| Mode | Portfolio value | Mod. duration | Yield vol (ann.) | Confidence | Horizon | VaR (linear) |
|---|---|---|---|---|---|---|
| From bond terms | 100,000 | ≈ 4.20 | 1.20% | 99% | 10 days | ≈ 1,300 |
| From duration inputs | 250,000 | 5.10 | 1.50% | 95% | 1 day | ≈ 2,500 |
This tool uses a parametric approach with yield volatility and first-order price sensitivity. Horizon scaling assumes independent daily yield moves.
- σy,h = σy · √(h / T) (yield volatility over horizon)
- DV01 = V · Dmod · 0.0001 (value change per 1 bp)
- VaR = V · Dmod · σy,h · z (linear, duration-based)
- Loss ≈ V·(Dmod·Δy − 0.5·C·Δy²) with Δy = z·σy,h (convexity-adjusted quantile approximation)
- ES = V · Dmod · σy,h · φ(z) / (1 − CL) (expected shortfall under a normal linear model)
Notes: Duration/convexity are computed from discounted cash flows in “From bond terms” mode. Convexity typically reduces the loss estimate for yield increases, all else equal.
- Select a calculation mode that matches your available data.
- Enter yield volatility, confidence level, and horizon days.
- Provide either bond terms or your portfolio duration inputs.
- Press Submit to view results above the form.
- Use CSV or PDF export for reporting and documentation.
Practical tip: If you have a portfolio of multiple bonds, compute portfolio market value, portfolio modified duration, and portfolio convexity, then use the “From duration inputs” mode.
Why Bond VaR Matters for Rate Risk
Bond portfolios can lose value quickly when yields rise. A 10 bp parallel shock can move price by roughly DV01 × 10, so managers need a repeatable loss yardstick each day. VaR translates rate risk into a single currency number for limit comparisons. It also helps prioritize hedges when positions compete for space.
Inputs That Drive the Estimate
This calculator focuses on market value, modified duration, yield volatility, confidence level, and horizon. Volatility is entered as an annualized yield standard deviation and scaled by √(horizon/trading days). For example, with V=100,000, Dmod=4.2, σy=1.20% annual, CL=99%, and a 10‑day horizon using 252 trading days, the linear VaR is about 1,300. Doubling duration roughly doubles VaR; doubling volatility does the same.
Duration and Convexity in the Model
Duration approximates the first‑order price response to yield changes, while convexity captures curvature. When “From bond terms” is selected, price, duration, and convexity are derived from discounted cash flows using the yield and coupon frequency. Convexity matters most for longer maturities and low‑coupon bonds, where the price‑yield curve bends more. The convexity‑adjusted VaR applies a quadratic approximation at the quantile shock and can reduce the loss estimate for yield increases.
Interpreting VaR and Expected Shortfall
VaR answers: “What loss level is exceeded only (1−CL) of the time under the model?” Expected Shortfall goes further by averaging losses beyond the VaR threshold, so it is always at least as large as VaR for the same inputs. Use VaR for limit monitoring and ES for tail‑risk reporting. If VaR rises while DV01 is stable, volatility or horizon assumptions are likely driving the change.
Controls, Reporting, and Model Limits
Use consistent volatility sources, such as rolling 60–250 day yield changes, and refresh them on a schedule. Document whether the portfolio is hedged and whether the volatility reflects the hedged exposure. Parametric VaR assumes a specific distribution and a parallel shift; it may miss curve twists, spread moves, and liquidity effects. Pair the estimate with scenario shocks, basis risk checks, and post‑trade backtesting to verify performance.
What does Bond VaR measure?
It estimates a potential loss level over a chosen horizon at a selected confidence, assuming yield moves follow the model inputs. It is a risk metric for monitoring, not a guarantee of maximum loss.
Which yield volatility should I enter?
Use an annualized standard deviation of yield changes for the relevant benchmark curve. Many teams compute it from 60–250 trading days of daily changes and annualize with √252, then review it monthly or quarterly.
Why does a longer horizon raise VaR?
The calculator scales yield volatility by √(horizon/trading days). Under the square‑root‑of‑time assumption, uncertainty grows with time, so the estimated loss threshold increases as the holding period extends.
When should I include convexity-adjusted VaR?
Include it for longer‑dated or low‑coupon bonds, or when yield shocks are not tiny. Convexity captures curvature in the price‑yield relationship and can materially change the loss estimate at high confidence levels.
How do I handle a portfolio with many bonds?
Compute total market value, plus portfolio modified duration and convexity (value‑weighted). Then use the duration input mode. For mixed currencies or curves, segment the portfolio and aggregate results cautiously.
What limitations should I keep in mind?
Parametric VaR can miss curve twists, spread moves, jumps, and liquidity effects. Backtest against realized P&L, and complement it with stress scenarios, historical shocks, and concentration checks.