What is the effective yield?
Key takeaways
– Effective yield (also called effective annual yield, EAY) measures the annual return on a bond when coupon payments are reinvested at the same rate the bond pays.
– It accounts for compounding; nominal (coupon) yield does not.
– For bonds with periodic coupon payments, EAY = (1 + r/m)^m − 1, where r is the annual coupon rate and m is the number of coupon payments per year.
– EAY assumes coupon reinvestment at the coupon (or stated) rate and therefore has limitations — real reinvestment rates usually differ.
(Source: Investopedia)
Understanding effective yield
– Nominal (coupon) yield: the stated annual coupon expressed as a percentage of face value (for example, a $1,000 bond with a $50 annual coupon has a 5% coupon yield).
– Current yield: annual coupon divided by the bond’s current market price (ignores reinvestment and capital gain/loss).
– Effective yield / EAY: the return after compounding coupon payments at the bond’s coupon rate (or at the reinvestment rate you assume). It expresses the true annualized increase in value from coupon receipts plus the interest earned on their reinvestment.
Why effective yield matters
– Shows how compounding increases total return relative to the nominal coupon rate.
– Useful to compare bonds and other investments on an apples-to-apples annualized, compounding basis.
– Helps convert commonly quoted bond yields (like bond-equivalent yields or YTM quoted on a semiannual basis) into an annual effective rate.
Formula and how to calculate it
– General formula for effective annual yield when coupons are reinvested at the coupon rate:
EAY = (1 + r/m)^m − 1
where:
r = annual coupon rate (as a decimal), and
m = number of coupon payments per year (e.g., m = 2 for semiannual).
– If you have a quoted yield-to-maturity (YTM) or bond-equivalent yield (BEY) quoted on a semiannual basis, convert it to EAY using:
EAY = (1 + (YTM / 2))^2 − 1
(For m compounding periods: EAY = (1 + YTM/m)^m − 1.)
Worked example (semiannual coupon)
– Bond face value: $1,000
– Coupon: 5% annual, paid semiannually → each payment = 2.5% × $1,000 = $25
– r = 0.05, m = 2 → EAY = (1 + 0.05/2)^2 − 1 = (1 + 0.025)^2 − 1 = 1.050625 − 1 = 0.050625 → 5.0625%
– Dollar view: Investor receives $25 in March, reinvests it at 2.5% for six months, so by September it’s $25 × (1 + 0.025) = $25.625. September coupon $25 + reinvested March coupon interest $0.625 gives total annual receipts ≈ $50.625, which is 5.0625% of $1,000.
Practical steps for investors
1. Identify the bond’s annual coupon rate (r) and the payment frequency (m).
2. Decide whether you assume reinvestment at the coupon rate or at some other realistic reinvestment rate. If using a different rate, replace r/m in the formula with that periodic reinvestment rate.
3. Compute EAY:
– If reinvestment rate = coupon rate: EAY = (1 + r/m)^m − 1.
– If reinvestment rate = i (annual), EAY = (1 + i/m)^m − 1 using i in decimal form.
4. If you have YTM expressed as a BEY (semiannual convention), convert YTM to EAY: EAY = (1 + YTM/2)^2 − 1. For other compounding frequencies use (1 + YTM/m)^m − 1.
5. Compare EAY to current yield and YTM:
– If YTM (converted to EAY) > EAY based on coupon reinvestment, the bond may be trading at a discount (price < par) — YTM includes expected capital gain.
– If YTM (converted to EAY) par).
6. Use spreadsheets/financial calculators to model cash flows if you want to include purchase price, reinvestment at variable rates, or capital gain/loss on sale:
– Excel: =((1 + r/m) ^ m) – 1 for EAY from coupon; or = (1 + YTM/2) ^ 2 – 1 for semiannual YTM → EAY.
– To model reinvested coupon accumulation, use FV(reinvest_rate/m, periods, -coupon_payment, 0).
Limitations and cautions
– Reinvestment assumption: EAY assumes coupons are reinvested at the same rate (coupon rate). In practice reinvestment rates change with market rates; if reinvested at lower/higher rates, realized return will differ.
– Price and capital gains/losses: EAY based solely on coupon compounding ignores the effect of buying a bond at a price different from par and any capital gain/loss realized at maturity or sale. Yield-to-maturity (or total return models) capture the combined effect of coupons plus price changes.
– Not all yields are quoted on the same basis—ensure you convert YTM/BEY to an effective annual figure before comparing.
When to use effective yield versus YTM or current yield
– Use effective yield to compare the compounding power of coupon reinvestment across securities.
– Use YTM when you plan to hold the bond to maturity and want the internal rate of return that incorporates price paid and redemption value.
– Use current yield for a quick snapshot of income relative to current price (but it ignores reinvestment and capital gain/loss).
Common quick formulas (summary)
– EAY from coupon rate: EAY = (1 + coupon_rate / m)^m − 1
– Convert semiannual YTM to EAY: EAY = (1 + YTM/2)^2 − 1
– Current yield = annual coupon / current price (no reinvestment or capital gains)
Further reading and source
This article summarized and drew examples from Investopedia’s explanation of effective yield: https://www.investopedia.com/terms/e/effectiveyield.asp
If you’d like, I can:
– Walk through a worked example using a non-par purchase price (showing total return with reinvestment).
– Provide an Excel template or step-by-step cell formulas to compute EAY, YTM→EAY conversion, and future value of reinvested coupons.