Wat is Effective duration, negative convexity?

The effective duration of a security whose cash flows depend on rates is $(P_- - P_+)/(2P\,\Delta y)$, where $P_\pm$ are its prices after shifting rates by $\pm\Delta y$ and re-running the model of its cash flows. A security has negative convexity over a range of rates when its effective duration falls as rates fall: its price rises less than it falls for equal moves.