# Par Bond

A bond that currently trades at its face value

## What is a Par Bond?

A par bond refers to a bond that currently trades at its face value. The bond comes with a coupon rate that is identical to the market interest rate. ### Summary:

• A par bond is a bond that currently trades at its face value.
• The bond comes with a coupon rate that is identical to the market interest rate.
• As the interest rate continually fluctuates, par bonds are uncommon to see.

### Understanding a Par Bond

A bond’s coupon rate is the rate of interest paid by the bond issuers on the bond’s face value. To understand why a bond with a coupon rate equal to the market interest rate is priced at par, consider the following examples:

#### Example 1: Discount Bond

Consider a bond with a 5-year maturity and a coupon rate of 5%. The market interest rate is 6%.

For the bond above, the coupon rate is below the market interest rate. In such a scenario, a rational investor would only be willing to purchase this bond at a discount to its face value because its coupon return is lower than the current market interest rate. In other words, the bond is generating a return lower than the market, and investors would only be willing to purchase the bond if it was issued at a discount.

Consider a bond with a 5-year maturity and a coupon rate of 5%. The market interest rate is 4%.

For the bond above, the coupon rate is above the market interest rate. In such a scenario, a rational investor would be willing to purchase the bond at a premium to its face value because its coupon return is higher than the current interest rate. In other words, the bond is generating a return higher than the market interest rate and, therefore, investors are willing to purchase the bond at a premium.

#### Example 3: Par Bond

Consider a bond with a 5-year maturity and a coupon rate of 5%. The market interest rate is 5%.

For the bond above, the coupon rate is equal to the market interest rate. In such a scenario, a rational investor would only be willing to purchase the bond at par to its face value because its coupon return is the same as the current interest rate. In other words, since the bond is generating a return equal to the market interest rate, investors would not be willing to offer a premium or require a discount – the bond is priced at par.

### Bond Pricing Formula

The present value formula is used to price a bond: Where:

• C equals the coupon payment;
• n equals the number of payment periods;
• i equals the interest rate; and
• FV equals the value at maturity. Face value is also known as par value.

### Example of a Par Bond

A bond with a face value of \$100 and a maturity of three years comes with a coupon rate of 5% paid annually. The current market interest rate is 5%. Using the bond pricing formula to mathematically confirm that the bond is priced at par, Shown above, with a coupon rate equal to the market interest rate, the resulting bond is priced at par.

### The Reality of Par Bonds in the Marketplace

Par bonds are uncommon in the market. The reason is that it is very rare for the market interest rate to equal the coupon rate of the bond. The market interest rate varies constantly. To illustrate the fact, the Bank of Canada provides interest rates on a trended basis. With interest rates constantly changing, it is uncommon for a bond’s coupon rate to match exactly with the market interest rate and be priced at par.