How do you immunize a bond portfolio using Treasury futures to match a liability duration target?

Portfolio immunization with futures involves adjusting the portfolio's effective duration to match the liability duration without trading the underlying bonds. This is far more capital-efficient than restructuring the cash portfolio, requiring only initial margin rather than full principal.\n\nImmunization Contract Formula:\n\nN = (D_target - D_portfolio) x MV_portfolio / (D_futures x Price_futures x Multiplier)\n\nWhere:\n- D_target = liability duration\n- D_portfolio = current portfolio modified duration\n- MV_portfolio = market value of the portfolio\n- D_futures = duration of the CTD bond (adjusted by CF)\n- Price_futures = current futures price (decimal)\n- Multiplier = contract size ($100,000 for T-bonds)\n\nWorked Example:\n\nCrestview Pension Fund has:\n- Asset portfolio: $800 million, modified duration = 6.2 years\n- Liabilities: PV = $750 million, modified duration = 9.8 years\n- Duration gap: 9.8 - 6.2 = 3.6 years (need to extend asset duration)\n\nUsing the 30-year T-bond futures:\n- Futures price: 118.50 ($118,500 per contract)\n- CTD bond modified duration: 14.3 years\n- CTD conversion factor: 0.8650\n- Futures effective duration: 14.3 / 0.8650 = 16.53 years\n\nContracts needed:\nN = (9.8 - 6.2) x 800,000,000 / (16.53 x 118,500)\n = 3.6 x 800,000,000 / 1,958,805\n = 2,880,000,000 / 1,958,805\n = 1,470 contracts (long)\n\nVerification:\nDuration contribution from futures: 1,470 x 16.53 x 118,500 / 800,000,000 = 3.60 years\nNew portfolio duration: 6.2 + 3.6 = 9.8 years (matches liability target)\n\nKey Considerations:\n\n1. Dollar duration matching is more precise: Instead of matching modified durations, match dollar durations (DV01 x market value) for better hedge accuracy\n2. Convexity mismatch: Duration matching protects against parallel shifts only. Large rate moves or curve reshaping expose convexity risk\n3. Rebalancing frequency: Duration drifts as time passes and rates change. Monthly or quarterly rebalancing is standard\n4. Futures roll costs: Contracts expire quarterly. Rolling the position incurs bid-ask costs and potential basis changes\n5. Margin requirements: While capital-efficient, margin calls during rate spikes can create liquidity stress\n\nMulti-Key-Rate Immunization:\n\nFor more precise hedging, decompose the duration gap across key rate tenors (2Y, 5Y, 10Y, 30Y) and use the appropriate futures contracts for each tenor. This protects against non-parallel curve movements.\n\nPractice immunization calculations in our FRM question bank.