How do I derive a blend of a 3Y future and 10Y future risk?

Question

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 1

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 2

You could decompose the portfolio dv01 by buckets (corresponding to the available futures) and hedge each bucket with the appropriate number of contracts.

Answer 3

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