What is the Coupon Equivalent Rate (CER)?
The Equivalent Coupon Rate (CER) is an alternative calculation of the coupon rate that is used to compare zero coupon and coupon fixed income securities. It is the annualized yield of a zero coupon bond when calculated as if it were paying a coupon. Also known as Bond Equivalent Yield (BEY) or Coupon Equivalent Yield (CEY).
- The Coupon Equivalent Rate (CER) is the annualized yield on a zero coupon bond, such as Treasury bills and commercial paper.
- It allows the comparison of zero coupon bonds and other fixed income securities.
- It is a nominal return and does not take composition into account.
The formula for the coupon equivalent rate is
CR=Market priceNominal value–Market price×Days to maturity36where:
How to Calculate the Coupon Equivalent Rate
The Equivalent Coupon Rate (CER) is calculated as:
- Find the discount at which the bond is trading, which is the face value minus the market value.
- Then divide the discount by the market price.
- Divide 360 by the number of days until expiration.
- That number (from # 3) is then multiplied by the number found in #. two.
What does the coupon equivalent rate tell you?
The Coupon Equivalent Rate (CER) allows an investor to compare a zero coupon bond with one that pays coupon. While most bonds pay investors annual or semi-annual interest payments, some bonds, called zero coupon bonds, do not pay any interest, but are issued at a large discount at par.
The investor earns a return on these discounted bonds when the bond matures. To compare the performance of coupon-paying 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 typically traded on a bank discount basis, so that the return can be comparable to the prices of coupon securities.
In effect, it establishes what the coupon rate of a discount instrument (such as a zero coupon, a Treasury bill, or a commercial paper) would be if the instrument had a coupon and had been sold at face value.
Because 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 typically receives more than he invested at maturity. Therefore, the CER is more accurate to use because it uses the investor’s initial investment as the basis for performance.
Example of how to use the coupon equivalent rate
For example, a $ 10,000 Treasury note that expires in 91 days sells for $ 9,800. Your coupon equivalent rate would be 8.08%, or (($ 10,000 – $ 9,800) / ($ 9,800)) * (360/91), which is 0.0204 * 3.96. Compared to a bond that pays an 8% annual coupon, we would choose the zero coupon bond since it has the highest rate (8.08%).
Or consider a current zero coupon Treasury STRIP (as of January 2019) expiring on August 15, 2019. The face value is $ 100 and the market price is $ 98.63 as of January 29, 2019. The Coupon Equivalent Rate (CER) is 2.54%, or (($ 100 – $ 98.63) / ($ 98.63) * (360/198).
The difference between the coupon equivalent rate and the yield to maturity
Yield to maturity (YTM) is the theoretical return that an investor would receive if they held the bond to maturity. But unlike Coupon Equivalent Yield (CER), Yield to Maturity takes compounding into account. Both are expressed as annualized rates.
Limitations on the use of the coupon equivalent rate
The equivalent coupon rate is an alternative way to calculate the yield on a bond. The equivalent coupon rate allows you to compare a zero coupon bond with a bond of a different term. However, it is a nominal return and does not take composition into account.