# Coupon Equivalent Rate (CER)

## What Is Coupon Equivalent Rate (CER)?

The coupon equivalent rate (CER) is an alternative calculation of coupon rate used to compare zero-coupon and coupon fixed-income securities. It is the annualized yield on a zero-coupon bond when calculated as though it paid a coupon. It is otherwise called the bond equivalent yield (BEY) or the coupon equivalent yield (CEY)

## Figuring out Coupon Equivalent Rate (CER)

Coupon equivalent rate (CER) permits an investor to compare a zero-coupon bond to a coupon-paying one. While most bonds pay investors annual or semi-annual interest payments, a few bonds, alluded to as zero-coupon bonds, don't pay interest by any means yet are rather issued at a deep discount to par.

The investor makes a return on these discount bonds when the bond develops. To compare the return on coupon-paying securities with that of zero-coupons in relative terms, analysts utilize the coupon equivalent rate formula. The coupon equivalent rate (CER) demonstrates the annualized yield on a short-term debt security that is normally quoted on a bank discount basis to such an extent that the yield can be comparable with citations on coupon-bearing securities.

In effect, it states what the coupon rate on a discount instrument, (for example, a zero-coupon, Treasury bill, or commercial paper) would be on the off chance that the instrument carried a coupon and had been sold at face value.

Since the quoted rate of bonds is calculated on the basis of the face value, this rate for bonds issued at a discount is inaccurate for comparing them to other coupon bonds. Discount or zero-coupon bonds are not sold at face value. They are sold at a discount, and the investor normally receives more than whatever they invested at maturity. Hence, it is more accurate to utilize the CER since it involves the investor's initial investment as the basis for yield.

The formula for coupon equivalent rate is:

$\begin&\text=\frac{\text-\text}{\text}\times\frac{360}{\text}\ &\textbf\ &\text=\text \end$

The coupon equivalent rate (CER) is calculated as:

- Find the discount the bond is trading at, which is face value less market value.
- Then, at that point, partition the discount by the market price.
- Partition 360 by the number of days until maturity.
- That number (from no. 3) is then duplicated by the number found in no. 2.

The coupon equivalent rate is an alternative method for working out the yield of a bond and considers a comparison of a zero-coupon bond to a bond of an alternate term. Nonetheless, it is a nominal yield and doesn't consider compounding.

The yield to maturity (YTM) is the hypothetical yield an investor would receive on the off chance that they held the bond to maturity. Yet, in contrast to the coupon equivalent yield (CER), the yield to maturity considers compounding. Both are communicated as annualized rates.

## CER Example

For instance, a $10,000 US T-bill that develops in 91 days is selling for $9,800. Its coupon equivalent rate would be 8.08%, or (($10,000 - $9,800)/($9,800)) * (360/91), which is 0.0204 * 3.96. Compared with a bond paying a 8% annual coupon we'd pick the zero-coupon bond given it has the higher rate {8.08% > 8%].

Or on the other hand think about a current zero-coupon Treasury STRIP that develops on March 15, 2022. The face value is $100 and the market price is $98.63 as of September 14, 2021. The coupon equivalent rate (CER) is 2.75%, or (($100 - $98.63)/($98.63) * (360/182 ).

## Features

- The coupon equivalent rate (CER) is the annualized yield of a zero-coupon bond when calculated as though it paid a coupon
- CER is a nominal yield and doesn't consider compounding.
- CER takes into account the comparison of zero-coupon bonds and other fixed-income securities.