Interest rate risk is quantified using sensitivity-based measures that translate small yield changes into price and P&L impacts, enabling precise hedging and portfolio construction. This article explains core methods: the sensitivity approach, price value of a basis point (PVBP), portfolio PVBP computation, hedging using PVBP, other practical PVBP applications, and duration.
Measurement of interest rate risk
Interest rate risk reflects how a bond or portfolio’s value changes when yields move, typically summarized via first- and second-order sensitivities. Core measures include DV01/PVBP for linear exposure, duration for elasticity to yield, and convexity for curvature adjustments under larger yield shifts. Effective frameworks also consider curve risk (key-rate durations), basis risk between benchmarks, and optionality that alters effective duration under rate scenarios.
Sensitivity approach
The sensitivity approach approximates price impact from small yield moves by linearizing the price–yield curve around current yield. For a bond, the first-order price change is ΔP ≈ −PVBP × Δy(bp), where PVBP is the price change per 1 bp (0.01%) move in yield. At the portfolio level, sensitivities are aggregated by summing instrument PVBPs—option-adjusted when relevant—to estimate total P&L for specified basis point shocks.
Price value of a basis point method
Price Value of a Basis Point (PVBP), also called DV01, is the absolute change in the instrument’s price for a 1 bp parallel shift in the relevant yield curve. PVBP can be computed by “bumping” the discount rate by +/−1 bp and revaluing, or via duration scaling: PVBP ≈ Modified Duration × Price × 0.0001. PVBP is reported per ₹100 face or per full position size, enabling direct translation of rate moves into currency P&L.
Computation of portfolio PVBP
Portfolio PVBP is the sum of position-level PVBPs across bonds, derivatives, and cash instruments aligned to the same curve. Steps:
- Compute clean-price PVBP for each instrument to the appropriate benchmark curve (e.g., G‑Sec for sovereigns, OIS for swaps).
- Adjust for instrument sign and notional (long positive, short negative).
- Aggregate by key curve tenors if using key-rate PVBP; otherwise sum for a parallel PVBP.
- Include derivative PVBP (e.g., swaps, futures) to reflect hedges and synthetic exposures.
Hedging using basis point value
PVBP hedging neutralizes small parallel shifts by offsetting portfolio PVBP with opposing PVBP from hedging instruments. Practical methods:
- Cash bond hedge: Take an offsetting position in a liquid benchmark (e.g., 10‑year G‑Sec) to align net PVBP near zero.
- Swap hedge: Enter a pay/fix or receive/fix interest rate swap to add or subtract PVBP efficiently without balance sheet usage.
- Futures hedge: Use interest rate futures on the closest benchmark; convert futures contract sensitivity to PVBP via conversion factors and CTD analytics.
- Key-rate neutralization: Match PVBP at selected maturities (e.g., 2y, 5y, 10y) to mitigate curve twist risk rather than only parallel shifts.
Other uses of PVBP
PVBP enables several practical risk and execution tasks:
- Sizing trades: Choose hedge notionals to achieve target PVBP reduction with minimal slippage.
- Comparing liquidity-adjusted risk: Prefer instruments with higher PVBP-per-liquidity ratios for efficient hedging in tight markets.
- Scenario P&L: Estimate day-one P&L under policy shocks (e.g., ±25 bps) by multiplying portfolio PVBP by shock size.
- Risk budgeting: Allocate PVBP limits to desks/strategies; monitor breaches and stress add-ons.
- Performance attribution: Attribute rate-driven P&L by curve buckets using key-rate PVBP changes.
Duration
Duration measures price elasticity to yield changes and underpins PVBP and hedge design.
- Macaulay duration is the PV‑weighted average time to receive cash flows, expressed in years.
- Modified duration converts Macaulay to a sensitivity: Dmod = Dmac / (1 + y/m), linking percent price change to yield change.
- Key-rate duration decomposes sensitivity by specific maturities on the curve, improving hedge precision for non-parallel shifts.
- Convexity refines estimates for larger yield moves; price change ≈ −Dmod × Δy + 0.5 × Convexity × (Δy)^2.
Practical workflow and tips
- Use clean price for PVBP reporting and add accrued interest separately for settlement calculations.
- For callable/putable structures, use option-adjusted duration/PVBP to reflect path-dependent cash flows.
- Align curve choice with instrument valuation (e.g., OIS discounting, G‑Sec benchmark) to avoid basis mismatch in hedging.
- Reconcile portfolio PVBP daily with P&L explains; large unexplained variances may indicate curve mapping or pricing issues.
- Combine PVBP neutrality with key-rate constraints and convexity checks to reduce residual curve and nonlinearity risk.
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