Our review of hedge fund trading strategies continues with a discussion of yield-curve arbitrage (YCA), a form of fixed income arbitrage. I have previously written about the yield curve, convexity, and duration. Recall that for bonds not offering embedded features (such as puts and calls), a bond’s price and the interest yield move in contrary directions, giving an inverse association involving duration and yield. Higher yields mean shorter durations. The $duration of a bond is product of the duration and the price (value); with units of dollar-years, it reflects duration changes in dollars rather than in percentages.
A parallel shift in a yield curve occurs when the yield on all maturities change by the same amount. More likely are changes in which the spread between short and long maturities increase (steepen) or decrease (flatten). A dumbbell portfolio is loaded up on bonds at the short and long ends of the yield curve; conversely, a bullet strategy involves the purchase of intermediate-maturity bonds. Yield-curve arbitrage is a trading strategy in which a trader exploits relative mispricings along the yield curve due to high institutional demand for selected maturities, among other reasons.
A well-known form of YCA is the so-called butterfly trade: long dumbbells (the “wings” of the butterfly) and short bullets (the butterfly’s “body’) in a net-zero $duration spread trade. For example, you might set up a portfolio in which you are long 4-year and 8-year maturities, and short 6-year maturities. Small parallel moves in the yield curve would have little effect on this portfolio, since it has a net $duration of zero. However, large parallel moves in either direction will guarantee a positive return due to the positive convexity (yield vs. price) of the portfolio – in effect, one expects greater convexity in the wings than in the body. That sounds good in theory; in practice, yield curves usually experience complex movement patterns that can have an unexpected affect on the outcome of a butterfly trade.
There are four popular types of butterfly trades:
- Cash and $duration neutral weighting – No cash is needed up front, since the cost of the long positions is offset by the proceeds from the short sale. Suitable prime brokerage structures are available such that the long position acts as collateral for the short position, so that zero cash flow is required initially. This strategy benefits from a flattening of the yield curve, because most of the $duration is in the wings of the butterfly.
- Fifty-fifty weighting regression – The trade is structured such that each wing of the butterfly has equal $duration. This strategy benefits from small changes to the yield curve, because the body is less convex than the wings. The position profits from a steepening of the yield curve. Note that this trade is not cash neutral, so return must exceed the cost of carry.
- Regression weighting – A sophisticated trade in which the linear regression measuring the spread between the short wing and the body is regressed against the spread between the body and the long wing. The more-volatile short wing is more likely to move away from the body than is the long wing. So, say for example we determine a regression coefficient of 0.5; it means that a 20 basis-point change in the short wing spread would imply a 10 basis-point move in the long wing spread. Since most of the $duration is in the long wing of the spread, the strategy benefits from a flattening of the yield curve.
- Maturity weighting – The relative maturities of the three components (short wing, body, and long wing) are used as the weighting of each component. The results of this strategy are very similar to the regression weighting scenario, except that the weighting factor will generally be higher than the regression coefficient.
There are calculated risk measures that can be used by traders to determine whether the spread on each of the butterfly strategies is attractive and invites investment. Advanced readers can look up the model developed by Nelson and Siegel to see how to partially hedge the risk exposures of different butterfly spreads.
Next time, we’ll continue our survey of fixed income arbitrage by taking a close look at basis trading.
 Nelson, C.R., and Siegel A.F., (1987) “Parsimonious Modeling of Yield Curves”, Journal of Business,
60 (4), , p.473-489.
Based in Chicago, Eric Bank has been writing business-related articles since 1985, and science articles since 2010. His articles appear on eHow and on numerous other websites. He holds a B.S. in biology and an M.B.A. from New York University. He also holds an M.S. in finance from DePaul University.