall in price in lower coupon rate.