Bond Price vs. Par. 2007 FRM

by David Harper, CFA, FRM, CIPM

FRM |

Learning Outcome

• LO 21.4: Describe the price of a bond relative to its par value when (i) coupon rate = YTM, (ii) coupon rate > YTM, and (iii) coupon rate < YTM.

Two ideas: 1. Price is pulled to par; 2. If coupon = YTM, then price = par

We previously defined a bond's yield to maturity (YTM)  as its internal rate of return (IRR) if the bond is held to maturity and if the coupons are reinvested at the YTM (if the coupons are reinvested at a higher/lower rate, the realized return will vary from the YTM).

For the above learning outcome, two ideas should help:

• The price of a bond converges toward its face (aka, par, principal) value as it approaches maturity. As they say, the price is "pulled to par"
• If the coupon rate (aka, nominal rate, coupon) happens to equal the YTM, the bond's price should equal its par value

To illustrate, consider a $100 face value bond where the yield to maturity (YTM) is 6%. The chart below plots the price of the bond against the years to maturity (YTM; x-axis) for five different variations on the bond. In red, the coupon pays 4% semiannually (i.e., 2% every six months). In green, the coupon pays 6%, which equals the YTM so this bond is constantly priced at par over time.

EditGrid example

This plot is simple because I just "re-price" the bond at each maturity/coupon. Here is the spreadsheet: