Bond Positions

3 bonds
Scope: This calculator uses modified duration for option-free bonds and assumes parallel yield curve shifts. For callable bonds or MBS, use effective duration.

Portfolio Examples

Load a preset to explore different portfolio strategies:

Assumptions

  • Market value weights (current prices, not face value)
  • Option-free bonds (no callable/putable features)
  • Parallel yield curve shifts assumed
  • First-order approximation (convexity not included)

Portfolio Metrics

Portfolio Modified Duration -- years
Portfolio DV01 --
Total Market Value --

Duration Contribution Breakdown

Bond Market Value Weight Duration Contribution

Duration Contribution Visualization

Understanding Portfolio Duration

What is Portfolio Duration?

Portfolio duration measures the overall interest rate sensitivity of a bond portfolio. It is calculated as the weighted average of the modified durations of individual bonds, where weights are based on each bond's market value as a proportion of the total portfolio value.

Portfolio duration answers a critical question: "How much will my portfolio's value change if interest rates move?"

The Portfolio Duration Formula

Dportfolio = Σ(wi × Di)

Where:

  • wi = Market value weight of bond i (MVi / Total MV)
  • Di = Modified duration of bond i

For example, if Bond A has a market value of $500,000 with duration 3.5 and Bond B has $500,000 with duration 7.0, the portfolio duration is: (0.50 × 3.5) + (0.50 × 7.0) = 5.25 years.

Portfolio DV01 (Dollar Duration)

DV01 (Dollar Value of 01) represents the dollar change in portfolio value for a 1 basis point (0.01%) change in interest rates:

DV01 = Portfolio Duration × Total MV / 10,000

DV01 is essential for hedging and risk management because it expresses interest rate risk in dollar terms rather than percentage terms.

Why Portfolio Duration Matters

  • Interest Rate Risk Management: Quantifies how much your portfolio value will change when rates move
  • Index Tracking: Match your portfolio duration to a benchmark for passive management
  • Asset-Liability Matching: Match portfolio duration to liability duration for pension funds and insurance companies
  • Immunization: Set portfolio duration equal to investment horizon to lock in returns
  • Hedging: Use DV01 to calculate hedge ratios for interest rate swaps or futures

Portfolio Strategies by Duration

  • Short Duration (1-3 years): Lower interest rate risk, suitable when expecting rising rates
  • Intermediate Duration (3-7 years): Balanced approach, typical for core bond portfolios
  • Long Duration (7+ years): Higher interest rate sensitivity, benefits from falling rates
  • Barbell Strategy: Combine short and long maturities, skipping intermediate
  • Bullet Strategy: Concentrate maturities around a target date

Limitations of Portfolio Duration

Portfolio duration is a powerful tool but has important limitations:

  • Parallel shift assumption: Assumes all rates move by the same amount (rarely true in practice)
  • Linear approximation: Duration is only accurate for small yield changes; for large moves, convexity matters
  • Option-free bonds only: Callable bonds, MBS, and floaters need effective duration, not modified duration
  • No credit risk: Duration measures interest rate risk only, not credit spread risk
CFA Exam Tip: Portfolio duration is a weighted average by market value, not by face value or number of bonds. Remember that changing the weights of existing bonds is often more practical than buying new bonds to adjust portfolio duration.

Frequently Asked Questions

Portfolio duration is the weighted average of the modified durations of individual bonds in a portfolio, where weights are based on each bond's market value as a proportion of total portfolio value. It measures the portfolio's overall sensitivity to interest rate changes.

Portfolio duration is calculated using the formula: D_portfolio = Sum(w_i x D_i), where w_i is the market value weight of each bond (bond market value divided by total portfolio market value) and D_i is the modified duration of each bond.

Portfolio DV01 (Dollar Value of 01) represents the dollar change in portfolio value for a 1 basis point (0.01%) change in interest rates. It is calculated as: Portfolio Duration x Total Market Value / 10,000. This metric is essential for interest rate risk management.

Portfolio duration is important because it: 1) Measures overall interest rate risk, 2) Enables portfolio immunization strategies, 3) Helps benchmark tracking for index funds, 4) Facilitates asset-liability matching, and 5) Guides hedging decisions for managing rate exposure.

Portfolio duration assumes: 1) Parallel yield curve shifts (all rates move equally), 2) Small yield changes (first-order approximation), 3) Option-free bonds (callable/MBS need effective duration). It also ignores credit risk and reinvestment risk. For large rate moves, convexity should be considered.
Important Disclaimer

This calculator is for educational purposes only. It calculates portfolio modified duration as a weighted average of individual bond durations, which is a first-order approximation assuming parallel yield curve shifts and option-free bonds. For callable bonds, MBS, or other securities with embedded options, use effective duration instead. This is not financial advice.

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