Bond Equivalent Yield (BEY): Definition, Formula, and Example

The Bond Equivalent Yield (BEY) is a method of expressing the annualized yield of a fixed-income security, such as a Treasury bill, commercial paper, or certificate of deposit, that does not pay periodic interest (coupon payments). Instead, these securities are typically sold at a discount and redeemed at maturity for their full face value. The difference between the purchase price and the face value represents the investor’s return.

BEY is particularly useful because it allows investors to compare the yields of short-term securities with different maturities or payment structures on an annualized basis. By converting the yield into an annualized figure, BEY provides a standardized way to evaluate the profitability of investments that may have varying time horizons, typically less than one year.

Unlike other yield metrics, such as the effective annual yield (EAY) or yield to maturity (YTM), BEY assumes simple interest rather than compound interest. This makes it a straightforward tool for quick comparisons, especially for discount instruments like Treasury bills.

Key Characteristics of BEY

Annualized Yield: BEY expresses the return as if the investment were held for a full year, even if the actual maturity is shorter.
Simple Interest Basis: It does not account for the compounding of interest, which simplifies calculations.
Used for Discount Securities: BEY is most commonly applied to zero-coupon securities, which do not pay periodic interest.
Standardization: It enables investors to compare yields across different securities with varying maturities.

Why is BEY Important?

BEY plays a vital role in the fixed-income market for several reasons:

Comparability: Short-term securities often have different maturities, such as 30 days, 90 days, or 180 days. BEY standardizes these yields, allowing investors to compare them directly with longer-term securities or other investment opportunities.
Decision-Making: For investors, understanding the annualized return of a short-term investment helps in assessing whether it aligns with their financial goals. BEY provides a clear picture of potential returns.
Market Analysis: BEY is widely used by financial analysts, portfolio managers, and traders to evaluate the attractiveness of money market instruments relative to other asset classes.
Regulatory and Reporting Purposes: Financial institutions and regulators often use BEY to report yields in a standardized format, ensuring consistency across markets.
Risk Assessment: By annualizing yields, BEY helps investors gauge the opportunity cost of tying up capital in short-term securities versus other investments.

The BEY Formula

The formula for calculating Bond Equivalent Yield depends on the type of security and its characteristics. For a discount security, such as a Treasury bill, the BEY is calculated as follows:BEY=(Face Value−Purchase PricePurchase Price)×(365Days to Maturity)BEY = \left( \frac{\text{Face Value} – \text{Purchase Price}}{\text{Purchase Price}} \right) \times \left( \frac{365}{\text{Days to Maturity}} \right)BEY=(Purchase PriceFace Value−Purchase Price)×(Days to Maturity365)

Explanation of Terms

Face Value: The amount the security will be worth at maturity (also called par value).
Purchase Price: The price paid to acquire the security.
Days to Maturity: The number of days remaining until the security matures.
365: The number of days in a year, used to annualize the yield (some calculations may use 360 days, depending on market conventions).

The formula essentially calculates the return as a percentage of the purchase price and then scales it to an annual basis by multiplying by the ratio of 365 days to the days to maturity.

Alternative Formula for Semi-Annual Coupon Bonds

For bonds that pay semi-annual coupons, BEY can also be used to compare their yields with those of discount securities. In this case, the BEY is derived from the bond’s yield to maturity (YTM) or quoted yield, adjusted to reflect an annualized return. The formula is:BEY=2×((1+YTM2)−1)BEY = 2 \times \left( (1 + \frac{\text{YTM}}{2}) – 1 \right)BEY=2×((1+2YTM)−1)

Where:

YTM is the yield to maturity expressed as a decimal (e.g., 5% = 0.05).

This version of the formula accounts for the semi-annual compounding of coupon-paying bonds and converts the yield into an equivalent annualized figure.

Step-by-Step Calculation of BEY

To illustrate how BEY is calculated, let’s walk through the steps using the formula for a discount security.

Determine the Face Value: Identify the amount the security will pay at maturity.
Identify the Purchase Price: Note the price paid to acquire the security.
Calculate the Return: Subtract the purchase price from the face value to find the dollar return.
Compute the Yield: Divide the dollar return by the purchase price to get the yield for the holding period.
Annualize the Yield: Multiply the yield by the ratio of 365 days to the number of days to maturity.

Let’s apply these steps in a practical example below.

Example 1: BEY for a Treasury Bill

Suppose an investor purchases a 90-day Treasury bill with the following details:

Face Value: $10,000
Purchase Price: $9,900
Days to Maturity: 90

Step-by-Step Calculation

Dollar Return: Face Value−Purchase Price=10,000−9,900=100\text{Face Value} – \text{Purchase Price} = 10,000 – 9,900 = 100Face Value−Purchase Price=10,000−9,900=100
Yield for the Period: Dollar ReturnPurchase Price=1009,900≈0.010101\frac{\text{Dollar Return}}{\text{Purchase Price}} = \frac{100}{9,900} \approx 0.010101Purchase PriceDollar Return=9,900100≈0.010101
Annualize the Yield: BEY=0.010101×36590≈0.010101×4.0556≈0.04096 or 4.096%BEY = 0.010101 \times \frac{365}{90} \approx 0.010101 \times 4.0556 \approx 0.04096 \text{ or } 4.096\%BEY=0.010101×90365≈0.010101×4.0556≈0.04096 or 4.096%

Result

The Bond Equivalent Yield for this Treasury bill is approximately 4.10%. This means that if the investor’s return were annualized, they would earn roughly 4.10% on their investment over a full year, assuming no compounding.

Example 2: Comparing Two Securities

To demonstrate the utility of BEY in comparing investments, consider two Treasury bills with different maturities:

T-Bill A: Face value of $10,000, purchase price of $9,850, 60 days to maturity.
T-Bill B: Face value of $10,000, purchase price of $9,700, 180 days to maturity.

Calculate BEY for T-Bill A

Dollar Return: 10,000−9,850=15010,000 – 9,850 = 15010,000−9,850=150
Yield for the Period: 1509,850≈0.015228\frac{150}{9,850} \approx 0.0152289,850150≈0.015228
Annualize the Yield: BEYA=0.015228×36560≈0.015228×6.0833≈0.09260 or 9.26%BEY_A = 0.015228 \times \frac{365}{60} \approx 0.015228 \times 6.0833 \approx 0.09260 \text{ or } 9.26\%BEYA=0.015228×60365≈0.015228×6.0833≈0.09260 or 9.26%

Calculate BEY for T-Bill B

Dollar Return: 10,000−9,700=30010,000 – 9,700 = 30010,000−9,700=300
Yield for the Period: 3009,700≈0.030928\frac{300}{9,700} \approx 0.0309289,700300≈0.030928
Annualize the Yield: BEYB=0.030928×365180≈0.030928×2.0278≈0.06270 or 6.27%BEY_B = 0.030928 \times \frac{365}{180} \approx 0.030928 \times 2.0278 \approx 0.06270 \text{ or } 6.27\%BEYB=0.030928×180365≈0.030928×2.0278≈0.06270 or 6.27%

Comparison

T-Bill A: BEY = 9.26%
T-Bill B: BEY = 6.27%

Based on BEY, T-Bill A offers a higher annualized return than T-Bill B. This comparison helps the investor decide which security provides better value, assuming other factors (e.g., risk, liquidity) are equal.

Limitations of BEY

While BEY is a valuable tool, it has certain limitations that investors should be aware of:

Assumes Simple Interest: BEY does not account for compounding, which may underestimate the true return of an investment if the proceeds are reinvested.
Short-Term Focus: BEY is designed for securities with maturities of less than one year. For longer-term bonds, metrics like yield to maturity (YTM) or effective annual yield (EAY) may be more appropriate.
Ignores Reinvestment Risk: BEY assumes the investor holds the security to maturity and does not reinvest the proceeds. In reality, reinvestment opportunities and rates can affect overall returns.
Market Conventions: Some markets use a 360-day year instead of 365, which can lead to slight variations in BEY calculations. Investors must ensure consistency when comparing yields.
Limited Scope: BEY is primarily used for discount securities and may not fully capture the complexities of coupon-paying bonds or other fixed-income instruments.

BEY vs. Other Yield Metrics

To fully appreciate BEY, it’s helpful to compare it with other common yield metrics:

Yield to Maturity (YTM): YTM accounts for all future cash flows (coupons and principal) and assumes reinvestment at the same rate. It is more comprehensive but complex than BEY.
Effective Annual Yield (EAY): EAY incorporates compounding, making it a better measure for investments with reinvestment opportunities.
Bank Discount Yield (BDY): BDY is another metric for discount securities but uses the face value as the denominator and a 360-day year, leading to different results than BEY.

For short-term, zero-coupon securities, BEY is often preferred due to its simplicity and focus on annualized returns without compounding.

Practical Applications of BEY

BEY is widely used in various financial contexts, including:

Portfolio Management: Portfolio managers use BEY to evaluate the performance of money market funds and short-term bond holdings.
Trading: Traders in the money market rely on BEY to quickly assess the relative value of Treasury bills, commercial paper, and other instruments.
Corporate Finance: Companies use BEY to compare the cost of short-term borrowing (e.g., commercial paper) with other financing options.
Personal Investing: Individual investors can use BEY to decide whether to invest in Treasury bills, CDs, or other short-term securities.

Conclusion

The Bond Equivalent Yield (BEY) is a powerful and straightforward tool for evaluating the annualized return of short-term, fixed-income securities. By standardizing yields, BEY enables investors to compare different investments on an equal footing, facilitating better decision-making. Its formula is easy to apply, requiring only basic information about the security’s face value, purchase price, and maturity.

Through examples, we’ve seen how BEY can be calculated and used to compare securities with different maturities. However, investors should remain mindful of its limitations, particularly its reliance on simple interest and its focus on short-term instruments. By combining BEY with other metrics and considering the broader investment context, individuals and professionals alike can make more informed choices in the fixed-income market.