CFA Level IFixed IncomeMedium
A 3-year annual-pay bond has an 8% coupon rate, a face value of $1,000, and a yield to maturity of 8%. The bond's Macaulay duration (in years) is closest to:
- A2.50
- B2.78
- C3.00
- D2.00
Show answer & explanationAnswer & explanation
Correct answer: B. 2.78
Since coupon = YTM, price = par = $1,000. PVs: Year1: 80/1.08=74.07; Year2: 80/1.08^2=68.59; Year3: 1,080/1.08^3=857.34; sum=1,000.00. Weighted time = (74.07×1 + 68.59×2 + 857.34×3)/1,000 = (74.07+137.17+2572.02)/1,000 = 2,783.27/1,000 = 2.78 years.
Why the other options are wrong
- A. Underestimates duration; the final payment dominates the weighted average.
- C. Equals maturity, which would only be true for a zero-coupon bond.
- D. Too low; ignores the heavy weighting of the large final cash flow.
Macaulay Duration
The weighted-average time (in years) until a bond's cash flows are received, with weights equal to the present value of each cash flow as a fraction of the bond's total price.
- For a zero-coupon bond, Macaulay duration equals maturity
- Higher coupons reduce Macaulay duration versus maturity
- Used as the basis for modified duration = MacDur/(1+YTM/m)
Memory trick: Duration is the time-weighted balance point of cash flows.