Halving a long position in a 30-year bond
Question
A portfolio holds a $100 million long position in a 30-year bond. What are the ways to reduce the interest-rate exposure to roughly that of a $50 million holding?
Short answer
Sell half, or hedge half the dollar duration with derivatives. The direct route is to sell $50 million of the bond. If you want to keep the bonds (cost, liquidity, tax), short Treasury bond futures sized so their dollar duration offsets half of the position's, enter a pay-fixed interest rate swap with matching DV01, or short another long bond in duration-weighted size. Each leaves basis or spread risk between the hedge and the bond.
Adapted from Crack, Heard on the Street, Q3.13, p.35; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Duration and Convexity: Measuring and Managing Interest Rate Sensitivity
- Derivation — From Binomial Trees to Black-Scholes in the Continuous Limit
- The Black-Scholes Formula Derived via Change of Measure
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