Read these again
- MODULE 24.2: CAPITAL ALLOCATION PRINCIPLES AND REAL OPTIONS
NUMERICALS TO REVISE
INTEREST RATE RISK
Question
Consider a bond that has two years remaining to maturity, a coupon of 4% paid semiannually, and a yield-to-maturity of 4.60%. Assuming it is 63 days into the first coupon period and a 30/360 basis, the bond’s annualized Macaulay duration is closest to:
A. 0.9419 years
B. 1.7666 years
C. 1.9416 years
Given
Face = 100
Coupon = 4% annual → 2% semiannual = 2
YTM = 4.60% annual → 2.30% per period
Coupon period = 180 days
Days elapsed = 63 → time to first CF = (180 − 63)/180 = 0.65 periods
Cash flows and timing
| Period | Time (periods) | CF | PV @ 2.3% | Weight | Time × Weight |
|---|---|---|---|---|---|
| 1 | 0.65 | 2 | 1.9707 | 0.0198 | 0.0129 |
| 2 | 1.65 | 2 | 1.9264 | 0.0193 | 0.0319 |
| 3 | 2.65 | 2 | 1.8830 | 0.0189 | 0.0501 |
| 4 | 3.65 | 102 | 93.8759 | 0.9420 | 3.4383 |
| Total | 99.6559 | 1.0000 | 3.5331 |
Macaulay duration
In periods = Σ(Time × Weight) = 3.5331
Annualized = 3.5331 / 2 = 1.7666 years
Answer
B