Question

A bond has a duration of 6.87 with a yield-to-maturity of 5.4. The current bond price is $1,151.48. Convexity for this bond is determined to be 114.46. What would be the bond's new price if interest rates suddenly increased by 1.37%? State your answer as a dollar amount with two decimal places.

Answer 1

The new price of the bond would be $1,140.69.

Step-by-step explanation:

To calculate the new price of the bond, we need to use the formula for the bond price change:

ΔP ≈ -[D × Δy × P'] / (1 + y)

Where:

• ΔP is the change in price
• D is the duration of the bond
• Δy is the change in yield-to-maturity
• P' is the initial price of the bond
• y is the initial yield-to-maturity of the bond

Plugging in the given values:

• D = 6.87
• Δy = 0.0137
• P' = $1,151.48
• y = 0.054

Calculating the change in price:

ΔP ≈ -[6.87 × 0.0137 × $1,151.48] / (1 + 0.054)

ΔP ≈ -$10.79

To find the new price of the bond, subtract the change in price from the initial price:

New price = $1,151.48 - $10.79 = $1,140.69