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

Coupon Equivalent Rate (CER) is an alternative calculation of the coupon rate used to compare zero coupon securities to coupon bonds. This is the annual yield of a zero coupon bond when calculated as if you paid the coupon. Also known as bond-equivalent yield (BEY) or coupon-equivalent yield (CEY).

Important point

- The Coupon Equivalent Rate (CER) is the annual yield of a zero-coupon bond when calculated as if you paid the coupon.
- CER allows you to compare zero coupon bonds with other bonds.
- CER is a nominal yield and does not take compound interest into account.

## Understand Coupon Equivalent Rate (CER)

Coupon Equivalent Rate (CER) allows investors to compare zero coupon bonds to coupon payment bonds. Most bonds pay investors annual or semi-annual interest, but some bonds, called zero-coupon bonds, do not pay any interest and instead are issued at a significant discount at face value.

Investors return these discount bonds when the bonds mature. Analysts use the coupon-equivalent rate formula to compare the rate of return of a security that pays a coupon to the rate of return of a zero coupon in a relative perspective. Coupon Equivalent Rate (CER) indicates the annual yield of short-term debt securities. This is usually quoted on a bank discount basis, so yields can be compared to quotes for securities with coupons.

In effect, the coupon rate for a discounted product (Zero Coupon, Treasury Securities, Commercial Paper, etc.) shows what happens if the product has a coupon and is sold at par.

This rate for discounted bonds is inaccurate when compared to other coupon bonds, as the market rate of bonds is calculated based on face value. Discount bonds and zero coupon bonds are not sold at par. They are sold at a discounted price and investors usually receive more than they invested at maturity. Therefore, it is more accurate to use CER because it uses the investor’s initial investment as the basis for the yield.

The formula for calculating the coupon equivalent rate is as follows.

$$

CR

= =

Face value

−

market price

market price

XX

360

Days to maturity

where:

CR

= =

Coupon equivalent rate

begin {aligned} & text {CR} = frac { text {Face Value}- text {Market Price}} { text {Market Price}} times frac {360} { text {Days until Maturity}} \ & textbf {where:} \ & text {CR} = text {coupon equivalent rate} end {aligned}

..CR= =market priceFace value−market price..XXDays to maturity360..where:CR= =Coupon equivalent rate..

The Coupon Equivalent Rate (CER) is calculated as follows:

- Find the discount on which the bond is traded. This 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.
- Then multiply that number (from number 3) by the number found in number 3. 2.2.

Coupon-equivalent rates are an alternative way to calculate bond yields, allowing you to compare zero-coupon bonds to bonds of different terms. However, this is a nominal yield and does not take compound interest into account.

Maturity yield (YTM) is the theoretical yield that an investor receives if he or she holds a bond until maturity. However, unlike the Coupon Equivalent Yield (CER), compound interest is considered for yields to maturity. Both are expressed annually.

## CER example

For example, the $ 10,000 US T-bill, which matures in 91 days, sells for $ 9,800. The coupon equivalent rate is 8.08%, or (($ 10,000- $ 9,800) / ($ 9,800)) * (360/91), or 0.0204 * 3.96. Choose zero coupon bonds because they have a higher rate {8.08%> 8%]compared to bonds that pay an 8% annual coupon.

Or consider the current Zero Coupon Treasury STRIP, which matures on March 15, 2022. The par value is $ 100 and the market price as of September 14, 2021 is $ 98.63. The coupon equivalent rate (CER) is 2.75%, that is, (($ 100-$ 98.63) / ($ 98.63) * (360/182).