May 14

Bond prices pulling to par - Practice question (Par 3)

by David Harper, CFA, FRM, CIPM

FRM |

Golfball on the grass.

Assume the following:

A flat yield curve at 6% (unrealistic)

  • A 30-year 4% coupon bond, par (face value)= $100 (30 years to maturity)
  • A 30-year 6% coupon bond, par (face value) = $100 (30 years to maturity)
  • A 30-year 8% coupon bond, par (face value) = $100 (30 years to maturity)

Question:

  • What is the price of the 4% coupon bond, using a calculator?
  • Without using a calculator, what is the price relationship among the three bonds (highest, lowest price)?
  • If the yield curve stays flat at 6% (unrealistic), what is the evolution in relationship among the three bond prices as they approach maturity?

 

(don't peek until you try)

 

 

 

 

 

Answer:

See the EditGrid below for an illustration of bond prices and their tendency to pull to par (Tuckman page 43.)

The price of the 4% coupon bond = $72.32.

If the coupon rate < yield, the bond must sell at a discount to par (how else to compensate the buyer?).

If the coupon rate > yield, the bond must sell at a premium (or the high coupon would be a "free lunch").

The 4% coupon will have the lowest price; the 6% coupon (under this unrealistic assumption) will always price at $100, and the 8% coupon will have the highest (premium) price. See the plots below.

As the bond approaches maturity, the premium/discount erodes (the bond pulls to par)

 

EditGrid:

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