Which shape represents positive convexity in finance?

Positive convexity in finance is represented by a "valley" shape. This shape indicates that as interest rates decrease, the price of a bond increases at an increasing rate, and vice versa for interest rate increases. This behavior is crucial for understanding the risk and return dynamics of fixed-income securities.

The reason a valley shape signifies positive convexity lies in the curvature of the bond's price-yield relationship. In this context, positive convexity suggests that the bond's price is more sensitive to decreases in interest rates than to increases, which is an advantageous characteristic for bondholders. It reduces the potential for losses when interest rates rise while allowing for greater gains when rates fall.

In contrast, a hill shape would imply negative convexity, where price sensitivity diminishes with falling interest rates. A flat shape would suggest no convexity, indicating a linear relationship between price and yield, which does not capture the complexities of interest rate risk effectively. A plateau area indicates a lack of responsiveness to interest rate changes, which is not indicative of positive convexity.