How do I calculate Macaulay duration and modified duration step by step?

Duration is the single most important risk measure in fixed income. Let's build it from scratch.

Macaulay Duration is the weighted-average time to receive a bond's cash flows, where weights are the present values of each cash flow as a fraction of the bond's total price.

Modified Duration adjusts Macaulay duration to directly estimate the percentage price change for a 1% change in yield.

Step-by-Step Example: Consider a bond issued by Northfield Energy:

• Face value: $1,000
• Coupon: 5% annual
• Maturity: 3 years
• YTM: 6%

Step 1 — Identify cash flows and discount:

Year	Cash Flow	PV Factor (1.06)^-t	PV of CF	Weight (PV/Price)	Year x Weight
1	$50	0.9434	$47.17	0.0499	0.0499
2	$50	0.8900	$44.50	0.0470	0.0941
3	$1,050	0.8396	$881.60	0.9321	2.7964
Total			$973.27	1.0000	2.9404

Macaulay Duration = 2.9404 years

Step 2 — Modified Duration:

ModDur = MacDur / (1 + y) = 2.9404 / 1.06 = 2.7740 years

Step 3 — Interpret: If YTM rises by 1% (100 bps), the bond's price will fall by approximately: %ΔP ≈ -ModDur x Δy = -2.7740 x 1% = -2.774%

On a $973.27 bond, that's roughly a$27.01 price drop.

Quick Rules:

• Higher coupon → lower duration (more cash flow arrives sooner)
• Longer maturity → higher duration
• Higher YTM → lower duration (future cash flows are discounted more heavily)
• Zero-coupon bond: Macaulay duration = maturity

Exam Tip: If you see "interest rate sensitivity" or "price risk" on the exam, think duration first. If they want a number in years, give Macaulay duration. If they want the price change estimate, use modified duration.

Practice duration calculations with our CFA Level I Fixed Income question bank.