Bond Equivalent Yield Calculator

Convert Discount Yield to Annualized Return

Calculate the bond equivalent yield (BEY) to convert discount yields from Treasury bills, commercial paper, and other short-term investments to annualized returns for easy comparison.

Example BEY Calculations

Common scenarios to help you understand bond equivalent yield calculations

90-Day Treasury Bill

Treasury Bill

Standard Treasury bill with 360-day calculation

Face Value: 10000 $

Purchase Price: 9850 $

Days to Maturity: 90 days

Method: 360-day

30-Day Commercial Paper

Commercial Paper

Short-term corporate debt instrument

Face Value: 50000 $

Purchase Price: 49750 $

Days to Maturity: 30 days

Method: 360-day

180-Day CD

Certificate of Deposit

Bank certificate of deposit with 365-day calculation

Face Value: 25000 $

Purchase Price: 24250 $

Days to Maturity: 180 days

Method: 365-day

60-Day Money Market

Money Market Instrument

Money market instrument with higher yield

Face Value: 100000 $

Purchase Price: 99000 $

Days to Maturity: 60 days

Method: 360-day

Other Titles
Understanding Bond Equivalent Yield: A Comprehensive Guide
Master the conversion of discount yields to annualized returns for better investment comparisons

What is Bond Equivalent Yield (BEY)?

  • Core Definition and Purpose
  • Why BEY Matters
  • Difference from Discount Yield
Bond Equivalent Yield (BEY) is a standardized method for comparing the yields of discount securities (like Treasury bills) with coupon-paying bonds. Since discount securities don't pay periodic interest but are sold at a discount to face value, BEY converts their discount yield to an annualized percentage that can be directly compared with traditional bond yields.
The Standardization Problem
Different types of securities use different yield calculation methods. Treasury bills quote discount yields, while bonds quote coupon yields. BEY provides a common language for comparing these different instruments, making it easier for investors to make informed decisions across various fixed-income products.
Mathematical Foundation
The BEY formula is: BEY = ((Face Value - Purchase Price) / Purchase Price) × (365 or 360 / Days to Maturity) × 100. This formula annualizes the discount earned over the holding period, allowing for direct comparison with annual coupon rates.

BEY Examples

  • A $10,000 Treasury bill purchased for $9,850 with 90 days to maturity has a BEY of approximately 6.08%
  • BEY allows comparison between a 5% coupon bond and a discount security with equivalent annual return

Step-by-Step Guide to Using the BEY Calculator

  • Data Collection
  • Input Process
  • Result Interpretation
Using the Bond Equivalent Yield Calculator requires accurate information about your discount security and understanding of the calculation method appropriate for your investment type.
1. Gather Security Information
Collect the face value (par value), purchase price, and days to maturity from your security documentation. The face value is the amount you'll receive at maturity, while the purchase price is what you paid. Days to maturity should be calculated from the purchase date to the maturity date.
2. Choose Calculation Method
Select between 360-day and 365-day year calculations. Treasury bills and most money market instruments use 360 days, while some other securities may use 365 days. Check your security's documentation for the correct method.
3. Interpret Your Results
The calculator provides multiple yield measures: Bond Equivalent Yield (the standardized annual rate), Annualized Return (total return annualized), Total Return (percentage gain), and Yield per Day (daily return rate). Use BEY for comparisons with other fixed-income investments.

Calculation Examples

  • Enter $10,000 face value, $9,850 purchase price, 90 days, and select 360-day method for Treasury bills
  • The calculator will show BEY around 6.08% for this example

Real-World Applications of BEY

  • Investment Comparison
  • Portfolio Management
  • Risk Assessment
Bond Equivalent Yield calculations are essential for professional money management, institutional investing, and individual investment decision-making across various fixed-income markets.
Comparing Different Investment Types
BEY allows direct comparison between Treasury bills, commercial paper, certificates of deposit, and traditional bonds. A 5% coupon bond can be compared with a Treasury bill yielding 4.8% BEY to determine which offers better risk-adjusted returns.
Portfolio Optimization
Money managers use BEY to construct optimal portfolios across different maturities and security types. By standardizing yields, they can identify the most attractive opportunities across the yield curve and different market segments.
Risk Management
BEY helps assess the relative value of different securities considering their risk profiles. Government securities typically have lower BEY than corporate instruments, reflecting their lower credit risk.

Application Examples

  • Compare 3-month Treasury bill BEY with 6-month commercial paper BEY for optimal cash management
  • Use BEY to evaluate whether to hold cash or invest in short-term instruments

Common Misconceptions and Correct Methods

  • Calculation Errors
  • Comparison Mistakes
  • Market Conventions
Understanding common mistakes in BEY calculations and market conventions helps investors make more accurate comparisons and avoid costly errors.
Day Count Conventions
Different markets use different day count conventions. Treasury bills use 360 days, while some corporate instruments use 365 days. Using the wrong convention can lead to significant yield calculation errors.
Compounding Assumptions
BEY assumes simple interest, not compound interest. This is appropriate for short-term instruments but may not reflect the true economic value for longer-term securities where compounding effects become significant.
Market Price vs. Par Value
Always use the actual purchase price, not the face value, in BEY calculations. The discount from face value represents the investor's return and must be accurately captured in the calculation.

Common Errors

  • Using 365 days for Treasury bills will overstate the BEY by approximately 1.4%
  • Comparing BEY with coupon yield without considering reinvestment risk can be misleading

Mathematical Derivation and Examples

  • Formula Development
  • Numerical Examples
  • Advanced Applications
Understanding the mathematical foundation of BEY calculations provides deeper insights into fixed-income valuation and helps in developing more sophisticated investment strategies.
Derivation of the BEY Formula
The BEY formula derives from the principle of annualizing the discount earned. If you earn a discount of (Face Value - Purchase Price) over Days to Maturity, the annualized rate is: ((Face Value - Purchase Price) / Purchase Price) × (365 or 360 / Days to Maturity) × 100. This converts the holding period return to an annual percentage rate.
Relationship to Other Yield Measures
BEY is related to other yield measures: Discount Yield = ((Face Value - Purchase Price) / Face Value) × (360 / Days to Maturity) × 100. BEY uses purchase price in the denominator and typically uses 365 days, making it higher than discount yield for the same security.
Advanced Applications
Professional investors use BEY in yield curve analysis, relative value analysis, and arbitrage strategies. Understanding BEY helps in identifying mispriced securities and optimizing portfolio allocations across different market segments.

Mathematical Examples

  • For a $10,000 Treasury bill purchased at $9,850 with 90 days: BEY = ((10000-9850)/9850) × (365/90) × 100 = 6.08%
  • The same security has discount yield = ((10000-9850)/10000) × (360/90) × 100 = 6.00%
  • BEY is always higher than discount yield for the same security