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.
\nFor a price \\(P(y)\\), the class defines modified duration and DV01 through the local derivative:
\n$$D=-\\frac{1}{P}\\frac{\\partial P}{\\partial y},\\qquad\nDV01=-\\frac{\\partial P}{10{,}000\\,\\partial y}.$$
\nThe 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.
","contentMarkdown":"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.\n\nFor a price \\(P(y)\\), the class defines modified duration and DV01 through the local derivative:\n\n$$D=-\\frac{1}{P}\\frac{\\partial P}{\\partial y},\\qquad\nDV01=-\\frac{\\partial P}{10{,}000\\,\\partial y}.$$\n\nThe 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.","dataUrl":"https://sharifhsn.dev/api/posts/interest-rate-risk-and-duration.json","date":"2024-10-24","datePublished":"2024-10-24","description":"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 …","site":"https://sharifhsn.dev","slug":"interest-rate-risk-and-duration","source":"FE-535 | Risk Management","sourceUrl":null,"tags":["Risk Management","Interest Rate Risk","Duration"],"title":"Interest Rate Risk and Duration","url":"https://sharifhsn.dev/blog/interest-rate-risk-and-duration/","version":"1","wordCount":84}