Convexity
Measures the curvature of the price-yield relationship — how duration itself changes.
Convexity captures the smile curve in bond pricing: the price-yield relationship isn't a straight line (duration's assumption), it's curved. When yields rise, prices fall less than duration predicts; when yields fall, prices rise more than duration predicts. This asymmetry is valuable — convexity is a 'good' thing. Including convexity improves price estimates for larger yield moves: ΔP/P ≈ −Dur×Δy + 0.5×Conv×(Δy²). For example, with duration 6 and convexity 50, a 1% yield rise causes ~5.5% price drop (not 6%), while a 1% yield fall causes ~6.5% price gain (not 6%). Higher convexity means the bond exhibits less downside and more upside, all else equal.
- Second derivative approximation via central difference
- Same 1bp shock as duration calculation
- Positive for standard bonds (price-yield curve is convex)
Modified Duration
Measures the percentage price change for a 1% yield change.
DV01
Dollar change in value for a 1 basis point (0.01%) yield move.
CS01
Dollar change in value for a 1 basis point move in credit spread.
Macaulay Duration
The weighted average time (in years) to receive the bond's cash flows.
Stress Test (Rate Shock)
Estimates impact of large yield moves using duration and convexity.
Value at Risk (VaR)
The maximum expected loss at a given confidence level — but doesn't tell you how bad the tail is.