Question

3. A bond investor, who is your client, does not fully understand how changes in interest rates affect the price. Could you please try to explain why does a bond price change when interest rates change?

Answer 1

A bond's price, at any point of time, is the PV the expected cash

flows from the bond, when discounted at the market rate of

interest.

The expected cash flows are:

*The maturity value of the bond, receivable at the end of the

maturity of the bond, and

*The periodic interest payments, semi-annual or annual, receivable

as per the terms of the bond at the coupon rate or stated rate.

The market rate may be:

1] Equal to the coupon rate, or

2] Greater than the coupon rate, or

3] Less than the coupon rate.

This being the case, the price of the bond will differ in each of the

above three situations.

For situation [1], the price will be equal to the face value of the

bond.

For situation [2], the price will be less than the face value of the

bond. The reason is that the expected cash flows get discounted

by a rate higher than the coupon rate, thereby rendering the PV

of the cash flows from the bond being lower. The result will be a

price less than the face value.

For situation [3], the price will be more than the face value of the

bond. The reason is that the expected cash flows get discounted

by a rate lower than the coupon rate, thereby rendering the PV

of the cash flows from the bond being higher. The result will be a

price more than the face value.

From the foregoing, it can be said that a bond's price will move

inversely with the change in market interest rates; that is when the

market interest rate rises above the coupon rate the bond price

will be lower than the face value and vice versa.