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Scaling Bond-Futures Hedge Ratios with CTD DV01 and Conversion Factor

Article Quant Q&A · Author: Flash7
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Summary

The question concerns estimating a hedge ratio between daily changes in a swap fixed rate and changes in a bond-futures forward yield. Since the swap maturity stays constant while the cheapest-to-deliver bond ages, the underlying risk exposures can drift over time and complicate a regression-based hedge estimate.

The response suggests approximating the futures contract’s DV01 using the cheapest-to-deliver bond’s DV01 divided by its conversion factor. A more refined proxy would use the forward DV01 of the bond as of delivery, again adjusted by the conversion factor. These measures offer a way to account for changing interest-rate sensitivity when constructing or interpreting the regression. The answer assumes that delivery-switch options and related effects are outside the problem; it gives no regression specification, data window, or empirical comparison of the proxies.

Key ideas

  • A swap and a bond future can have changing relative rate sensitivities as the cheapest-to-deliver bond ages.
  • A basic futures DV01 proxy divides the cheapest-to-deliver bond DV01 by its conversion factor.
  • A more refined proxy uses the bond’s forward DV01 at delivery, adjusted by the conversion factor.
  • Delivery-switch options and other related effects are excluded from the suggested approximation.

Tags

Fixed incomeFuturesRisk management
Full text
# Regression swap vs bond future


# Regression swap vs bond future












I have to perform a regression to get an hedge ratio. The dependent variable is the change on day of a swap fixed rate (f.i. 10y) and the independent variable is the change on day of a bond future forward yield (f.i. Bund). How to account for the time decay of the bond? As days pass by, the 10y swap has the same maturity, but the CTD of the bond future has a lower time to maturity.

## Answer by user68819 (score 1)

https://quant.stackexchange.com/a/79460

You can proxy the dv01 of a bond fut as dv01 of ctd / CF of ctd. Fancier if dv01 of fwd ctd (as of delivery) / CF.

Given your question, I'd assume you aren't thinking about switch options etc.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.