How do you construct a cross-hedge using T-note futures for a corporate bond portfolio, and what are the main sources of basis risk?

Cross-hedging a corporate bond portfolio with Treasury futures introduces basis risk because the hedge instrument (Treasuries) and the hedged asset (corporates) have imperfectly correlated yield movements. The hedge ratio must be adjusted for this correlation, typically through a yield beta or regression-based approach.\n\nYield Beta Adjustment:\n\nThe yield beta measures how much corporate yields move per unit change in Treasury yields:\n\nYield Beta (b) = Delta(Corporate Yield) / Delta(Treasury Yield)\n\nAdjusted hedge ratio:\nN = (DV01_portfolio / DV01_futures) x b\n\n`mermaid\ngraph TD\n A[\"Corporate Bond Portfolio
DV01 = $125,000/bp\"] --> B[\"Unadjusted hedge
1,601 contracts\"]\n A --> C[\"Regression analysis
Yield beta = 1.15\"]\n C --> D[\"Adjusted hedge
1,841 contracts\"]\n B --> E[\"Under-hedged if
credit spreads widen
with Treasury rally\"]\n D --> F[\"Better hedge for
parallel rate moves\"]\n F --> G[\"Still exposed to
spread-specific risk\"]\n style G fill:#ff6b6b\n`\n\nWorked Example:\n\nLaurelton Capital holds $350 million in BBB corporate bonds:\n- Portfolio DV01: $125,000 per bp\n- 10-year T-note futures DV01: $78.10 per contract\n- Regression of corporate yield changes on Treasury yield changes (36 months):\n - Yield beta: 1.15\n - R-squared: 0.82\n\nUnadjusted contracts: $125,000 / $78.10 = 1,601\nBeta-adjusted contracts: 1,601 x 1.15 = 1,841 contracts\n\nThe extra 240 contracts account for the historical tendency of BBB yields to move more than Treasury yields (spread widening during selloffs, tightening during rallies).\n\nSources of Basis Risk:\n\n1. Credit spread changes: The largest source. If BBB spreads widen 30 bps while Treasuries are unchanged, the portfolio loses but the hedge gains nothing. Unhedgeable with Treasuries alone.\n\n2. Yield beta instability: The 1.15 beta was estimated from historical data and may shift. During stress periods, beta can spike to 1.5+ as corporates sell off relative to Treasuries (flight-to-quality).\n\n3. Curve exposure: If the portfolio has a different maturity distribution than the 10-year futures, non-parallel curve shifts create residual exposure.\n\n4. Sector effects: BBB industrials, utilities, and financials can have very different spread dynamics. A blended beta may not fit any single sector well.\n\nR-Squared Interpretation:\n\nThe R-squared of 0.82 means Treasury yield changes explain 82% of corporate yield variance. The remaining 18% is idiosyncratic spread risk that cannot be hedged with Treasuries. For a pure rate hedge, this is acceptable. For total return hedging, credit default swap (CDS) protection or credit index hedges are needed.\n\nLearn more about cross-hedging strategies in our FRM materials.