Macaulay Duration Calculator

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✓ Fact checked by David Chen, CFA | Senior Financial Analyst

The Macaulay Duration Calculator is an essential tool for bond investors to measure a fixed-income security’s interest rate sensitivity. It calculates the weighted average time until all cash flows are received, expressed in years.

Macaulay Duration Calculator

Macaulay Duration
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Current Bond Price: $0.00

Macaulay Duration Formula

$$ MacD = \frac{\sum_{t=1}^{n} \frac{t \cdot C}{(1+y)^t} + \frac{n \cdot M}{(1+y)^n}}{P} $$

Formula Source: Investopedia – Macaulay Duration

Variables:

  • Face Value (M): The amount paid at bond maturity.
  • Coupon Rate (C): The annual interest rate paid by the bond issuer.
  • YTM (y): The internal rate of return (yield) of the bond.
  • Years to Maturity (n): The remaining life of the bond.
  • Price (P): The present value of all future cash flows.

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What is Macaulay Duration?

Macaulay duration is a measure of the time it takes for an investor to be repaid the bond’s price by the bond’s total cash flows. It is the weighted average time until all the cash flows are received.

Unlike simple maturity, it accounts for the timing and size of coupon payments. A higher Macaulay duration indicates that the bond’s price is more sensitive to changes in interest rates.

How to Calculate Macaulay Duration (Example)

Assume a $1,000 bond with a 5% coupon, 2 years to maturity, and a 6% YTM paid annually:

  1. Year 1: Calculate PV of $50 coupon = $50 / (1.06)^1 = $47.17.
  2. Year 2: Calculate PV of $1,050 (coupon + principal) = $1,050 / (1.06)^2 = $934.50.
  3. Bond Price: $47.17 + $934.50 = $981.67.
  4. Weighted Time: (1 × $47.17) + (2 × $934.50) = $1,916.17.
  5. Duration: $1,916.17 / $981.67 = 1.952 years.

Frequently Asked Questions (FAQ)

What is the difference between Macaulay and Modified duration? Macaulay measures time in years, while Modified duration measures the percentage change in price for a 1% change in yield.

Is duration the same as maturity? No. Maturity is the final payment date. Duration is shorter for coupon bonds because you receive some cash earlier.

How does YTM affect duration? Higher YTM leads to lower duration because future cash flows are discounted more heavily, making early cash flows more valuable.

Does a zero-coupon bond have duration? Yes, for a zero-coupon bond, the Macaulay duration is exactly equal to its time to maturity.

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