What is a required condition for a butterfly designed to lower convexity?

A butterfly spread is a strategy that involves the use of multiple bonds or options to create a position that benefits from changes in the yield curve while mitigating risk, particularly in terms of convexity. To specifically lower convexity, one essential condition is stable interest rates or a steepening yield curve.

When interest rates are stable, the price of a bond or a series of bonds tends to be more predictable, which allows for the creation of a butterfly structure that can effectively limit exposure to interest rate movements. A steepening yield curve can enhance the effectiveness of this strategy by allowing the investor to capitalize on movements between varying maturities without significantly increasing exposure to convexity risk. In other words, if the yield curve steepens, it suggests that short-term rates may decrease or remain stable while long-term rates increase, enabling the butterfly position to potentially profit as it reduces exposure to price volatility associated with larger shifts in interest rates.

The other conditions mentioned do not align as well with the objective of reducing convexity. Churning interest rates can lead to increased uncertainty and price volatility, which would counteract the benefits of implementing a butterfly spread. Rate volatility typically increases convexity, making it contrary to the goal of minimizing it. Long-maturity bonds only would not inherently accomplish