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I'm doing a study at Rutgers on the TUT spread. The TUT spread is composed of 2 2-year treasuries and 1 10-year treasury per spread. I was trying to estimate the historical volatility of the spread, and only have historical volatility of each product individually.

Would the spread volatility just be the sum of the spread's components (ie. 10 year treasury has 3% historical volatility and 2 year treasury has 4% volatility, each spread volatility would be 3%+3%+4%?) not accounting for correlation

Also would the contract multiplier be calculated in the same way (10 year future $100,000 + $200,000 + $200,000?

Thank you!

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  • $\begingroup$ you'd need to account for correlation I think $\endgroup$
    – rubikscube09
    Apr 14, 2022 at 17:46
  • $\begingroup$ I ran correlation back, and they're so correlated that they're pretty much the same product. the only difference is the return when the fed hikes rates and the 2 year outperforms the 10 year (if you're short) $\endgroup$
    – JamieC113
    Apr 14, 2022 at 17:48
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    $\begingroup$ Right, so $\mathrm{Var}(X - Y) = \mathrm{Var}(X) + \mathrm{Var}(Y) - 2 \mathrm{Cov}(X,Y)$, and in this case because $X,Y$ are strongly correlated (as you surmised), the variance of the spread will be lower than the sum of their variances (fluctuations in one cancel out fluctuations in the other). $\endgroup$
    – rubikscube09
    Apr 14, 2022 at 18:14
  • $\begingroup$ That makes sense! I was thinking that that was a possible outcome, too. So the spread volatility should be 2*2 year volatility - 1*10 year volatility $\endgroup$
    – JamieC113
    Apr 14, 2022 at 18:53
  • $\begingroup$ @rubikscube09 also, the contract's notional size should be calculated in the same way right? $\endgroup$
    – JamieC113
    Apr 14, 2022 at 20:53

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