Sandeep,

The logic is this. Convexity can also be thought of as the propensity for the DURATION of a bond to change when INTEREST RATES change.

So, when interest rates go down, you would wish to have longer duration bonds (because they'll experience more price appreciation.) A bond with high positive convexity will indeed tend to increase in duration when interest rates decrease. So that's better for you.

A bond with negative convexity will DECREASE in duration as interest rates go down -- exactly the opposite of what you want. Therefore you get a worse price return.

What's really happening here is that the expected cash flows of the negatively convex bond change as interest rates go down (either through principal prepayment or calls.) That's why the duration decreases.

On the other side of the coin, negatively convex bonds INCREASE in duration when yields go up. So that's bad compared to positively convex bonds.