Negative convexity Callable bonds

The price volatility characteristic of a callable bond is important to understand. The characteristic of a callable bond—that its price appreciation is less than its price decline when rates change by a large number of basis points—is referred to as negative convexity. But notice from Exhibit 4.16 that callable bonds do not exhibit this characteristic at every yield level. When yields are high (relative to the issue s coupon... 

EXHBIT 4.17 Negative Convexity Region of the Price/Yield Relationship for a Callable Bond... 

The convexity measure increases with the square of maturity it decreases as both coupon and yield rise. It is a function of modified duration, so index-linked bonds, which have greater duration than conventional bonds of similar maturities, also have greater convexity. For a conventional vanilla bond, convexity is almost always positive. Negative convexity occurs most frequently with callable bonds. 

---