Positive Butterfly

A positive butterfly is a non-parallel yield curve shift in which short- and long-term rates shift upward by a greater magnitude than medium term rates. This yield curve shift effectively decreases the curvature of the curve.

The yield curve is a graph that plots the yields of similar-quality bonds against their maturities, ranging from shortest to longest. The yield curve shows the yields of bonds with maturities ranging from 3 months to 30 years and, thus, enables investors at a quick glance to compare the yields offered by short-term, medium-term and long-term bonds. The short end of the yield curve based on short-term interest rates is determined by expectations for the Federal Reserve policy; it rises when the Fed is expected to raise rates and falls when interest rates are expected to be cut. The long end of the yield curve is influenced by factors such as the outlook on inflation, investor demand and supply, economic growth, institutional investors trading large blocks of fixed-income securities, etc.

In a normal interest rate environment, the curve slopes upward from left to right, indicating a normal yield curve. However, the yield curve changes when prevailing interest rates in the markets change. When the yields on bonds change by the same magnitude across maturities, we call the change a parallel shift. When the yields change in different magnitudes across maturities, the resulting change in the curve is a non-parallel shift. A non-parallel change in interest rates may lead to a negative or positive butterfly, which are terms used to describe the shape of the curve after it shifts. The connotation of a butterfly is given because the intermediate maturity sector is likened to the body of the butterfly and the short maturity and long maturity sectors are viewed as the wings of the butterfly.

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

A positive butterfly occurs when short-term and long-term interest rates increase at a higher rate than intermediate-term rates. To put this another way, medium-term rates increase at a lesser rate than short- and long-term rates, causing a non-parallel shift in the curve that makes the curve less humped, that is, less curved. For example, assume the yields on 1-year Treasury bills and 30-year Treasury bonds move upward by 100 basis points (1%). If during the same period, the rate of 10-year Treasury notes remains the same, the convexity of the yield curve will increase.