## What Is the Effective Yield?

The effective yield is the return on a bond that has its interest payments (or coupons) reinvested at the same rate by the bondholder. Effective yield is the total yield an investor receives, in contrast to the nominal yield—which is the stated interest rate of the bond's coupon. Effective yield takes into account the power of compounding on investment returns, while nominal yield does not.

### Key Takeaways

- The effective yield is calculated as the bond’s coupon payments divided by the bond’s current market value
- Effective yield assumes coupon payments are reinvested. Reinvested coupons mean the effective yield of a bond is higher than the nominal (stated coupon) yield.
- To compare a bond's effective yield and its yield-to-maturity, the effective yield must be converted to an effective annual yield.
- Bonds trading with an effective yield higher than the yield-to-maturity sell at a premium. If the effective yield is lower than the yield-to-maturity, the bond trades at a discount.

## Understanding 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 year. Effective yield is calculated by dividing the coupon payments by the current market value of the bond.

Effective yield is one way that bondholders can measure their yields on

bonds. There's also the current yield, which represents a bond’s annual

return based on its annual coupon payments and current price, as opposed to the face value.

Though similar, current yield doesn't assume coupon reinvestment, as effective yield does.

The drawback of 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.

## Effective Yield vs. Yield-to-Maturity (YTM)

The yield-to-maturity (YTM) is the rate of return earned on a bond that is held until maturity. To compare the effective yield to the yield-to-maturity (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.

YTM is what's called a bond equivalent yield (BEY). Investors can find a more precise annual yield once they know the BEY for a bond if they account for the time value of money in the calculation. This is known as an effective annual yield (EAY).

## Example of Effective Yield

If an investor holds a bond with a face value of $1,000 and a 5% coupon paid semi-annually in 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 current 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 as follows:

- 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, the number of payments per year is two.

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%.