Prepayment Risk

Schweser Says: Book 3 Pg 116 Prepayment risk is the cause of the negative convexity, which means the mortgage** security loses more from a given increase in yield than it gains from a corresponding **decrease in yield. This doesnt dseem to be correct. This is correct only for security that has -ve convexity all along while mtgg securities have both +ve and -ve convexity somewhere on the curve or the other. Can someone confirm this?

It sounds like they are only describing the left portion of the curve where it displays the negative convexity.

In such a case, we cant say with precision if loss for given yiled increase will be more than gain for a yield decrease, dont you think?

The statement you quoted is correct, because the bolded portion only applies to when the security is displaying negative convexity. At higher interest rates where it has positive convexity, then the bolded portion will not apply as you suggested.

Yeah, the bold part appears to be describing “negative convexity”, not mortgage securities. The sentence is a bit confusing, but it looks correct once you look at it.

We can because that portion of the curve is displaying negative convexity. Those are the properties of negative convexity.

As interest rates rise further and the curve no longer displays negative convexity then the opposite would hold true. I believe the statement is saying: WHERE the mtg security displays negative convexity, the bond will have lower gains for rate decreases than the losses incurred if rates had increased (but only for the portion of the curve that displays negative convexity).