Interest Rate Risk and Duration
- Risk Management
The interest-rate-risk notes approximate how a bond portfolio changes when yields move. Duration is the first-order sensitivity of price to yield; convexity captures the curvature that duration misses.
For a price \(P(y)\), the class defines modified duration and DV01 through the local derivative:
$$D=-\frac{1}{P}\frac{\partial P}{\partial y},\qquad DV01=-\frac{\partial P}{10{,}000\,\partial y}.$$
The signs reflect the inverse relation between price and yield. A duration-only hedge is adequate for a small parallel move, while convexity matters for larger moves or portfolios whose cash flows are spread across maturities.