Bond-equivalent yield (BEY) is a way of comparing the returns of different bonds that have different payment frequencies. For example, some bonds pay interest annually, while others pay semi-annually or quarterly. BEY converts the yield of any bond to an annualized basis, assuming that the bond pays interest semi-annually. This makes it easier to compare bonds with different payment structures and maturities.
Treasury bills are short-term debt securities issued by the U.S. government. They do not pay interest, but are sold at a discount to their face value. For example, a 180-day treasury bill with a face value of $100 might be sold for $95. The investor will receive $100 at maturity, earning a profit of $5.
Basic Theory
The bond-equivalent yield is an annualized yield that allows for the comparison of yields on securities with different compounding periods. Treasury Bills are short-term securities that do not make regular interest payments, but they are issued at a discount and redeemed at par value upon maturity.
The formula for calculating the bond-equivalent yield for Treasury Bills is as follows:
BEY = ((Discount/Face Value) * (365/Days to Maturity)) * 100
Where:
- Discount is the difference between the face value of the Treasury Bill and its purchase price.
- Face Value is the nominal or par value of the Treasury Bill.
- Days to Maturity is the number of days until the Treasury Bill matures.
- The factor (365/Days to Maturity) annualizes the yield.
Procedures
Excel Formulas
- Enter Data: Set up an Excel table with the following columns: Purchase Price, Face Value, Days to Maturity, and BEY.
- Input Data: Enter the relevant data for your Treasury Bill scenario into the respective columns.
- Apply Formula: In the BEY column, use the formula:
=((B2-A2)/B2)*(365/C2)*100Assuming A2 is the Purchase Price, B2 is the Face Value, and C2 is the Days to Maturity.
- Format Cells: Format the BEY column as a percentage for better readability.
Scenario: Calculating Bond-Equivalent Yield
Let’s consider a Treasury Bill with the following details:
- Purchase Price: $9,750
- Face Value: $10,000
- Days to Maturity: 90 days
Apply the formula mentioned earlier to find the Bond-Equivalent Yield.
Excel Table Example
| Purchase Price | Face Value | Days to Maturity | BEY |
|---|---|---|---|
| $9,750 | $10,000 | 90 | Formula Result |
Calculation
Result
The Bond-Equivalent Yield for the given Treasury Bill scenario is approximately 1.014%.
Other Approaches
- Using RATE Function: Excel’s RATE function can be used to calculate the yield of an investment with periodic interest payments. Adjustments can be made to align with Treasury Bill characteristics.
- Yield Function: For Treasury Bills, the YIELD function in Excel can be used to calculate the yield based on the security’s par value, purchase price, and maturity date.
