Macaulay duration

What is it?

Macaulay duration is the weighted average time until an investor recovers the money paid for a bond, where each cash flow is weighted by its share of the bond's present value. For a coupon-paying bond, duration is generally shorter than maturity.

The following formula is used:

Macaulay Duration = ∑ ( Time × CashFlow ÷ (1 + Yield) ^ Time ) ÷ BondPrice

• BondPrice – current market price of the bond, including accrued interest.
• CashFlow – coupon payment, or coupon plus redemption amount for the final one.
• Time – time from today until the cash flow, in years.
• Yield – annual rate used for discounting, taken as the bond's yield to worst.

Macaulay duration is best read as the bond's effective term. A ten-year bond with a large coupon may behave like a five-year one, and duration makes that comparable across issues with different coupons and maturities.

It is measured in years.