Negative Butterfly

What Is a Negative Butterfly?

A negative butterfly is a non-parallel shift in the yield curve where long and short-term yields fall more, or rise less, than intermediate rates.

A negative butterfly shift effectively humps the plot of the yield curve. The opposite of a negative butterfly, where long and short-term yields rise more, or fall less, than intermediate rates, is called a positive butterfly.

Understanding a Negative Butterfly

Yield curves are graphic displays of the interest rates of similar-quality bonds relative to their maturity dates. Yield curves do not attempt to predict the future of bond rates, but the relative position of current rates can help investors make decisions about which bonds are likely to pay off best in the future. They are used to illustrate investor sentiments about the value of various bond maturities.

The most common yield curve plots the yields of U.S. Treasuries (short-, medium-, and long-term bonds). Usually, the Treasury yield curve presents a rising arc from left to right, with short-term bonds on the left yielding less than medium-term bonds in the center and long-term bonds on the right. This is because investors generally expect a higher yield as they are lending their money for more extended periods of time.

The reasons for yield curve shifts are complicated and depend on investor sentiment, economic news, and Federal Reserve policy, among other factors. However, bond yields don’t always follow standard rules. For example, short- and long-term rates could decrease by 75 basis points (0.75), while intermediate rates only decrease by 50 basis points, (0.50). The resulting hump in the center of the graph is a negative butterfly shift. The reverse is a positive butterfly (where the graph looks U-shaped).

From a bond trading perspective, why it happens is less important than what to do about it. Most importantly, butterfly shifts present traders with arbitrage opportunities, since the rate variances can be marketed to maximize short-term profit. A common bond trading refrain when the yield curve becomes a negative butterfly is to sell the belly and purchase the wings, which means to sell the higher-rate intermediate bonds — or the belly of the butterfly — and acquire the short- and long-term bonds (which are the outside low-hanging wings of the butterfly in the graphic model). In this way, traders attempt to even out their exposure to bond maturities that are shifting out of parallel. In reality, bond traders will factor in many variables when strategizing buy and sell orders, including the average maturity date of bonds in their portfolio — although the shape of the yield curve is an important indicator.

Negative Butterfly vs. Positive Butterfly

A negative butterfly occurs when short-term interest rates and long-term interest rates decrease by a greater degree than intermediate-term interest rates, accentuating the hump in the curve.

On the other hand, a positive butterfly occurs when short-term interest rates and long-term interest rates increase at a higher rate than intermediate-term rates. This creates a non-parallel shift in the curve, making the curve less humped (or less curved). For example, assume that the yields on 1-year Treasury bills move upward by 100 basis points. For example, assume the yields on 1-year Treasury bills and 30-year Treasury bonds move upward by 50 basis points (0.50%). The yields of 30-year Treasury bonds also move upward by 50 basis points (0.50%). Suppose that during this same time period, the rate of 10-year Treasury notes remained the same; the convexity of the yield curve would increase, creating a positive butterfly.