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 knowthe 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:
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 = 1.0252 – 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%.
FAQs
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.
How is effective yield calculated? ›
Effective annual yield is calculated using the formula: (1+r/n)^n-1. Where r is the interest rate or coupon rate and n is the number of times the interest is paid per year.
What is an example of a yield calculation? ›
For example, if there is a Treasury bond with a face value of $1,000 that matures in one year and pays 5% annual interest, its yield is calculated as $50 / $1,000 = 0.05 or 5%.
How to calculate effective yield on FD? ›
A: The formula to calculate the effective yield on an FD is (1 + i/n)^n - 1, where 'i' represents the interest rate and 'n' represents the number of compounding periods per year. The formula for effective yield calculation is very important while choosing investments.
How do you calculate the EIR? ›
Effective annual interest rate = ( 1 + ( nominal rate ÷ number of compounding periods ) ) ^ ( number of compounding periods ) - 1.
How do you approximate effective yield? ›
Effective Yield = [1 + (i/n)]n – 1
Where: i – The nominal interest rate on the bond. n – The number of coupon payments received in each year.
How to calculate effective yield in Excel? ›
To calculate the current yield of a bond in Microsoft Excel, enter the bond value, the coupon rate, and the bond price into adjacent cells (e.g., A1 through A3). In cell A4, enter the formula "= A1 * A2 / A3" to render the current yield of the bond.
How to calculate %yield? ›
How to calculate yield
- Determine the market value or initial investment of the stock or bond.
- Determine the income generated from the investment.
- Divide the market value by the income.
- Multiply this amount by 100.
The earnings yield is the inverse ratio to the price-to-earnings (P/E) ratio. The quick formula for Earnings Yield is E/P, earnings divided by price. The yield is a good ROI metric and can be used to measure a stocks rate of return.
How do you calculate mean yield? ›
To calculate the annual yield, you need to divide the total return by the initial investment and multiply it by 100 to get the annual yield as a percentage. Then depending on the number of years you held the asset, divide the annual yield by that number to determine the average annual yield.
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.
What is the difference between 7 day yield and effective yield? ›
7-day yield vs.
It estimates the percentage an account would earn in a year with compounding interest. On the other hand, 7-day yield does not take compounding (reinvesting your earnings) into account. To see that calculation for a money market fund, look for the “compound effective” yield.
What is the constant effective yield? ›
The constant yield amount is calculated by multiplying the adjusted basis by the yield at issuance and then subtracting the coupon interest. This method is also known as the effective or scientific method of amortization.
How do you explain effective interest rate? ›
The annual 'effective' rate reflects the amount paid over the year if the interest is added to the account balance every month. This number reflects the true return you can expect on your investment, because it includes the effect of compound interest.
What is the formula for effective return rate? ›
The formula for EAR is: EAR = (1 + i/n)^n - 1 where i is the stated interest rate as a decimal and n is the number of interest payments per year. The stated interest rate is typically given as a percentage so remember to divide that percentage by 100 to get the decimal version.
How to calculate EIR in Excel? ›
How to compute effective interest rates in excel? The EFFECT function is used to compute it in Excel. The formula is put as EFFECT (nominal_rate, npery). Here, the nominal rate is the rate mentioned in the financial instrument, and npery is the number of compounding periods per year.
How is effective rate calculated? ›
The effective interest rate is the actual percent interest that a borrower pays on their loan or earns on their investment. The formula for effective interest rate is EAR = {(1 + i/n)^n - 1} * 100, where i is the nominal rate as a decimal and n is the number of compounding periods per year.
What is the formula for the effective APY? ›
APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year. The formula for calculating APY is (1+r/n)n - 1, where r = period rate and n = number of compounding periods.
What is the formula for effective yield stress? ›
The yield stress formula is given by σ y = E − ϵ y where σ y is the yield stress, E is the Young's modulus, and ϵ y is the yield strain.
How do you calculate the 7 day effective yield? ›
The seven-day yield is a method for estimating the annualized yield of a money market fund. It is calculated by taking the net difference of the price today and seven days ago and multiplying it by an annualization factor. Since money market funds tend to be very low risk, the higher the seven-day yield the better.
