## What is the 'Effective Yield'

The effective yield is the yield of a bond which has its coupons reinvested after payment has been received by the bondholder. Effective yield is the total yield an investor receives in relation to the nominal yield or coupon of a bond. Effective yield takes into account the power of compounding on investment returns, while nominal yield does not.

## BREAKING DOWN 'Effective Yield'

Bondholders can measure their yields on bonds in a number of ways. The current yield represents a bond’s annual return based on its annual coupon payments and current price, as opposed to the face value. It is calculated by dividing the coupon payments by the current market value of the bond. The yield to maturity (YTM) is the rate of return earned on a bond that is held until maturity. It is a bond equivalent yield (BEY), not an effective annual yield (EAY). A third measure of bond yield is the effective yield.

The effective yield is a measure of the coupon rate, which is the interest rate stated on a bond and expressed as a percentage of the face value. Coupon payments on a bond are typically paid semi-annually by the issuer to the bond investor. This means that the investor will receive two coupon payments per annum. For example, if an investor holds a bond with a face value of $1,000 and 5% coupon paid semi-annually on March and September, he will receive (5%/2) x $1,000 = $25 twice a year for a total of $50 in coupon payments.

However, the effective yield is a measure of return on a bond assuming the coupon payments are reinvested. If payments are reinvested, then his effective yield will be greater than the stated coupon yield or nominal yield, due to the effect of compounding. Reinvesting the coupon will produce a higher yield, because interest is earned on the interest payments. The investor in the example above will receive a little more than $50 annually using the effective yield evaluation. The formula for calculating effective yield is:

i = [1 + (r/n)]^{n} – 1

where i = effective yield

r = nominal rate

n = number of payments per year

Following our initial example presented above, the investor’s effective yield on his 5% coupon bond will be:

i = [1 + (0.05/2)]^{2} – 1

i = 1.025^{2} – 1

i = 0.0506, or 5.06%

Note that since the bond pays interest semi-annually, payments will be made twice to the bondholder per year, hence, number of payments per year is 2.

From the calculation above, the effective yield of 5.06% is clearly higher than the coupon rate of 5% since compounding is taken into consideration. To understand this another way, let’s scrutinize the details of the coupon payment. In March the investor receives 2.5% x $1,000 = $25. In September, due to interest compounding, he will receive (2.5% x $1,000) + (2.5% x $25) = 2.5% x $1,025 = $25.625. This translates to an annual payment of $25 in March + $25.625 in September = $50.625. The real interest rate is, therefore, $50.625/$1,000 = 5.06%.

To compare the effective yield to the YTM, convert the YTM to an effective annual yield. If the YTM is greater than the bond’s effective yield, then the bond is trading at a discount to par. On the other hand, if the YTM is less than the effective yield, the bond is selling at a premium.

The drawback with using the effective yield is that it assumes that coupon payments can be reinvested in another vehicle paying the same interest rate. This also means that it assumes the bonds are selling at par. This is not always possible, considering the fact that interest rates change periodically, falling and rising due to certain factors in the economy.