Definition
– Bond equivalent yield (BEY) is a simple annualized return used to express the yield of a discounted fixed-income instrument (for example, a zero-coupon bond or a Treasury bill) on a comparable yearly basis. It lets investors compare short-term discounted securities with longer-term bonds that quote annual yields.
How the BEY works (concept)
– For discounted issues that pay no periodic coupons, the raw return equals the difference between the bond’s face (par) value and the price paid. BEY takes that raw return and annualizes it on a 365-day basis so you can compare it to quoted annual bond yields.
– BEY is an arithmetic (simple) annualization, not a compound or yield-to-maturity (YTM) calculation.
Formula and variables
– Formula: BEY = [(Face value − Purchase price) / Purchase price] × (365 / d)
– Face value = par amount to be received at maturity
– Purchase price = price paid today
– d = number of days until the bond matures
– Assumption: the formula uses a 365-day year to annualize. If you use a different day-count convention, adjust accordingly.
Step-by-step checklist (quick)
1. Confirm the instrument is a discounted, noncoupon security (or you intend a simple annualized comparison).
2. Record face value (par), purchase price, and days until maturity (d).
3. Compute raw return: (Face − Price) / Price.
4. Annualize: multiply raw return by (365 / d).
5. Compare the resulting BEY to other annual yields, remembering BEY does not compound intra-year.
Worked numeric example
– Situation: You buy a zero-coupon bond that pays $1,000 at maturity. You pay $900 today. Maturity is in 6 months (≈ 182.5 days).
1. Raw return = (1,000 − 900) / 900 = 100 / 900 = 0.111111… = 11.11%.
2. Annualization factor = 365 / 182.5 = 2.
3. BEY = 11.11% × 2 = 22.22% (rounded).
– Interpretation: On a simple annualized basis, this discounted six‑month purchase is equivalent to a 22.22% yearly return. That makes it comparable, on the same annual basis, to yields quoted for coupon bonds or other fixed‑income instruments. Remember this ignores intra‑year compounding.
Practical notes and cautions
– Use BEY when you need a straightforward annual comparison between discounted short-term securities and instruments quoted as annual yields.
– BEY is not the same as yield to maturity (YTM); YTM accounts for compounding and reinvestment assumptions, while BEY is a simple annualization.
– Check the day‑count convention and whether the market quotes yields on a different basis (some markets use 360-day years).
– Spreadsheet software commonly has functions or templates to compute BEY—use them to reduce arithmetic errors.
References
– Investopedia — Bond Equivalent Yield: https://www.investopedia.com/terms/b/bey.asp
– U.S. Department of the Treasury — Treasury Securities (TreasuryDirect): https://www.treasurydirect.gov/ (see the “Treasury Bills” and auction material for yield conventions
– FINRA — Bonds: https://www.finra.org/investors/learn-to-invest/types-investments/bonds
– U.S. Securities and Exchange Commission — Beginner’s Guide to Bonds: https://www.investor.gov/introduction-investing/investing-basics/investment-products/bonds
Educational disclaimer: This information is educational and general in nature. It is not personalized investment advice, tax advice, or a recommendation to buy or sell any security. For decisions that affect your finances, consult a licensed financial professional who can consider your individual circumstances.