PV01
PV01 (Present Value of a Basis Point, also called DV01 or Dollar Value of a Basis Point) measures the change in the price (present value) of a fixed income instrument or portfolio for a one basis point (0.01%) decrease in yield, expressed in dollar terms. PV01 is the primary metric for quantifying and managing interest rate risk in fixed income portfolios, enabling precise calculation of hedge ratios, comparison of rate sensitivity across instruments of different durations and notional sizes, and aggregation of interest rate exposure across complex multi-instrument portfolios.
Key takeaways
- PV01 = -∂P/∂y × 0.0001, where P is the bond price and y is the yield; equivalently, PV01 = Modified Duration × Price × 0.0001, making it both a dollar-denominated and percentage-denominated risk measure.
- A portfolio with a PV01 of $50,000 will gain approximately $50,000 in value for each 1 basis point decrease in yields (and lose $50,000 for each 1 bp increase in yields), enabling straightforward P&L attribution.
- Hedge ratios using PV01 are calculated as: Number of Hedge Contracts = Portfolio PV01 / Futures Contract PV01, ensuring the hedge instrument's interest rate sensitivity matches the portfolio's.
- PV01 aggregation across a portfolio requires careful attention to the yield curve structure—PV01s calculated at different yield curve points (key rate durations) should be aggregated by maturity bucket rather than simply summed, to capture curve risk.
- For non-parallel yield curve shifts, key rate PV01 (also called key rate DV01) measures sensitivity to changes at specific maturities (2yr, 5yr, 10yr, 30yr), providing a more granular and precise risk profile than a single PV01 number.
Explanation
PV01 (or DV01) is the workhouse risk metric of fixed income trading desks, portfolio management teams, and risk management functions globally. Its appeal is straightforward: it expresses interest rate risk in dollar terms that are directly interpretable, comparable across instruments, and actionable for hedging. A portfolio manager who knows that their portfolio has a PV01 of $150,000 knows precisely that a 10 basis point rise in rates will cost approximately $1.5 million, and can calculate exactly how many 10-year Treasury futures contracts (each with a PV01 of approximately $850) they would need to sell to hedge that exposure.
The calculation of PV01 for a simple fixed-rate bond flows directly from modified duration. For a bond with a modified duration of 7.5 years, a price of $1,000, and face value of $1,000: PV01 = 7.5 × $1,000 × 0.0001 = $0.75 per bond. For a $100 million position (100,000 bonds), the portfolio PV01 is $75,000. This means the portfolio gains $75,000 in value for each basis point decrease in yield. The modified duration—the weighted average time to receive cash flows from the bond, discounted and modified for yield—is thus the key input to PV01 calculation for straightforward bonds.
The PV01 of complex fixed income instruments requires numerical estimation rather than analytical formula. For mortgage-backed securities with prepayment optionality, the effective PV01 is estimated by repricing the MBS at yield ± 1 basis point using an OAS model that holds the OAS constant while shifting the yield curve, then computing (P_{y-1bp} - P_{y+1bp}) / 2. For interest rate swaps, the PV01 of the fixed leg equals the duration of the fixed rate payments; the PV01 of the floating leg equals approximately the duration to the next reset date. The net PV01 of a receiver swap (receive fixed, pay floating) is the difference—approximately the duration of the fixed leg for swaps where the floating leg resets frequently.
Key rate PV01 analysis decomposes the total interest rate sensitivity of a portfolio into sensitivity at specific maturities along the yield curve, providing a granular risk picture beyond the parallel shift assumption. A 10-year corporate bond portfolio might have a total PV01 of $200,000, but 60% of that sensitivity is at the 10-year point on the curve, 25% at the 5-year point (from coupon cash flows), and 15% at intermediate maturities. If the risk manager only hedges the total PV01 with 10-year futures, the 5-year curve risk remains unhedged—key rate analysis reveals this residual exposure. Hedge funds running curve-steepener or curve-flattener trades explicitly target specific key rate PV01 profiles, buying duration in one maturity bucket while selling duration in another.
The PV01 framework extends seamlessly to credit-risky instruments through credit spread sensitivity (PVCS01—Present Value of a Credit Spread Basis Point) and to inflation-linked bonds through breakeven sensitivity. For a comprehensive fixed income risk model, traders monitor DV01 (nominal rate sensitivity), PVCS01 (credit spread sensitivity), inflation sensitivity, and foreign exchange sensitivity simultaneously, aggregating these risk dimensions into a multi-dimensional risk report that captures all material sources of P&L volatility in a fixed income portfolio.
Formula
PV01 = Modified Duration × Price × 0.0001; PV01 ≈ (P_{y-1bp} - P_{y+1bp}) / 2; Hedge Ratio = Portfolio PV01 / Futures PV01
Example
A fixed income portfolio manager runs a $500 million portfolio of investment-grade corporate bonds with an aggregate modified duration of 6.2 years. The portfolio's PV01 = 6.2 × $500M × 0.0001 = $310,000 per basis point. The manager expects a hawkish Federal Reserve announcement to drive the 10-year Treasury yield up by 15 basis points. The expected P&L impact: -$310,000 × 15 = -$4.65 million. To hedge 50% of this rate risk, the manager sells 10-year Treasury futures. Each 10-year future has a DV01 of approximately $880 (assuming a cheapest-to-deliver bond with modified duration of 8.8 years and a $100,000 notional per contract): contracts needed = ($310,000 × 50%) / $880 = approximately 176 contracts sold short. If rates rise 15 bps as expected, the portfolio loses $4.65M on its long bonds, but the futures hedge gains approximately $2.33M (176 contracts × $880 × 15 bps), reducing the net loss to approximately $2.32M.
Related terms
Aggregation Basis Bond Bond Ladder Cdo Squared Cheapest To Deliver Corporate Bond Credit Spread Duration Dv01 Exchange Face Value