Question

"Immediately after a coupon payment it is true that if the yield is greater than the coupon rate then the price is less than the par value. But between coupon payment dates, this statement may not be correct." Is this true? Explain.

Answer 1

Immediately after the Coupon payment dates, if the yield is greater than coupon rate, the bond price will be less than the par value, because Present Value of the sum of future cash flows discointed at yield will be lower than the coupon rate.

But between the coupon payment dates, the price will include the interest of the bond between last coupon payment till date. Hence the price may not be less than par.

For example ,

Consider a 5 year bond , face value=$1000 Coupon rate =6%

After 3 years of issue and immediately after payment of third coupon, if the market yield is 6.25%,the price of the bond calculated below:

PV of 4^th coupon=60/1.0625=$56.47

PV of 5^th coupon=60/(1.0625^2)=$53.15

PV of maturity payment=1000/(1.0625^2)=$885.81

Sum of PV=Market value=(56.47+53.15+885.81)=$995.43

This is less than par value of $1000

But , before the coupon payment, the market price will include the interest rate of approximately $60 which will increase the market value . hence, the market value between coupon payment dates may not be less than the par value , if yield is higher than the coupon rate