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Modified Duration Calculator

Calculate the modified duration of a bond to measure price sensitivity to yield changes.

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Calculation Parameters

Specify your inputs below.

Calculated Result

Modified Duration (Years) 6.34
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Expert Tip

Modified duration scales down Macaulay duration to express the exact percentage price change per 1% yield shift.

How this Calculator Works

This calculator computes the Modified Duration of a bond, estimating the percentage price change of the bond in response to a 1% change in yield. It adjusts Macaulay duration to reflect compounding yields. Risk managers use it to hedge portfolios.

Formula & Methodology

Modified Duration = Macaulay Duration / (1 + y / m) - Macaulay Duration is the weighted average time to receive all cash flows. - y is the yield to maturity (YTM) as a decimal. - m is the coupon frequency per year.

Step-by-Step Calculation Example

Here is a step-by-step example showing how the calculations are performed:

A bond has a Macaulay duration of 4.5 years, a yield to maturity of 6%, and pays semiannually (m = 2). 1. Calculate denominator: 1 + 0.06 / 2 = 1.03. 2. Divide Macaulay duration by denominator: 4.5 / 1.03 = 4.37. Result: The modified duration is 4.37 years.

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Detailed Insights & Expert Guide

ℹ️ About this Calculation

This fixed income and debt investment calculator analyzes bond pricing, coupon yield to maturity (YTM), Macaulay/modified duration, credit risk spreads, and debt coverage ratios based on Wall Street fixed income analytics.

Variable Glossary

Input

Fixed Income Data

Par value ($1,000), coupon rate %, payment frequency, maturity years, corporate credit spread, or tax rate %.

Parameter

Bond Performance

Yield to Maturity (YTM %), present bond price ($), modified duration (years), or Tax-Equivalent Yield (TEY).

How to Calculate Step-by-Step

1

Step 1

Input bond face value, annual coupon interest rate, or corporate credit default swap (CDS) basis points.

2

Step 2

Select payment schedule frequency (annual, semi-annual) and years remaining until maturity date.

3

Step 3

Review calculated yield to call/maturity, interest rate sensitivity duration, or debt service coverage (DSCR).

FAQ

How does bond duration measure interest rate risk?
Modified duration estimates the approximate percentage change in a bond's price for a 1% (100 bps) shift in interest rates. Higher duration indicates greater price sensitivity to rate moves.
What is Tax-Equivalent Yield (TEY) for municipal bonds?
Tax-Equivalent Yield = Municipal Tax-Exempt Yield / (1 - Marginal Tax Rate). It shows the pre-tax yield a taxable bond would need to equal the after-tax yield of a tax-free municipal bond.
Can fixed income calculators guarantee bond trading outcomes?
No. Bond pricing models assume clean compounding yields and fixed reinvestment rates. Secondary market prices fluctuate based on liquidity, credit rating revisions, and market interest rate movements.