Interest-Rate Risk

Macaulay Duration

Duration is the PV-weighted average time to each cash flow.

highlighted = computed this step

Duration formula

Macaulay duration is the PV-weighted average period where each discounted payment is weighted by its period and normalized by price.

DMac=∑t⋅PV(Ct)∑PV(Ct)=331121 periods\text{D}_{\text{Mac}}=\frac{\sum t\cdot\text{PV}(C_t)}{\sum \text{PV}(C_t)}=\frac{331}{121} \text{ periods}
Macaulay durationPV-weighted average timing of discounted cash flows.Macaulay durationPeriodCash flowPVWeightt * weight1$100.00$90.911/111/112$100.00$82.6410/12120/1213$1,100.00$826.45100/121300/121Price = Σ PV$1,000.00Duration = Σ t * weight331/121 periods

Exact vs rounded duration

For this par bond, the exact value is 331/121 periods, about 2.7355 periods at four-decimal display.

331/121≈2.7355331/121\approx 2.7355