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This the 3rd in a series of butterfly swaps.

  1. Cash & Duration Neutral Butterfly (aka Duration-Hedged Barbell)
  2. Fifty-Fifty Butterfly Swap
  3. Regression Weighted Butterfly Swap
  4. Maturity Weighted Butterfly Swap

Note: Although this type of swap shows positive convexity at changes of + or – 25 basis points, it does not necessary display positive convexity for smaller yield changes.

Typically, short-term interest rates tend to move faster than long-term rates. In order to adapt the butterfly weightings to compensate for this, a regression coefficient is needed. On the sheet called coefficient, I calculated the spreads between the Body minus the short Wing and the long Wing minus the Body on a daily basis over the last 5 years. Then with Excel’s built in regression analysis, I calculated the coefficient between the two spreads.

Then using the formula below, I calculated the new weightings of the two Wings. An advantage of the regression weighting, rather than the fifty-fifty ( both of which are not cash neutral) is that the initial cost of the swap can be reduced. Using my default bond data, the fifty-fifty swap required borrowing $4,790,064, while the regression weighted swap required only $3,657,847.

If the number one is substituted for the calculated coefficient, the weighting become the same as the fifty-fifty butterfly swap.

Like other swaps in this series, instantaneous parallel shifts, either up or down, will show a profit (positive convexity).

Download: Fifty-Fifty-R.xlsx


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