Bond Equivalent Yield Calculator (+ Formula)

The Bond Equivalent Yield (BEY) Calculator is a tool used to compare bonds with different payment schedules on an equivalent annualized basis. This is particularly important for bonds that pay interest semi-annually or are discounted bonds like Treasury bills, which don’t pay periodic interest. By using the BEY, investors can accurately compare the returns of different bonds and make informed decisions when choosing between various fixed-income securities.

The BEY allows investors to annualize the yield of a bond so that it can be directly compared to other investments, such as stocks or bonds with different payment structures.

Formula

The Bond Equivalent Yield can be calculated using two primary methods, depending on the available information. One formula is used when the bond’s price and days to maturity are known, while another is used if the bond’s Yield to Maturity (YTM) is available.

Formula 1: Using Bond Price and Days to Maturity

BEY = ( (Face Value – Price) / Price ) * (365 / Days to Maturity)

Where:

• Face Value: The bond’s par value, typically $1,000 for most bonds.
• Price: The current market price of the bond.
• Days to Maturity: The number of days remaining until the bond matures.

This formula calculates the bond’s yield by comparing its price and face value, adjusted for the number of days remaining until maturity, and annualizing it.

Formula 2: Using Yield to Maturity (YTM) for Semi-Annual Bonds

BEY = 2 * ( (1 + YTM / 2)² – 1)

Where:

• YTM: The bond’s Yield to Maturity, expressed as a decimal (e.g., 0.05 for 5%).

This formula converts the bond’s semi-annual yield into an annualized equivalent, making it easier to compare bonds that make different coupon payments over time.

Key Terms:

• Bond Equivalent Yield (BEY): The annualized yield of a bond that accounts for semi-annual or other payment structures, allowing for comparison with other investments.
• Yield to Maturity (YTM): The total return expected on a bond if held until maturity, taking into account all coupon payments and the difference between purchase price and face value.
• Face Value: The nominal or par value of the bond, which is typically $1,000.
• Price: The current market price of the bond.

General Reference Table for Bond Equivalent Yield and Terms

Here’s a general reference table that helps explain key bond-related terms and the relationship between different bond yields:

Term	Definition
Bond Equivalent Yield	Annualized yield that accounts for semi-annual coupon payments or discounted bonds.
Yield to Maturity (YTM)	The total return on a bond if held until maturity, including interest and capital gains.
Face Value	The par value of the bond, typically $1,000.
Price	The current market price of the bond.
Days to Maturity	Number of days remaining until the bond matures and the face value is repaid.

This table helps users understand the basic terms that influence bond yields and makes it easier to grasp how the BEY is calculated.

Example

Let’s go through an example to see how the Bond Equivalent Yield Calculator works.

Scenario:

You are evaluating a Treasury bill with a face value of $1,000, currently priced at $980, and maturing in 180 days. You want to calculate the bond equivalent yield.

1. Step 1: Plug in the values to the first BEY formula:
   • Face Value = $1,000
   • Price = $980
   • Days to Maturity = 180
   BEY = ((1,000 – 980) / 980) * (365 / 180)
2. Step 2: Calculate:
   • Price difference = 1,000 – 980 = $20
   • Price difference as a percentage = $20 / 980 = 0.02041 (or 2.041%)
   • BEY = 0.02041 * (365 / 180) = 0.04141 (or 4.141%)

So, the bond equivalent yield for this Treasury bill is 4.141%.

Scenario 2: Using YTM

If the bond pays interest semi-annually and its YTM is 5%, you can calculate the BEY using the second formula.

BEY = 2 * ( (1 + 0.05 / 2)² – 1)

• Step 1: BEY = 2 * ( (1 + 0.025)² – 1)
• Step 2: BEY = 2 * (1.050625 – 1) = 2 * 0.050625 = 0.10125

So, the bond equivalent yield is 10.125% for a semi-annual coupon bond with a 5% YTM.

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