Bond Equivalent Yield Calculator
Calculate the Bond Equivalent Yield (BEY) for discount bonds like Treasury bills. Convert money market yields to annual bond-equivalent rates for accurate comparison with coupon-bearing securities.
BEY at Different Maturities and Prices
| Days to Maturity | Purchase Price | Discount ($) | Holding Return | BEY | Effective Annual Yield |
|---|
What is Bond Equivalent Yield (BEY)?
Bond Equivalent Yield (BEY) is a method of calculating the annualized yield on a discount security (like Treasury bills or commercial paper) that allows for direct comparison with coupon-bearing bonds. Since discount securities don't pay interest but instead are sold below face value, BEY converts their return into an equivalent annual yield based on a 365-day year.
BEY is particularly important for institutional investors who need to compare returns across different types of fixed-income investments. It standardizes yields so that a 91-day Treasury bill can be meaningfully compared to a 10-year Treasury note.
Money market instruments like T-bills are often quoted using the bank discount rate, which understates true yield. BEY provides a more accurate measure of return that can be compared directly with yields on coupon bonds quoted on a semi-annual basis.
The Bond Equivalent Yield Formula
The standard formula for calculating BEY is:
Calculate the BEY for a Treasury bill with:
- Face Value: $10,000
- Purchase Price: $9,800
- Days to Maturity: 182 days
Step 1: Calculate the discount: $10,000 - $9,800 = $200
Step 2: Calculate the return: $200 / $9,800 = 0.0204 (2.04%)
Step 3: Annualize: 0.0204 × (365/182) = 0.0409 (4.09%)
BEY = 4.09%
BEY vs. Bank Discount Rate
The bank discount rate (also called the discount yield) is another common way to express T-bill yields, but it differs from BEY in important ways:
| Feature | Bond Equivalent Yield | Bank Discount Rate |
|---|---|---|
| Base for return calculation | Purchase price (actual investment) | Face value (redemption amount) |
| Days in year | 365 days | 360 days |
| Yield level | Higher (more accurate) | Lower (understates true return) |
| Comparability | Can compare with bond yields | Money market convention only |
BEY vs. Yield to Maturity (YTM)
While BEY and YTM both express annualized returns, they differ in their treatment of reinvestment and compounding:
- BEY: Assumes simple interest (no compounding) and annualizes by multiplying by (365/days). It does not account for reinvestment of proceeds.
- YTM: Assumes all cash flows are reinvested at the same rate and uses compound interest. For coupon bonds, it considers both coupon payments and principal return.
For short-term discount securities, BEY is preferred because there are no intermediate cash flows to reinvest, and the simple interest calculation is appropriate for the short holding period.
Effective Annual Yield
The Effective Annual Yield (EAY) accounts for compounding and provides an even more accurate measure of return:
EAY is always slightly higher than BEY because it accounts for the compounding effect of reinvesting at the same rate multiple times per year.
Common Discount Securities
BEY is commonly used for these types of instruments:
Treasury Bills (T-Bills)
Short-term U.S. government securities with maturities of 4, 8, 13, 17, 26, and 52 weeks. They are considered risk-free and highly liquid.
Commercial Paper
Unsecured, short-term corporate debt typically issued by large corporations with high credit ratings. Maturities range from 1 to 270 days.
Banker's Acceptances
Time drafts drawn on and accepted by banks, commonly used in international trade financing. They trade at a discount and mature at face value.
Repurchase Agreements (Repos)
Short-term collateralized borrowing, where securities are sold with an agreement to repurchase them at a higher price.
Factors Affecting BEY
Several factors influence the BEY of a discount security:
- Discount Amount: A larger discount (lower purchase price) relative to face value increases BEY.
- Time to Maturity: Shorter maturities result in higher annualized yields for the same dollar discount because the return is earned over a shorter period.
- Credit Risk: Higher-risk issuers must offer larger discounts (higher yields) to attract investors.
- Market Interest Rates: When rates rise, new T-bills are issued at larger discounts, increasing BEY.
- Liquidity: Less liquid securities may trade at larger discounts.
Practical Applications
Comparing Investment Options
BEY allows investors to compare returns on T-bills with yields on bonds, CDs, or other fixed-income investments on an apples-to-apples basis.
Cash Management
Corporate treasurers use BEY to evaluate short-term investment options for excess cash and optimize returns while maintaining liquidity.
Benchmarking
Money market fund managers compare their fund's yield against T-bill BEY as a risk-free benchmark.
Frequently Asked Questions
Why is BEY higher than the bank discount rate?
BEY is higher for two reasons: (1) it uses the actual purchase price (smaller number) as the denominator rather than face value, and (2) it uses a 365-day year instead of 360 days. Both factors increase the calculated yield.
Can BEY be used for coupon bonds?
BEY is specifically designed for discount securities. For coupon bonds, yield to maturity (YTM) is the appropriate measure as it accounts for both coupon payments and price changes.
How does the day count convention affect BEY?
Using 360 days instead of 365 will produce a slightly higher BEY. The 365-day convention (actual/365) is standard for BEY calculations, while 360 days (30/360) is used for bank discount rates.
Is BEY the same as APY?
No. Annual Percentage Yield (APY) accounts for compounding, similar to Effective Annual Yield (EAY). BEY uses simple interest assumptions without compounding. For short-term securities, the difference is small but measurable.
Why do T-bills trade at a discount?
T-bills don't pay periodic interest (coupons). Instead, investors earn their return by purchasing at a discount to face value and receiving the full face value at maturity. The discount represents the interest earned.