Butterfly trades are so named because of a vague resemblance between certain concentrations of bond holdings along the yield curve and parts of a butterfly. A "dumbbell" portfolio has a concentration of long- and short-maturity bonds while holding fewer bonds of intermediate maturity. The dumbbell forms the "wings" of the butterfly. A "bullet" portfolio is the opposite -- heavily weighted in intermediate-maturity bonds -- and the bullet forms the butterfly's "body." A trader enters a long butterfly trade by buying the wings and shorting the body.
Profits and losses from butterfly trades depend on how the yield curve changes shape over time and on whether the shape change is uniform throughout all maturities or affects certain maturities more than it does others -- in part due to the bonds' durations. The duration of a bond is, roughly speaking, its payback period. Higher yielding bonds have shorter durations because you receive more interest than you would with a low-yielding bond. A bond's duration decreases as its maturity date approaches, so short-term bonds have lower durations. A bond's "$duration" is the product of its price and its duration, expressed in dollar-years.
A bond trader can calculate her portfolio's $duration at any time. Butterfly fixed-income trades often involve the simultaneous buying and shorting of bonds of different maturities, such that net change to the portfolio's $duration is zero. The profit potential of such trades rests in part on the portfolio's "convexity," which is the U-shaped relationship you get when you plot bond prices against their yields. For example, imagine two bonds having the same duration and yield, and that interest rates suddenly change. The price of the bond with greater convexity will be less affected by interest rate changes than will the less convex bond. A butterfly strategy can exploit this difference, because intermediate-term bonds are less convex than are either long-term or short-term bonds.
In a simple example of a butterfly trade, a bond trader might load up on bonds with maturities of four and eight years -- the butterfly's wings -- and short the six-year bonds, which constitute the butterfly's body. Furthermore, the trader buys and shorts bonds such that the portfolio's total $duration doesn't change because of the trades. A characteristic of this strategy is that the wings are more convex than the body. The trade requires no upfront cash, since the proceeds from the shorted bonds offset the cost of the purchased bonds. If the long-term bond yields drop, the yield curve "flattens" -- the yield difference between long-term and short-term bonds decreases -- the butterfly trade will score a profit because the bond prices of the more-convex wings will increase more than those of the less-convex body.
Many variations on the butterfly exist, allowing traders to profit from a steepening, flattening or unchanging yield curve. Each strategy also carries its own risks, but generally, if the yield curve defies a butterfly trader's expectations, losses will result. Traders can partially hedge their butterfly trade risks with other, offsetting trades.