Bond Equivalent Yield
Bond Equivalent Yield
Bond equivalent yield converts returns from securities with different compounding periods into a standardized semi-annual equivalent yield. It allows you to compare a Treasury bill, a monthly-pay corporate bond, and an annual-pay European gilt on an apples-to-apples basis.
Key takeaways
- BEY annualizes a short-term yield or adjusts a yield with a different compounding frequency to the U.S. standard of semi-annual compounding
- A 3-month Treasury bill yielding 5% does not earn 5% per year; it earns approximately 5.09% annualized as BEY
- Bond equivalent yield assumes semi-annual compounding, the U.S. bond market standard
- Without BEY, comparing a monthly-pay MBS to a semi-annual-pay corporate bond would be misleading because of different compounding
- BEY is especially important for short-term securities like T-bills, commercial paper, and money market instruments
The problem: different payment frequencies
A 3-month Treasury bill does not pay coupons; it is issued at a discount and matures at par. If you buy a $10,000 face value T-bill that expires in 3 months and you pay $9,875 today, you earn $125 in 3 months. What is your yield?
Simple calculation: $125 / $9,875 = 1.27% for 3 months. Annualize naively: 1.27% × 4 quarters = 5.08%.
But this is not quite right because of compounding. If you earn 1.27% every quarter, you earn more than 5.08% annually because of reinvestment. The true annualized return is (1.0127)^4 − 1 = 5.17%.
The U.S. bond market uses a different standard: bond equivalent yield, or BEY. BEY assumes semi-annual compounding. So a quarterly return is annualized as if you were earning it every six months, not every quarter.
The BEY formula
For a T-bill or money market instrument with a holding period of less than one year:
BEY = (Par value − Purchase price) / Purchase price × 365 / Days held
Where:
- Par value = face amount at maturity
- Purchase price = what you paid today
- Days held = the actual number of days until maturity
For our T-bill example:
BEY = ($10,000 − $9,875) / $9,875 × 365 / 91 = 1.27% × 4.01 = 5.09%
This 5.09% is the bond equivalent yield. It is what you would earn if you held this T-bill and reinvested the proceeds every six months at the same rate (a simplifying assumption, but the standard for comparison).
Converting between different compounding frequencies
BEY is also used to standardize bonds with different payment frequencies. A bond paying monthly coupons, a bond paying semi-annual coupons, and a bond paying annual coupons all exist in the U.S. market. To compare their yields fairly, you convert to BEY (semi-annual equivalent).
The conversion formula is:
BEY = (1 + Periodic yield)^(Number of periods per year / 2) − 1
Wait, that is not quite right. More precisely:
If a bond's periodic yield (monthly, annual, etc.) is y, the semi-annual equivalent yield is:
BEY = 2 × [(1 + y)^(2 / frequency) − 1]
For example:
- Monthly yield of 0.3%: BEY = 2 × [(1.003)^(2/12) − 1] = 2 × [0.00498] = 0.996% semi-annually = 1.99% annualized
- Actually, to express as annual BEY: BEY = 2 × [(1.003)^2 − 1] = 2 × [0.00601] = 1.20% annualized. (The calculation is a bit involved; the key idea is that semi-annual compounding is the standard.)
In practice, most traders and calculators have BEY built in. You input the yield and the frequency, and it returns the BEY. You do not usually hand-calculate.
T-bills and the money market
Treasury bills are short-term U.S. government debt, maturing in 4, 13, 26, or 52 weeks. They are issued at a discount (below par) and pay no coupons. You buy a T-bill for less than face value, wait, and collect par at maturity. The return is the difference.
T-bills are quoted in the money market using discount rate, not BEY. The discount rate is a simplified calculation that does not account for the actual number of days or compounding. For example, a T-bill might be quoted as a 4.5% discount rate.
The BEY of that T-bill would be higher than 4.5%, perhaps 4.6% or 4.7%, depending on the days to maturity. Traders and investors should know the BEY, not the discount rate, to compare T-bills with coupon bonds fairly.
Corporate bonds and payment frequency
Most U.S. corporate bonds pay semi-annually. So the YTM you see quoted is already on a semi-annual basis (the standard). No conversion is needed.
But floating-rate bonds might pay quarterly. A floating-rate bond with SOFR + 200 bps and quarterly payments has a different compounding structure than a semi-annual bond. To compare the two fairly, you convert the quarterly yield to BEY.
For a quarterly yielding bond with an annual yield of 5%, the BEY is:
BEY = 2 × [(1 + 0.05/4)^2 − 1] = 2 × [(1.0125)^2 − 1] = 2 × [0.0251] = 5.02%
Very close, because quarterly and semi-annual compounding are not too different. But the difference matters when yields are high or compounding periods are vastly different.
Mortgage-backed securities and monthly payments
Mortgage-backed securities pay monthly (because mortgages pay monthly). The stated yield on an MBS is often quoted as monthly, but for comparison with a semi-annual corporate bond, you need to convert to BEY.
An MBS with a monthly yield of 0.33% (which is 4% annualized naively) has a BEY of:
BEY = 2 × [(1.0033)^6 − 1] = 2 × [0.0200] = 4.00% annualized
Wait, that does not work out. Let me reconsider. If the annual yield is 4%, paid monthly, the monthly yield is 4% / 12 = 0.33%. The semi-annual equivalent is (1.0033)^6 − 1 = 2.00%. Annualized, that is 4.00%. So the BEY is 4.00%, the same as the stated annual yield. This makes sense because 12 months is divisible by 6 months, and the compounding works out to the same answer.
The point is that MBS yields should be quoted as BEY for comparison. Some MBS quotes use different conventions (like street convention), which can be confusing.
International bonds and BEY
A European bond with annual coupons trades at a different basis than a U.S. bond with semi-annual coupons. To compare, you convert the European bond's annual yield to BEY (semi-annual equivalent).
A UK gilt yielding 3% annually (semi-annual equivalent yield, since that is the UK standard) has a BEY of:
BEY = 2 × [(1 + 0.03/2)^1 − 1] = 2 × [(1.015) − 1] = 2 × [0.015] = 3.00%
Actually, the UK quote is often already on a semi-annual basis, so BEY = 3.00%. If it is on an annual basis, the semi-annual equivalent would be slightly higher.
The key is understanding the convention. U.S. bonds are semi-annual; European bonds are annual; MBS are monthly. When comparing across borders, use BEY to normalize.
BEY and money market funds
A money market fund invests in short-term securities: T-bills, commercial paper, bank certificates of deposit. The fund might report its yield as a 7-day yield or a 30-day yield. These are short-term yields, not annualized.
To annualize, you convert to BEY. If a money market fund reports a 7-day yield of 0.10%, the BEY is:
BEY = 0.10% × (365 / 7) = 5.21%
Again, this is a simplified annualization; the exact calculation depends on the specific days and compounding assumptions. But the idea is clear: BEY converts short-term yields to annualized equivalents so you can compare a money market fund to a bond fund.
Practical use: comparing bonds
You are considering two investments:
Investment A: Corporate bond
- Coupon: semi-annual
- YTM: 4.50%
Investment B: MBS
- Coupon: monthly
- Stated yield: 4.40%
Which is better? You cannot compare 4.50% to 4.40% directly because they use different compounding. You convert the MBS yield to BEY:
Assuming 4.40% stated annual yield on monthly compounding:
- Monthly yield = 4.40% / 12 = 0.3667%
- Semi-annual equivalent = (1.003667)^6 − 1 = 2.2259%
- Annualized BEY = 2.2259% × 2 = 4.45%
Now you can compare: Corporate bond YTM of 4.50% vs. MBS BEY of 4.45%. The corporate bond is slightly more attractive (assuming same credit quality and maturity).
BEY and bond fund comparisons
When comparing bond funds, use the stated BEY yield or YTM. Most funds report their yield as BEY, even if their holdings have different payment frequencies. The fund converts all yields to BEY and reports a weighted average. This allows investors to compare a short-term bond fund, an intermediate bond fund, and a long-term bond fund on an equal basis.
Historical BEY context
In the 1970s and 1980s, when interest rates were very high (15%, 20%), the difference between simple and compound yields was large. An investment earning 15% annually but compounded monthly would earn about 16% annualized. BEY calculations were essential for accurate comparison.
In the 2010s, with near-zero rates, BEY made less difference, but the convention persisted. As rates rose again in 2022–2023, the differences between compounding frequencies became more material.
Common mistakes
Mistake 1: Confusing discount rate with BEY. A T-bill quoted at a 4% discount rate does not yield 4% BEY. The BEY is higher, perhaps 4.06% or 4.08%, depending on days to maturity. Do not treat them as the same.
Mistake 2: Comparing stated yields across different frequencies without converting. If one bond yields 5% semi-annually and another yields 4.9% annually, you cannot say the first is better without converting to BEY. The annual 4.9% might convert to 4.95% BEY, making it very close.
Mistake 3: Ignoring BEY in fund comparisons. A fund investing in MBS will have different yields than a fund investing in corporate bonds, partly because of payment frequency. Always compare on a BEY basis (or YTM or YTW) to understand true relative value.
Conclusion: BEY standardizes the playing field
Bond equivalent yield is a technical standard, but it is essential for fair comparison. Whenever you are comparing yields across different bond types, payment frequencies, or time horizons, use BEY. It ensures you are comparing apples to apples and not being misled by different compounding assumptions.
Process
Related concepts
Next
Bond equivalent yield normalizes yields across different payment frequencies. But yields are only one part of a bond's return. The other part is price change, which depends on how much a bond's price moves when interest rates shift.