Compute dollar duration (duration × price) for a 1% parallel yield move.
Bond Parameters
Enter the bond's clean price and modified duration to calculate Dollar Duration
Formula Used
Dollar Duration = Modified Duration × Clean Price
Measures the dollar price change for a 1% (100 basis points) parallel shift in the yield curve. Divide by 100 to get PVBP (DV01) for per-basis-point sensitivity.
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**Dollar Duration** is the fundamental metric that translates a bond's interest rate sensitivity from percentage terms into actual dollar values. While modified duration tells you the percentage price change for a 1% yield move, dollar duration tells you the **actual dollar P&L** you'll experience.
Why Dollar Terms Matter
Percentage-based duration is useful for comparing securities, but portfolio managers and risk officers need to know actual P&L impact. A 5-year duration bond sounds less risky than a 10-year duration bond, but if the 5-year position is $100 million and the 10-year position is $10 million, the dollar risk may be reversed. Dollar duration resolves this ambiguity.
The Universal Risk Language
Dollar duration has become the standard language for communicating interest rate risk across fixed income desks, asset managers, and risk committees. Unlike percentage measures that require mental scaling, dollar duration immediately conveys the stakes: "A 50-basis-point rate rise costs us $2.5 million" is actionable information.
The Dollar Duration Formula and Components
Dollar duration is calculated by multiplying modified duration by the bond's clean price, giving the dollar price change per $100 face value for a 1% (100 bps) yield change.
The Calculation Identity
The formula for Dollar Duration is:
Dollar Duration = Modified Duration × Clean Price
Understanding the Components
Each component contributes to the final dollar sensitivity:
**Modified Duration**: Percentage price sensitivity per 1% yield change. Higher duration means greater sensitivity.
**Clean Price**: The bond's quoted market price excluding accrued interest. Premium bonds (price > 100) have higher dollar duration than discount bonds, all else equal.
**Result**: Dollar change per $100 face value for a 100-basis-point yield move.
Scaling to Position Size
To calculate total position dollar duration, scale by position size:
Position Dollar Duration = (Dollar Duration / 100) × Position Face Value
This gives you the actual P&L in dollars for your specific position when yields change by 1%.
Interpreting Dollar Duration and Risk Levels
Dollar duration interpretation depends on both the absolute value and your portfolio's risk tolerance and hedging capability.
Dollar Duration by Duration Category
Very High Duration (10+ years): Dollar duration exceeds $10 per $100 face. Long-dated Treasuries, zero-coupon bonds, and long-duration corporates. Significant P&L volatility from rate changes.
High Duration (7-10 years): Dollar duration around $7-10 per $100 face. Intermediate-to-long corporates and municipalities. Active hedging often appropriate.
Moderate Duration (4-7 years): Dollar duration around $4-7 per $100 face. Core investment-grade bonds. Balanced risk-return for most portfolios.
Low Duration (2-4 years): Dollar duration around $2-4 per $100 face. Short-term notes and floating-rate structures. Manageable rate risk.
Very Low Duration (<2 years): Dollar duration below $2 per $100 face. Money market instruments and near-maturity bonds. Minimal rate sensitivity.
Risk Limit Frameworks
Institutional investors often establish dollar duration limits:
**Absolute Limits**: Maximum dollar duration per sector or portfolio (e.g., $5 million max dollar duration).
**Relative Limits**: Dollar duration as percentage of AUM (e.g., 1% of portfolio value per 100 bps).
**VaR Integration**: Dollar duration feeds into Value-at-Risk calculations for comprehensive risk management.
Relationship Between Dollar Duration and PVBP
Dollar Duration and PVBP (DV01) are closely related, differing only by a factor of 100.
The Conversion Formula
The relationship between Dollar Duration and PVBP is:
PVBP (DV01) = Dollar Duration / 100
This makes intuitive sense: if dollar duration measures change per 100 bps (1%), then PVBP measures change per 1 bp, which is 1/100th of that.
When to Use Each Metric
**Dollar Duration**: Best for understanding P&L impact of significant rate moves (25-100+ bps) and for scenario analysis.
**PVBP (DV01)**: Best for day-to-day hedging, calculating hedge ratios, and fine-tuning duration exposure.
**Both Together**: Comprehensive risk reporting includes both metrics for different audiences and use cases.
Portfolio Aggregation and Risk Limits
Dollar duration's key advantage is simple portfolio-level aggregation since it's denominated in dollars.
Summation Property
Total portfolio dollar duration equals the sum of individual position dollar durations:
Long positions contribute positive dollar duration (lose money when rates rise).
Short positions contribute negative dollar duration (gain money when rates rise).
Net dollar duration indicates overall portfolio rate sensitivity in dollar terms.
Hedging Applications
Dollar duration enables precise hedge ratio calculation:
To hedge a $5 million dollar duration exposure, find a hedging instrument with equivalent (negative) dollar duration.
Treasury futures, interest rate swaps, and inverse ETFs can provide offsetting dollar duration.
Partial hedging reduces dollar duration to target level rather than zero.
Dynamic Risk Management
Dollar duration changes continuously as markets move:
As yields fall, duration rises, increasing dollar duration exposure.
As bonds approach maturity, duration and dollar duration decline.
Portfolio rebalancing and new purchases alter total dollar duration.
Conclusion
Dollar Duration is the essential metric for translating **interest rate risk** from abstract percentages into actionable dollar P&L. By multiplying modified duration by price, it enables immediate understanding of portfolio stakes.
Whether you're setting risk limits, calculating hedge ratios, or communicating exposure to stakeholders, dollar duration provides the common language for fixed income risk management. Combined with PVBP for fine-grained hedging and convexity for large rate moves, dollar duration forms the foundation of professional interest rate risk analysis.
Frequently Asked Questions
Common questions about Dollar Duration and interest rate risk
What is Dollar Duration?
Dollar Duration measures the dollar change in a bond's price for a 1% (100 basis points) change in yield. It is calculated as Modified Duration × Clean Price. This metric translates percentage-based duration into actual dollar P&L sensitivity, making risk immediately actionable for portfolio management.
How is Dollar Duration related to PVBP (DV01)?
PVBP (DV01) equals Dollar Duration divided by 100. While Dollar Duration measures price change per 1% (100 bps) yield move, PVBP measures price change per 1 bp yield move. Both express rate sensitivity in dollar terms but at different granularities. PVBP is preferred for day-to-day hedging; Dollar Duration for scenario analysis.
Why use Dollar Duration instead of Modified Duration?
Modified Duration is percentage-based and requires mental scaling to understand actual P&L impact. Dollar Duration immediately tells you how many dollars you'll gain or lose. For a $50 million portfolio, saying "we'll lose $2.5 million if rates rise 50 bps" is more actionable than saying "duration is 5 years."
How do I aggregate Dollar Duration across a portfolio?
Sum individual position dollar durations, treating long positions as positive and short positions as negative. This simple summation works because dollar duration is denominated in dollars. The net sum indicates total portfolio sensitivity to parallel yield curve shifts expressed in P&L terms.
Does Dollar Duration change over time?
Yes, Dollar Duration changes continuously. As yields change, duration changes (higher yields compress duration). As bonds approach maturity, duration shortens. Price changes also affect dollar duration since it's duration × price. Regular recalculation is essential for accurate risk measurement.
How do I use Dollar Duration for hedging?
Calculate your portfolio's total dollar duration, then find hedging instruments (Treasury futures, swaps) with sufficient dollar duration to offset. If your portfolio has $5 million dollar duration and you want to reduce it to $2 million, sell hedging instruments with $3 million dollar duration.
What are the limitations of Dollar Duration?
Dollar Duration assumes parallel yield curve shifts and ignores convexity. For large rate moves, convexity causes actual P&L to deviate from Dollar Duration predictions. It doesn't capture curve steepening/flattening risk. For bonds with embedded options, effective duration must be used instead of modified duration.
How does convexity affect Dollar Duration accuracy?
Dollar Duration provides a linear approximation. Positive convexity (most bonds) means bonds gain more than Dollar Duration predicts when rates fall, and lose less when rates rise. For rate moves exceeding 25-50 bps, adding a convexity adjustment improves accuracy significantly.
Should I use modified or effective duration for Dollar Duration?
Use modified duration for bullet bonds without embedded options. For callable bonds, putable bonds, MBS, and structured products, use effective duration (calculated from price sensitivity to rate changes). Effective duration captures optionality effects that modified duration misses.
What Dollar Duration level requires active hedging?
This depends on risk tolerance and investment horizon. As a general guideline: portfolios with dollar duration exceeding 1-2% of AUM per 100 bps should consider active hedging. Aggressive portfolios may tolerate higher levels, while conservative portfolios (pension funds, insurance) often hedge to much lower thresholds.
Summary
The Dollar Duration Calculator translates interest rate sensitivity from percentages into actionable dollar P&L terms.
It is essential for portfolio risk measurement, enabling straightforward aggregation and hedge ratio calculation.
Use this tool to quantify dollar exposure, set risk limits, and size duration hedges using Treasury futures or swaps.
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Compute dollar duration (duration × price) for a 1% parallel yield move.
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