## What is the Coupon Equivalent Rate (CER)?

The Coupon Equivalent Rate (CER) is an alternative calculation of the coupon rate used to compare zero coupon and coupon fixed income securities. This is the annualized return of a zero coupon bond when it is calculated as if it were paying a coupon. It is also known as the bond equivalent yield (BEY) or coupon equivalent yield (CEY).

Key points to remember

- The Coupon Equivalent Rate (CER) is the annualized yield of a zero coupon bond when it is calculated as if it were paying a coupon.
- CER compares zero coupon bonds and other fixed income securities.
- The CER is a nominal return and does not take into account membership.

## Understanding the Coupon Equivalent Rate (CER)

The Coupon Equivalent Rate (CER) allows an investor to compare a zero coupon bond to a coupon bond. While most bonds pay investors annual or semi-annual interest, some bonds, called zero coupon bonds, pay no interest but are instead issued at a steep discount to par.

The investor realizes a return on these discounted bonds when the bond matures. To compare the performance of paid securities with that of zero coupons in relative terms, analysts use the coupon equivalent rate formula. The Coupon Equivalent Rate (CER) indicates the annualized return on a short-term debt security that is generally quoted on a bank discount basis, so the return may be comparable to quotations on securities carrying coupons.

This is because it indicates what the coupon rate would be on a discount instrument (such as a zero coupon, treasury bill or commercial paper) if the instrument carried a coupon and had been sold at its face value.

Since the quoted rate for bonds is calculated on the basis of face value, this rate for bonds issued at a discount is inaccurate when compared to other coupon bonds. Discount or zero coupon bonds are not sold at face value. They are sold at a discount and the investor generally receives more than what he invested at maturity. Thus, it is more accurate to use the CER because it uses the initial investment of the investor as the basis of return.

The formula for the equivalent coupon rate is:

$$

RC

=

Nominal value

–

Market price

Market price

×

360

Days until maturity

or:

RC

=

Equivalent coupon rate

begin {aligned} & text {CR} = frac { text {Face value} – text {Market price}} { text {Market price}} times frac {360} { text { Days to Maturity}} & textbf {where:} & text {CR} = text {Coupon equivalent rate} end {aligned}

RC=Market priceNominal value–Market price×Days until maturity360or:RC=Equivalent coupon rate

The equivalent coupon rate (CER) is calculated as follows:

- Find the discount at which the bond is trading, that is, the face value minus the market value.
- Then divide the discount by the market price.
- Divide 360 by the number of days to maturity.
- This number (of # 3) is then multiplied by the number found in #. 2.

The equivalent coupon rate is another way of calculating the yield of a bond and allows you to compare a bond with zero coupon to a bond of different duration. However, this is a nominal return and does not take into account the composition.

The return to maturity (YTM) is the theoretical return an investor would receive if they held the bond to maturity. But unlike the equivalent coupon yield (CER), the yield to maturity takes into account the composition. Both are expressed as annualized rates.

## CER example

For example, a $ 10,000 US Treasury bill maturing in 91 days sells for $ 9,800. Its equivalent coupon rate would be 8.08%, or (($ 10,000 – $ 9,800) / ($ 9,800)) * (360/91), or 0.0204 * 3.96. Compared to a bond paying an annual coupon of 8%, we would choose the zero coupon bond since it has the higher rate {8.08%> 8%].

Or consider a current zero coupon Treasury STRIP that matures March 15, 2022. Face value is $ 100 and market price is $ 98.63 as of September 14, 2021. Coupon Equivalent Rate (CER) is 2.75%, or (($ 100 – $ 98.63) / ($ 98.63) * (360/182).

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