What is the Dollar Duration
Dollar duration (often discussed alongside “DV01” and “money duration”) converts a bond’s interest‑rate sensitivity into a dollar amount. It estimates how much the market value of a bond (or a portfolio of bonds) will change for a given change in yield. Practically, it gives a simple, tradable measure of interest‑rate risk — useful for risk reporting and for sizing hedges.
Key Takeaways
– Dollar duration = price sensitivity expressed in dollars for a specified yield change.
– DV01 is the dollar change for a 1 basis‑point (0.01%) yield shift; dollar duration for a 100 bps change equals DV01 × 100.
– Calculation uses modified duration and current price and is accurate only for small yield moves because bond prices are not perfectly linear in yields (convexity).
– Portfolio dollar duration is the sum of individual bond dollar durations (or the market value weighted sum).
– Use dollar duration to measure exposure, compare instruments, and size hedges — but adjust for convexity, non‑parallel yield curve moves, and embedded options.
Understanding Dollar Duration in Bond Investments
Formula and relationship to duration
– Modified duration (Dmod) measures percentage price change per 1.0 (i.e., 100%) change in yield; in practice it’s scaled for small yield changes.
– Dollar change for a yield change Δy (in decimal, e.g., 0.0001 = 1 bp) is approximated by:
Dollar change ≈ − Dmod × Price × Δy
– DV01 (Dollar Value of an 01) is the dollar change when Δy = 0.0001 (1 basis point):
DV01 = − Dmod × Price × 0.0001
– Dollar duration for a 100 bps (1%) move = DV01 × 100 = − Dmod × Price × 0.01
Example (simple)
– Bond price = $1,000, modified duration = 6.0
– DV01 = −6.0 × $1,000 × 0.0001 = −$0.60 → price falls ≈ $0.60 per 1 bp rise
– For a 100 bps rise: ≈ −$60
Interpreting signs and magnitudes
– Negative sign indicates price falls when yields rise (typical for plain‑vanilla bonds).
– Larger dollar duration = greater dollar exposure to a given yield move.
– Comparing dollar duration across bonds requires considering market value: a small bond position with high duration might be less risky than a large position with low duration.
Practical Steps — How to Calculate Dollar Duration
1. Gather inputs
– Current clean market price (or full price) of the bond.
– Modified duration (from analytics or computed from cash flows and yield).
– Desired yield change Δy (expressed in decimal; 0.0001 = 1 bp, 0.01 = 100 bps).
2. Compute DV01 (per 1 bp)
– DV01 = − Dmod × Price × 0.0001
3. Compute dollar duration for other Δy
– Dollar change for Δy = − Dmod × Price × Δy
– For 100 bps use Δy = 0.01, or multiply DV01 by 100.
4. Portfolio dollar duration
– For each security compute DV01 (or dollar duration for a chosen Δy).
– Sum them: Portfolio DV01 = Σ (market value_i × Dmod_i × 0.0001 × (−1))
– Alternatively compute market‑value weighted modified duration and multiply by portfolio market value and Δy.
5. Use results for reporting and hedging
– To hedge: Hedge units = Portfolio DV01 / DV01_of_hedge_instrument (round/adjust for contract size and convexity).
Example hedging step (using DV01)
– Portfolio DV01 = −$12,000 (i.e., loses $12,000 per 1 bp rise)
– Treasury futures DV01 per contract = −$600
– Contracts needed ≈ 12,000 / 600 = 20 contracts (short futures to offset a rise in yields)
Comparing Dollar Duration with Other Duration Methods
– Macaulay duration: weighted average time to receive cash flows (in years). Useful for immunization and duration matching but not dollar pricing directly.
– Modified duration: Macaulay duration adjusted for yield; gives percentage price change per unit change in yield. It’s the core input to calculate dollar duration.
– Dollar duration / DV01: converts modified duration into an absolute dollar exposure; most directly useful for risk reporting and hedge sizing.
Limitations and Considerations for Using Dollar Duration
1. Linear approximation; ignores convexity
– Dollar duration is a first‑order (linear) approximation. For large yield moves, the second‑order effect (convexity) matters and will make the true price change differ from the DV01 estimate.
2. Dependence on current yield and price
– DV01 changes as yields move and as time passes. Recompute periodically or after major rate moves.
3. Embedded options and non‑standard features
– Callable, putable, or amortizing bonds and many structured products have option risk; their effective duration can change dramatically depending on rates and option exercise probabilities. Dollar duration based on modified duration can be misleading unless effective duration is used.
4. Parallel vs. non‑parallel yield curve moves
– Dollar duration typically assumes a small, parallel shift in the yield curve. Realistic scenarios include twists, steepening, or butterfly moves — these require more sophisticated risk measures (key rate duration, principal component analysis).
5. Liquidity, credit spread risk, and other sources of price change
– Dollar duration captures only interest rate (yield) sensitivity. Credit spread widening, liquidity shocks, and changes in credit quality produce price moves that dollar duration does not measure.
6. Aggregation and netting
– When aggregating across many instruments, careful attention to sign conventions and market value basis is required. Some instruments (e.g., futures) have DV01 per contract that is seasonally standardized and needs conversion.
Practical Tips
– Use DV01 for quick, rough hedges and position‑sizing; include convexity adjustments for larger moves.
– For callable/embedded option products, use effective duration rather than modified duration to compute dollar exposure.
– When managing portfolios across multiple maturities, use key‑rate DV01 (per maturity bucket) to capture non‑parallel moves.
– Recalculate DV01 after significant market moves or rebalancing.
– Combine DV01 with scenario analysis (e.g., parallel ±50 bps, steepening, flattening) to see dollar impacts under realistic curve changes.
The Bottom Line
Dollar duration (and DV01) turns interest‑rate sensitivity into a dollar metric that is easy to interpret, report, and use for hedge sizing. It’s a first‑order tool: simple, practical, and widely used by portfolio managers and traders. However, it is an approximation — convexity, embedded options, and non‑parallel yield curve changes limit its accuracy for large moves or complex instruments. Use DV01 as a starting point, supplement it with convexity and key‑rate analyses, and update frequently to reflect changing yields and positions.
Source
– Investopedia, “Dollar Duration” (Julie Bang) — used as the primary reference for definitions and practical framing.