Hedging Bond Portfolios with Multiple Treasury Futures
Summary
The document considers how to hedge a government bond portfolio using available short- and long-maturity futures. It cautions that a single quoted risk measure or maturity match is not enough to determine an effective blend: DV01 is nonlinear, and duration and DV01 are distinct objectives. The desired hedge also depends on how the portfolio is weighted and whether the goal is risk reduction or return replication.
Suggested approaches include regressing portfolio returns on tradable factors or directly on futures, then using estimated betas to set hedge weights. Another approach fits the yield curve and combines bonds to approximate the portfolio's weighted average life. Alternatively, the portfolio's DV01 can be split into maturity buckets and hedged with the corresponding futures contracts. These are alternatives rather than a worked solution; the excerpt provides no calculations or comparative performance evidence, and stresses that the appropriate method depends on the hedge objective and portfolio details.
Key ideas
- A futures hedge should reflect the chosen objective, such as matching duration, matching DV01, or replicating returns.
- DV01 is nonlinear, so a simple maturity-based blend may not capture portfolio risk.
- Return regressions on tradable factors or futures can be used to estimate hedge weights.
- Yield-curve fitting and maturity-bucket DV01 hedging are alternative construction methods.
- Portfolio weighting and available instrument details affect the hedge design.
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Full text
# How do I derive a blend of a 3Y future and 10Y future risk? # How do I derive a blend of a 3Y future and 10Y future risk? So I have a portfolio of Govt. bonds that I'm trying to hedge with futures. Let's take one of the bonds out of the portfolio as an example. In bloomberg, every bond and its future counterparts has a "Risk" rating. There are only 2 futures available, a 3Y and a 10Y. Bond A - maturity 08/01/23 - has a risk rating of "4.278" Future 3Y - Risk Rating of "2.42" Future 10Y - Risk Rating of "10.66" How do I get to a maturity-matched blend of the risk rating for the futures available? I want the correlation of the bond returns and the blended future returns to be high. TIA ## Answer by jason m (score 1, accepted) https://quant.stackexchange.com/a/47473 DV01 is non-linear. There are a few ways you could do this: - Regress your bond portfolio returns (if long enough, if not synthetically extend back using current weights and the returns on those assets) on factors that you can trade. Eg: Mkt (S&P 500), Credit (Some tradeable index via etf or other source), ..., etc Trade the weighted combination of those factors to hedge your exposure - Construct a yield curve fit via some interpolation that "makes sense" This may require some solving for parameters Compute the weighted combination of the two bonds that gets you to a reasonable weighted average life that approximates your portfolio risk - Do the same regression approach above, but on the futures themselves The beta on these respective futures will be your portfolio weight. ## Answer by David Duarte (score 1) https://quant.stackexchange.com/a/50938 You could decompose the portfolio dv01 by buckets (corresponding to the available futures) and hedge each bucket with the appropriate number of contracts. ## Answer by HF_douche (score 0) https://quant.stackexchange.com/a/46944 Im not sure what objective is? -Do you just want to have the same average duration or the same average DV01? These are not the same thing - If you want to replicate the returns of a basketbof bonds, how are you weighting them? Equal notional or equal $ volatility or something else (market cap for instance) Need more info
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