# Coupon Equivalent Yield (CEY)

## What it is:

The **coupon equivalent yield **is the effective annual interest rate earned on a bond. It is used to understand what the annual return is or would have been on an investment lasing less than one year.

The formula for CEY is:

*(Interest Paid, in Dollars, Between Now and Maturity / Purchase Price) x (365 / Days to Maturity)*

## How it works (Example):

Let's assume you purchased a $10,000 Company XYZ bond today for $9,950. The 5% coupon bond matures in exactly 48 days. Between now and then, you will receive one half of one interest payment (the issuer makes semiannual interest payments). Using these circumstances and the formula above, we can determine that the bond's effective annual interest rate is:

*($250 / $9,950) x (365 / 48) = 19.11%*

Thus, your 48-day investment had an effective annual return of 19.11%. This is not the actual return; it is what your return would have been if you essentially could have purchased the bond and received the $250 every 48 days for a year.

For zero-coupon bonds, which don’t have coupon payments, the coupon equivalent yield is simply the amount paid for the bond divided by the dollar return. For example, if the Company XYZ bond had been a T-bill, the coupon equivalent yield would be:

*($10,000 - $9,950) / $9,950 = 0.50%*

As you can see, the coupon makes a big difference.

## Why it Matters:

Borrowers typically make interest payments more than once a year, and bond payments are no different: the typical coupon bond pays interest once every six months. But investors have the opportunity to reinvest those payments, and this increases the return on the investment. The coupon equivalent yield helps the investor calculate exactly what that improved return is or would have been.

However, it is important to note that the formula assumes the investor can reinvest those interest payments at a rate equal to the bond's coupon rate. This is not always possible, depending on prevailing market rates and the investor's financial goals.