How does the duration-based hedge ratio differ from the DV01 approach, and when should each be used?

Duration-based and DV01-based hedge ratios are mathematically related but expressed differently. Understanding when each formulation is more convenient helps avoid errors on the exam and in practice.\n\nDuration-Based Hedge Ratio:\n\nN = -(D_P x P) / (D_F x F)\n\nWhere D_P = portfolio duration, P = portfolio value, D_F = futures duration, F = futures contract value.\n\nDV01-Based Hedge Ratio:\n\nN = -DV01_P / DV01_F\n\nWhere DV01_P = portfolio dollar change per bp, DV01_F = futures dollar change per bp.\n\nMathematical Equivalence:\n\nSince DV01 = Duration x Value / 10,000:\n\nDV01_P / DV01_F = (D_P x P / 10,000) / (D_F x F / 10,000) = (D_P x P) / (D_F x F)\n\nThey are identical when using the same duration measure (modified or effective).\n\nWorked Example -- Both Methods:\n\nSterling Bank needs to hedge a $200 million mortgage-backed securities portfolio.\n\n| Metric | MBS Portfolio | 10Y T-note Futures |\n|---|---|---|\n| Modified duration | 4.85 years | 6.92 years (CTD) |\n| Market value | $200,000,000 | $112,750 per contract |\n| DV01 | $97,000 | $78.07 per contract |\n| CF (CTD) | -- | 0.9034 |\n\nDuration method:\nN = (4.85 x 200,000,000) / (6.92 x 112,750) = 970,000,000 / 780,230 = 1,243 contracts\n\nDV01 method:\nN = $97,000 / $78.07 = 1,243 contracts\n\nIdentical result.\n\nWhen to Prefer Each:\n\n| Situation | Preferred Method | Reason |\n|---|---|---|\n| Simple bond portfolio | Either works | Mathematically equivalent |\n| Complex instruments (MBS, callables) | DV01 | Effective duration is embedded in DV01 already |\n| Cross-market hedging | DV01 | Different notionals make duration comparison misleading |\n| Exam questions | Match the given data | Use whichever inputs are provided |\n| Key rate hedging | DV01 by tenor bucket | Duration is a single-point measure |\n\nNegative Convexity Caveat:\n\nFor MBS portfolios, the effective duration changes dramatically with rates (negative convexity from prepayment risk). Sterling Bank's hedge of 1,243 contracts works at current rates, but a 50 bp rally could shorten MBS duration to 3.1 years while the futures duration barely changes, leaving the portfolio over-hedged. Dynamic rebalancing or options overlays address this.\n\nPractice both hedge ratio methods in our FRM question bank.