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What This Calculator Does
This calculator computes the Macaulay Duration of a bond. This represents the time-weighted average payback period of its coupon stream and final par repayment, serving as a core measure of fixed-income interest rate risk.
How to Use This Calculator
Enter par value, annual coupon rate, current bond price, years to maturity, yield to maturity, and payment frequency. Click Calculate to compute the Macaulay Duration.
How the Calculation Works
The underlying math engine processes your inputs using exact formulas. This systematic approach ensures professional, institutional-grade calculation precision:
Mathematical Formula
Formula Legend:
- · t = Period index of the cash flow.
- · CF_t = Cash flow amount at period t (coupon payment or final par repayment).
- · y = Yield to maturity per discounting period.
- · Price = Current market price of the bond.
Practical Example
Assume an annual-pay bond with 3 years to maturity, a $1,000 face value, a 6.0% coupon rate, currently priced at $1,000 (YTM is 6.0%):
Step-by-Step Mathematical Walkthrough:
- 1 Year 1 Cash Flow is $60. Discounted at 6.0%: $60 / 1.06 = $56.60. Weighted time: 1 * $56.60 = 56.60.
- 2 Year 2 Cash Flow is $60. Discounted at 6.0%: $60 / (1.06)^2 = $53.40. Weighted time: 2 * $53.40 = 106.80.
- 3 Year 3 Cash Flow is $1,060. Discounted at 6.0%: $1,060 / (1.06)^3 = $890.00. Weighted time: 3 * $890.00 = 2,670.00.
- 4 Sum of weighted times: 56.60 + 106.80 + 2,670.00 = 2,833.40.
- 5 Macaulay Duration = $2,833.40 / Price ($1,000) = 2.83 years.
Important Assumptions & Notes
- Yield to maturity remains constant across all cash flow periods.
- The payment schedule is perfectly regular with no early redemptions.
- Days are calculated on a standard 30/360 or actual basis.
Common Mistakes or Considerations
- Confusing Macaulay Duration (which is measured in years) with Modified Duration (which is a percentage sensitivity indicator).
- Assuming zero-coupon bonds have a duration shorter than their maturity (they always have a duration equal to maturity).
Frequently Asked Questions
What is Macaulay Duration?
Macaulay Duration is the weighted average time an investor must hold a bond until the present value of its cash flows equals the amount paid for the bond. It is measured in years.
How does coupon rate affect bond duration?
Higher coupon rates result in shorter durations. This is because higher coupons return cash to the investor faster, reducing the relative weight of the final par repayment.
How does years to maturity affect duration?
Longer years to maturity lead to longer durations because more cash flows occur in the distant future, increasing sensitivity to rate shifts.
What is the duration of a zero-coupon bond?
The Macaulay Duration of a zero-coupon bond is exactly equal to its time to maturity, as there are no intermediate cash flows to recover capital earlier.
How is Macaulay Duration useful for portfolio immunization?
Investors use it to immunize portfolios by matching the duration of their bond assets to the duration of their liabilities, neutralizing the impact of interest rate changes.