Kelly Clark, CFA, is a fixed income analyst for Convex Capital. She is evaluating a 15-year bond with a 6.0% coupon. At the current interest rate of 5.5%, the bond is priced at $1,050.62. Clark calculates that a 25 basis point drop in interest rates increases the bond's price to $1,077.20, while a 25 basis point increase in interest rates reduces the bond's price to $1,024.90. Based on the information provided, calculate the bond's effective duration.
Click on the arrows to vote for the correct answer
A. B. C.C
To calculate the bond's effective duration, we need to use the formula:
Effective Duration = (-1) * (ΔP / P) / ΔY,
where: ΔP is the change in bond price, P is the initial bond price, ΔY is the change in yield (interest rate).
Given the information in the question, let's calculate the effective duration step by step.
Step 1: Calculate the change in bond price (ΔP) for a 25 basis point drop in interest rates.
ΔP = $1,077.20 - $1,050.62 = $26.58
Step 2: Calculate the change in bond price (ΔP) for a 25 basis point increase in interest rates.
ΔP = $1,024.90 - $1,050.62 = -$25.72
Note that the change in price for an increase in interest rates is negative.
Step 3: Calculate the change in yield (ΔY).
ΔY = (25 basis points) / 100 = 0.25%
Step 4: Calculate the effective duration.
Effective Duration = (-1) * [(ΔP / P) / ΔY]
For a 25 basis point drop in interest rates: Effective Duration = (-1) * [($26.58 / $1,050.62) / 0.0025] ≈ (-1) * (0.0253205 / 0.0025) ≈ (-1) * 10.1282 ≈ -10.13
For a 25 basis point increase in interest rates: Effective Duration = (-1) * [(-$25.72 / $1,050.62) / 0.0025] ≈ (-1) * (-0.0244635 / 0.0025) ≈ (-1) * 9.7854 ≈ -9.79
Step 5: Average the two effective durations to find the bond's effective duration.
Average Effective Duration = (|-10.13| + |-9.79|) / 2 ≈ 19.92 / 2 ≈ 9.96
Therefore, the bond's effective duration is approximately 9.96.
The correct answer is C. 9.96.