Bond Duration, Modified Duration & Convexity Risk Simulator
Simulates non-linear bond price behavior, Macaulay duration, Modified duration, and second-order Taylor series convexity adjustments under interest rate shifts from -300 bps to +300 bps.
Target Audience Application
Manage duration risk in corporate reserve accounts, ensuring debt-service escrow funds do not suffer severe principal drawdowns during monetary policy tightening cycles.
Stress-test client bond allocations against sudden parallel shifts in the yield curve, demonstrating why high-convexity bonds outperform low-convexity bonds in both rising and falling rate regimes.
Model systemic interest rate risk, bank balance-sheet duration mismatches, and unrealized losses on held-to-maturity (HTM) sovereign debt portfolios.
Understand why long-term bond ETFs (like TLT) experience violent price swings when rates change by even 50 basis points, and how duration determines volatility.
Duration & Second-Order Convexity Equation
ΔP / P ≈ -D* × Δy + 0.5 × C × (Δy)²Where:
D* = Modified Duration = Macaulay Duration / (1 + y / m)C = Convexity Measure (Curvature of price-yield relationship)Δy = Change in Yield (Yield shock in decimals)
Duration Classification & Risk Tiers
- Ultra-Short Duration (< 1 Year): Negligible rate sensitivity. Used for capital preservation and liquidity.
- Short Duration (1–3 Years): Minimal price volatility. A 100 bps rate hike causes an approximate 2% to 3% price decline.
- Intermediate Duration (4–7 Years): Balanced risk/yield. A 100 bps rate shock triggers a 5% to 7% drawdown.
- Long Duration (> 10 Years): High volatility. A 200 bps rate hike can cause price drawdowns exceeding 25% to 35%.
Institutional Methodology & Underwriting Dossier
Simulates non-linear bond price behavior, Macaulay duration, Modified duration, and second-order Taylor series convexity adjustments under interest rate shifts from -300 bps to +300 bps.
1. Target Audience & Practical Application
How different financial market participants apply this quantitative model to real-world capital allocation:
Manage duration risk in corporate reserve accounts, ensuring debt-service escrow funds do not suffer severe principal drawdowns during monetary policy tightening cycles.
Stress-test client bond allocations against sudden parallel shifts in the yield curve, demonstrating why high-convexity bonds outperform low-convexity bonds in both rising and falling rate regimes.
Model systemic interest rate risk, bank balance-sheet duration mismatches, and unrealized losses on held-to-maturity (HTM) sovereign debt portfolios.
Understand why long-term bond ETFs (like TLT) experience violent price swings when rates change by even 50 basis points, and how duration determines volatility.
2. Duration & Second-Order Convexity Equation
ΔP / P ≈ -D* × Δy + 0.5 × C × (Δy)²Where:
D* = Modified Duration = Macaulay Duration / (1 + y / m)C = Convexity Measure (Curvature of price-yield relationship)Δy = Change in Yield (Yield shock in decimals)
3. Duration Classification & Risk Tiers
- Ultra-Short Duration (< 1 Year): Negligible rate sensitivity. Used for capital preservation and liquidity.
- Short Duration (1–3 Years): Minimal price volatility. A 100 bps rate hike causes an approximate 2% to 3% price decline.
- Intermediate Duration (4–7 Years): Balanced risk/yield. A 100 bps rate shock triggers a 5% to 7% drawdown.
- Long Duration (> 10 Years): High volatility. A 200 bps rate hike can cause price drawdowns exceeding 25% to 35%.