How do you calculate a DV01-based hedge ratio using Treasury futures, and what adjustments are needed for the CTD bond?

A DV01-based hedge ratio matches the dollar interest rate sensitivity of a cash position with an offsetting futures position. The key insight is that a Treasury futures contract's DV01 is not its own -- it inherits the risk characteristics of the CTD bond, scaled by the conversion factor.\n\nHedge Ratio Formula:\n\nNumber of contracts = (DV01_portfolio / DV01_CTD) x CF_CTD\n\nWhere:\n- DV01_portfolio = dollar value of 1 bp for the position being hedged\n- DV01_CTD = dollar value of 1 bp for the CTD bond (per $100,000 face)\n- CF_CTD = conversion factor of the CTD bond\n\n`mermaid\ngraph LR\n A[\"Portfolio DV01
$45,000 per bp\"] --> B[\"Divide by CTD DV01
$78.50 per bp\"]\n B --> C[\"Multiply by CF
0.8215\"]\n C --> D[\"Contracts needed
471 contracts\"]\n E[\"Key adjustment:
CF translates CTD
risk into futures risk\"] --> C\n`\n\nWorked Example:\n\nPrestonburg Insurance holds a $500 million portfolio of investment-grade corporate bonds with a DV01 of $45,000 per basis point. They want to hedge duration risk using T-bond futures.\n\nCTD Bond: 4.375% coupon, maturing 2052\n- DV01 per $100,000 face: $78.50\n- Conversion factor: 0.8215\n\nStep 1: Raw contract count\nContracts = $45,000 / $78.50 = 573.25\n\nStep 2: Apply conversion factor\nAdjusted contracts = 573.25 x 0.8215 = 470.93 => 471 contracts\n\nStep 3: Verify the hedge\nFutures DV01 per contract = DV01_CTD / CF_CTD = $78.50 / 0.8215 = $95.56\nTotal futures DV01 = 471 x $95.56 = $45,009 (matches portfolio DV01)\n\nWhy the Conversion Factor Matters:\n\nWithout the CF adjustment, you would use 573 contracts and be over-hedged. The conversion factor scales the CTD bond's risk to the futures contract's standardized terms. Since the futures contract settles based on the CF-adjusted invoice price, the hedge must reflect this scaling.\n\nPractical Complications:\n\n1. Yield beta: Corporate bond yields may not move 1:1 with Treasury yields. A yield beta adjustment (typically 0.85-1.10) scales the hedge further\n2. CTD switches: If rates move enough to change the CTD, the futures DV01 shifts discontinuously\n3. Basis risk: The spread between the hedged instrument and Treasuries fluctuates independently\n4. Rebalancing: As rates move, DV01s change (convexity effect), requiring periodic hedge ratio updates\n\nAdjusted Formula with Yield Beta:\n\nContracts = (DV01_portfolio / DV01_CTD) x CF_CTD x Yield Beta\n\nIf Prestonburg estimates a 0.92 yield beta: 471 x 0.92 = 433 contracts\n\nDive deeper into DV01 hedging in our FRM Valuation and Risk Models section.