What is convexity risk in bank assets and how is it measured?

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AcadiFi · Accepted Answer

Convexity risk is the second-order sensitivity of asset value to interest rate changes. For option-free bonds convexity is positive and beneficial: prices rise more on a rate fall than they drop on an equal rate rise. For callable bonds, MBS, and other assets with borrower-held prepayment options convexity is negative: price gains from rate falls are capped because the issuer or borrower repays early, while price losses from rate rises are amplified by extension. Measurement uses effective convexity = (P_down + P_up - 2*P_base) / (P_base * dy^2) where P_up and P_down are prices under symmetric rate shocks and dy is the shock size. Example: a $100M MBS position with base price 101, price under -50 bp of 101.8, price under +50 bp of 99.9. Effective convexity = (101.8 + 99.9 - 2*101) / (101 * 0.005^2) = (-0.3) / 0.002525 = -119. ```mermaid flowchart LR S[Rate shock] --> U[Price up scenario] S --> D[Price down scenario] U --> C[Convexity
second derivative] D --> C ``` Negative convexity of that magnitude means a 100 bp move produces a loss beyond duration of -0.5 * 119 * $100M * 0.01^2 = -$0.6M per 100 bp squared. Hedging convexity uses long-dated options or OTM swaptions; duration hedges alone leave a curved residual. FRM asks candidates to contrast option-free (positive convex) with MBS (negative convex) and to explain why duration-matched portfolios still lose money under large rate moves.

What is convexity risk in bank assets and how is it measured?

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