How to Calculate Bond Price with Negative Yield in Excel

When a bond's yield becomes negative, it means the bond is trading at a premium to its face value. Calculating the bond price with a negative yield in Excel requires understanding the relationship between yield, price, and face value. This guide explains the formula, Excel implementation, and provides a practical example.

What is Bond Price with Negative Yield?

Bond price with negative yield occurs when the bond is trading above its face value. This typically happens when interest rates have fallen below the bond's coupon rate, making the bond more attractive to investors. The negative yield reflects the discount from the face value.

Key terms:

Face Value (FV) - The nominal value of the bond
Coupon Rate - The annual interest rate paid by the bond
Yield to Maturity (YTM) - The internal rate of return of the bond
Negative Yield - Indicates the bond is trading above face value

The Formula

The bond price with negative yield can be calculated using the following formula:

Bond Price = (Face Value × (1 + Yield)) / (1 + Coupon Rate)

Where:

Yield is the negative yield (expressed as a decimal)
Coupon Rate is the annual interest rate (expressed as a decimal)

For example, if the face value is $1,000, coupon rate is 5% (0.05), and yield is -2% (-0.02), the bond price would be calculated as:

($1,000 × (1 - 0.02)) / (1 + 0.05) = $980.39

Excel Calculation Steps

Enter the face value in cell A1
Enter the coupon rate (as decimal) in cell B1
Enter the negative yield (as decimal) in cell C1
In cell D1, enter the formula: =A1*(1+C1)/(1+B1)
Format cell D1 as currency to display the bond price

For a more complex calculation with multiple periods, you would use the PV function with the negative yield as the rate parameter.

Worked Example

Let's calculate the bond price for a bond with:

Face Value: $1,000
Coupon Rate: 6% (0.06)
Negative Yield: -3% (-0.03)

Using the formula:

Bond Price = ($1,000 × (1 - 0.03)) / (1 + 0.06) = $969.70

This means the bond is trading at $969.70, which is above its $1,000 face value due to the negative yield.

FAQ

Why does a negative yield mean the bond is trading above face value?: A negative yield indicates that the bond is paying less interest than its current market price, making it more valuable to investors. This causes the bond to trade above its face value.
How does negative yield affect bond price?: Negative yield increases the bond's price because investors demand higher returns, making the bond more attractive despite the lower coupon rate.
Can I use the same formula for positive yields?: Yes, the formula works for both positive and negative yields. For positive yields, the bond price will be below face value.
What Excel function can I use for more complex calculations?: For multi-period bonds, use the PV function with the negative yield as the rate parameter: =PV(rate, nper, pmt, fv)
When would a bond have a negative yield?: Bonds typically have negative yields when interest rates fall below the bond's coupon rate, making the bond more valuable to investors.