CFA Level II ExamFixed IncomeHard
A financial institution is evaluating a fixed-rate bond with a remaining maturity of 5 years, a coupon rate of 4.0% paid semi-annually, and a current yield to maturity of 3.5%. If the institution wants to calculate the bond's approximate modified duration, what would be the first step in this calculation?
- ACalculate the bond's convexity.
- BEstimate the bond's price sensitivity to a 1% change in yield.
- CDetermine the bond's effective duration.
- DCalculate the bond's Macaulay duration.
Show answer & explanationAnswer & explanation
Correct answer: D. Calculate the bond's Macaulay duration.
Modified duration is derived directly from Macaulay duration. The formula for modified duration is Macaulay Duration / (1 + YTM / number of coupon payments per year). Therefore, the first step to calculate modified duration is to calculate Macaulay duration.
Why the other options are wrong
- A. Incorrect. Convexity is a separate measure of interest rate risk, typically calculated after or alongside duration, but not a prerequisite for modified duration.
- B. Incorrect. While modified duration measures price sensitivity, this option describes the output or interpretation of modified duration, not the first step in its calculation.
- C. Incorrect. Effective duration is used for bonds with embedded options, which this bond does not explicitly have. It's a different duration measure.
Macaulay vs. Modified Duration
Macaulay duration is the weighted average time until a bond's cash flows are received, while modified duration is a measure of a bond's price sensitivity to yield changes, derived from Macaulay duration.
- Macaulay duration is expressed in years.
- Modified duration is Macaulay duration divided by (1 + YTM/frequency).
- Modified duration is used to estimate percentage price change for a given yield change.
- For bonds with embedded options, effective duration is more appropriate.
Memory trick: Macaulay comes 'before' Modified, like 'M' before 'M' in the alphabet.