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Weighting the trades, and weighting and interpreting their yield spreads.
Investors who want to sell rich securities or buy cheap securities and maintain their portfolio durations often employ butterfly trades. A butterfly trade typically uses three securities of different durations. The shortest- and longest-duration instruments are the wings; the middle-duration instrument is the body. Investors can, of course, buy and sell multiple issues that net out to constant duration.
Much of what comes easily in considering these trades is misleading. Consequently, butterfly trade structures and their yield spreads are often misunderstood. Our objective is to explain some of the hazards.
BUTTERFLY TRADE WEIGHTING
There are multiple ways to weight (or structure) butterfly trades. Three common weighting schemes are cash- and duration-neutral, fifty-fifty, and regression. We detail the relative merits of each.
Cash- and Duration-Neutral Weighting
Cash- and duration-neutral weighting is often employed by "real money" accounts - pension funds, insurance companies, central banks. Such accounts often want to swap out of one bond into two others, keeping their durations constant, and without putting up or taking out cash, because they keep little or no cash and do not use borrowed funds.1
For example, suppose we want to look at a cashand duration-neutral butterfly of 5s/1 Os/30s. Further suppose the values as in Exhibit 1.2
To decide how much market value of each wing we need to structure a cash- and duration-neutral butterfly correctly, we need to solve two equations:
The market value of the 10s is $10,304,460 ($10 million par times a fill price of 103.0446%). Market value of the 5s is 0.6631 x $10,304,460 = $6,832,887, and the market value of the bonds is $3,471,573.
The par values of 5s and 30s are $6,832,887/ 101.6857 = $6,719,615 and $3,471,573/100.8351 $3,442,822, respectively (to be rounded). Are the durations matched?
The wings have $6,832,887 x 4.201 + $3,471,573 x 13.178 = 74,453,347 duration dollars compared with the body, which has $10,304,460 x 7.225 = 74,449,724 duration dollars. The values differ only because of rounding at intermediate steps. Consequently, with equal duration dollars and equal market values, we have devised a cash- and duration-neutral butterfly.
Fifty-Fifty Weighting
The second way to weight a butterfly trade is to place 50% of the duration dollars in each wing.4...