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Bond Equivalent Yield Calculator

Calculate bond equivalent yield (BEY), bank discount yield, and effective annual yield (EAY) for short-term discount securities.

Standard Money Market Instruments

1-click benchmark presets

Security Parameters

$
Specify dollar purchase price
$
days
Year Day-Count Basis

Bond Equivalent Yield (BEY)

4.9%

+13 bps higher than Bank Discount Yield (4.8%) · 90 days to par redemption

Bank Discount Yield
4.8%
Actual / 360 · Par Base
Money Market Yield
4.9%
Actual / 360 · Price Base
Effective Annual Yield
5.0%
Compounded · 365 Days
Holding Period Yield
1.2%
90-day absolute return
Purchase Price Paid
$9,880.00
98.80% of Par
Dollar Discount / Gain
+$120.00
Total cash earned at par
BEY vs BDY Spread
+13 bps
+0.126% spread
Continuous Yield
4.9%
Logarithmic rate

Maturity Face Value Cash Composition

  • Purchase Price Invested$9,880.0098.8%
  • Dollar Discount (Interest Earned)$120.001.2%

Yield Convention Comparison

Side-by-side reconciliation of standard money market and bond market yield metrics for this security.

Metric / ConventionDay CountBasisAnnual YieldSpread vs BEY
Bank Discount Yield (BDY / Quoted Rate)
Dealer quote convention for T-bills based on face value & 360-day year
Actual / 360Face Value (Par)4.8%-13 bps
Money Market Yield (MMY / CD Equivalent)
Simple annualized yield on actual investment price using 360-day year
Actual / 360Purchase Price4.9%-7 bps
Bond Equivalent Yield (BEY / Investment Yield)Primary
Annualized yield on 365-day basis for direct comparison to coupon bonds
Actual / 365Purchase Price4.9%0 bps (Benchmark)
Effective Annual Yield (EAY / APY)
Full compound annual yield accounting for reinvestment over 365 days
Compounded / 365Purchase Price5.0%+9 bps

How bond equivalent yield is calculated

Mathematical walkthrough translating discount price and money market quotes into a 365-day bond equivalent yield.

  1. 1. Calculate Dollar Discount and Holding Period Yield

    D=F−P,HPY=F−PPD = F - P, \quad \text{HPY} = \frac{F - P}{P}

    With face value F = $10,000.00 and purchase price P = $9,880.00, the dollar discount is D = $120.00. The unannualized holding period yield is 1.2% over 90 days.

  2. 2. Compute Bank Discount Yield (BDY)

    Yd=F−PF×360tY_d = \frac{F - P}{F} \times \frac{360}{t}

    Under dealer quoting conventions, dividing the discount by face value ($10,000.00) and scaling by a 360-day year yields a Bank Discount Yield of 4.8%.

  3. 3. Compute Money Market Yield (MMY)

    Ymmy=F−PP×360t=360×Yd360−(t×Yd)Y_{\text{mmy}} = \frac{F - P}{P} \times \frac{360}{t} = \frac{360 \times Y_d}{360 - (t \times Y_d)}

    Scaling the holding period yield by a 360-day year yields a Money Market Yield of 4.9%.

  4. 4. Compute Bond Equivalent Yield (BEY)

    BEY=F−PP×365t=365×Yd360−(t×Yd)\text{BEY} = \frac{F - P}{P} \times \frac{365}{t} = \frac{365 \times Y_d}{360 - (t \times Y_d)}

    Because days to maturity (90 days) is less than or equal to 182 days, BEY uses the 365-day annualization on purchase price, producing a BEY of 4.9% (+13 bps higher than BDY).

  5. 5. Compute Effective Annual Yield (EAY)

    EAY=(1+F−PP)365t−1\text{EAY} = \left(1 + \frac{F - P}{P}\right)^{\frac{365}{t}} - 1

    Compounding the holding period return over a full 365-day year yields an Effective Annual Yield of 5.0% (+9 bps above BEY).

Maturity Sensitivity Matrix

Yield and price comparisons across standard money market tenors at the benchmark discount yield of 4.8%.

TenorPurchase PriceDiscount EarnedBank DiscountMoney MarketBond EquivalentEffective Annual
1 Month (30d)
$9,960.00+$40.004.8%4.8%4.9%5.0%
2 Months (60d)
$9,920.00+$80.004.8%4.8%4.9%5.0%
3 Months (90d - Benchmark)Current
$9,880.00+$120.004.8%4.9%4.9%5.0%
6 Months (180d)
$9,760.00+$240.004.8%4.9%5.0%5.0%
9 Months (270d)
$9,640.00+$360.004.8%5.0%5.0%5.1%
1 Year (360d)
$9,520.00+$480.004.8%5.0%5.0%5.1%
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What Is Bond Equivalent Yield (BEY)?

Bond Equivalent Yield (BEY), also known as the investment yield, is a standardized annualized yield calculation used across global fixed-income markets. It converts the quoted discount rate of short-term money market securities (such as US Treasury bills, commercial paper, and banker's acceptances) into a 365-day yield that can be directly compared with conventional coupon-bearing bonds.

Short-term discount instruments do not pay periodic coupon interest. Instead, they are issued at a discount to their face (par) value and mature at full face value. Because dealers traditionally quote these instruments using a 360-day year and calculate the percentage discount against the face value rather than the cash paid, quoted discount rates significantly understate an investor's true return. The bond equivalent yield solves this discrepancy by scaling returns to a 365-day year based on the actual purchase price invested.

For broader coupon-paying securities, you can analyze annual cash flow yields with the bond current yield calculator or price multi-year fixed-income debt using the bond calculator.

Why Discount Rates Understate Your Real Investment Return

To understand why BEY is essential, consider how dealer quotes operate in money markets. When a bank or broker quotes a 90-day Treasury bill at 4.80%, they are citing the Bank Discount Yield (BDY). This quote introduces two major distortions:

  1. The 360-Day Day-Count Convention: The discount yield assumes a commercial year of only 360 days (twelve 30-day months) instead of the actual 365 days in a calendar year (or 366 in a leap year). This shortens the annualized timeline and deflates the annualized return.
  2. Par Value Base vs. Actual Investment: The percentage discount is calculated against the maturity face value (FF) rather than the capital you actually paid (PP). Because you invest less than face value (P<FP < F), your effective return per dollar invested is higher than the percentage discount on par.

For instance, buying a $10,000 face value bill for $9,880 generates a $120 return on a $9,880 investment (a 1.215% cash return in 90 days), whereas the discount rate treats that $120 return as 1.200% of $10,000. You can inspect standalone discount math with the bank discount calculator.

Mathematical Formulas for Money Market Yields

The relationship between discount yields, money market yields, bond equivalent yields, and compound effective annual yields follows strict mathematical conventions.

1. Bank Discount Yield (BDY)

The bank discount yield (YdY_d) scales the dollar discount (D=F−PD = F - P) against face value (FF) over a 360-day year:

Yd=F−PF×360tY_d = \frac{F - P}{F} \times \frac{360}{t}

2. Money Market Yield (MMY / CD Equivalent Yield)

The money market yield (YmmyY_{\text{mmy}}) corrects the denominator by using the purchase price (PP), while retaining the 360-day day-count convention:

Ymmy=F−PP×360t=360×Yd360−(t×Yd)Y_{\text{mmy}} = \frac{F - P}{P} \times \frac{360}{t} = \frac{360 \times Y_d}{360 - (t \times Y_d)}

3. Bond Equivalent Yield (BEY)

For maturities of 182 days or fewer (half a year or less), BEY scales the money market return to a 365-day calendar year:

BEY=F−PP×365t=365×Yd360−(t×Yd)\text{BEY} = \frac{F - P}{P} \times \frac{365}{t} = \frac{365 \times Y_d}{360 - (t \times Y_d)}

When days to maturity exceed 182 days (such as 270-day or 360-day bills), standard US Treasury and CFA Institute conventions account for semi-annual compounding, using the quadratic formulation:

BEY=−2t365+2(t365)2−(2t365−1)(1−FP)2t365−1\text{BEY} = \frac{-\frac{2t}{365} + 2\sqrt{\left(\frac{t}{365}\right)^2 - \left(2\frac{t}{365} - 1\right)\left(1 - \frac{F}{P}\right)}}{2\frac{t}{365} - 1}

4. Effective Annual Yield (EAY)

The Effective Annual Yield accounts for the full compounding of interest over an entire 365-day year, assuming reinvestment at the same holding period yield:

EAY=(1+F−PP)365t−1\text{EAY} = \left(1 + \frac{F - P}{P}\right)^{\frac{365}{t}} - 1

To convert between nominal rates and compound yields across other asset classes, refer to the APR to APY calculator and measure rate differences using the basis point calculator.

Step-by-Step Worked Example: 90-Day Treasury Bill

Suppose an investor purchases a 90-day US Treasury bill with a face value of $10,000 for a discounted purchase price of $9,880. Let us walk through the complete calculation hierarchy:

Step 1: Calculate Dollar Discount

D=$10,000−$9,880=$120.00D = \$10{,}000 - \$9{,}880 = \$120.00

Step 2: Calculate 90-Day Holding Period Yield (HPY)

HPY=$120$9,880=0.0121457 (or 1.2146%)\text{HPY} = \frac{\$120}{\$9{,}880} = 0.0121457 \text{ (or } 1.2146\% \text{)}

Step 3: Calculate Bank Discount Yield (360-Day, Par Base)

Yd=$120$10,000×36090=0.0120×4=4.800%Y_d = \frac{\$120}{\$10{,}000} \times \frac{360}{90} = 0.0120 \times 4 = 4.800\%

Step 4: Calculate Money Market Yield (360-Day, Price Base)

Ymmy=$120$9,880×36090=0.0121457×4=4.858%Y_{\text{mmy}} = \frac{\$120}{\$9{,}880} \times \frac{360}{90} = 0.0121457 \times 4 = 4.858\%

Step 5: Calculate Bond Equivalent Yield (365-Day, Price Base)

BEY=$120$9,880×36590=0.0121457×4.05556=4.926%\text{BEY} = \frac{\$120}{\$9{,}880} \times \frac{365}{90} = 0.0121457 \times 4.05556 = 4.926\%

Step 6: Calculate Effective Annual Yield (Compounded, 365-Day)

EAY=(1+0.0121457)36590−1=(1.0121457)4.05556−1=5.018%\text{EAY} = (1 + 0.0121457)^{\frac{365}{90}} - 1 = (1.0121457)^{4.05556} - 1 = 5.018\%

In this scenario, the quoted dealer discount rate of 4.80% translates to a true Bond Equivalent Yield of 4.93% (a 13 basis point pickup) and an Effective Annual Yield of 5.02% (a 22 basis point pickup).

Comparing Yield Metrics in Fixed-Income Portfolios

When managing cash and fixed-income portfolios, ranking instruments by their raw quoted yield can lead to suboptimal asset allocation. The table below summarizes key differences among standard yield measures:

Yield MetricDay CountCalculation BasePrimary Purpose
Bank Discount Yield (BDY)Actual / 360Face Value (Par)Trading floor quote convention for T-bills
Money Market Yield (MMY)Actual / 360Purchase PriceComparison with commercial paper and CDs
Bond Equivalent Yield (BEY)Actual / 365Purchase PriceDirect comparison with Treasury notes and bonds
Effective Annual Yield (EAY)Compounded / 365Purchase PriceTotal annual wealth growth assuming reinvestment

For securities subject to interest rate shifts and price fluctuations, sensitivity can be further evaluated alongside bond convexity calculator metrics to quantify non-linear price responsiveness.

Frequently asked questions

Why is Bond Equivalent Yield always higher than Bank Discount Yield?
BEY is always higher than BDY for two structural reasons: First, BEY uses a 365-day year rather than a 360-day year, multiplying the daily rate by 365/360 (an automatic 1.39% increase). Second, BEY divides the cash return by the discounted purchase price rather than the higher maturity face value, which increases the return percentage per dollar invested.
When should I use BEY instead of Money Market Yield (MMY)?
Use BEY whenever you are deciding between a short-term discount instrument (like a 6-month T-bill) and a coupon-bearing instrument (such as a 2-year Treasury note or corporate bond). Coupon bonds pay semi-annually and quote yields on a 365-day annual basis. Money Market Yield is best suited for comparing money market instruments against 360-day commercial paper or bank certificates of deposit.
Why does the BEY formula change for maturities longer than 182 days?
Because standard Treasury notes pay coupons every 6 months (approximately 182.5 days), coupon bond yields reflect semi-annual compounding. For a discount bill maturing in more than 182 days, a simple linear annualization would fail to reflect compounding across half-year periods. The exact quadratic Treasury formula provides an exact semi-annual compounding match.
How do leap years affect Bond Equivalent Yield?
In a leap year with 366 calendar days, the numerator in the day-count factor increases from 365 to 366. This slightly increases the annualized yield because the investor holds the instrument for one additional day within the calendar year.
Can I calculate BEY if I only have the quoted discount percentage?
Yes. You can toggle the input mode in this calculator to Discount Yield (%) and enter the dealer quote. The calculator immediately derives the implied dollar purchase price and calculates the exact BEY, MMY, and EAY.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.