On Practice Question Hull 4.33:- @David Harper CFA FRM If Price % Decline of Portfolio A is less that is Risk/Exposure of Portfolio A is less, then shouldn't Convexity of Portfolio A be less than of that Portfolio B ..?
With respect to one above, for very small changes in yield, the convexity adjustment is not required as the majority of the change in price is explained by the first derivative
Delta B/(B) = - (1/B) * dB/dY *Delta Y where the Mac D is explained by -(1/P) *dP/dY
With respect to your second question, convexity smoothens out the price changes, as @David Harper CFA FRM likes to point out, convexity is a Bond Investor's friend both ways, so, if the price changes are less compared to a change in Yields, it implies that the convexity is more
Consider this, convexity is your curvature, if the curvature is more, say, (1/2)*c*(dY)^2 is more, the negative change in price to Yield effect is reduced. Therefore, if the Price decline is lower, the Convexity is higher
Thanks so much @QuantMan2318 - I see now the point I had missed ..
In this case though, since the Yield change was +ve, the Convexity Factor acted in the opposite direction to the Duration Factor and so Lower Price Decline meant Higher Convexity. But just to solidify my understanding, if the Yield Change was -ve, then the Duration Factor of the Price change would have been +ve and then in that case, the Convexity Factor would have increased the Price Change and so in case of a -ve Yield Change, Higher Price Change would mean Higher Convexity ...? I guess /hope that's what @David Harper CFA FRM means when he says Convexity can cut it both ways.. ??