Just after a hand on this one:- how do interest rate changes negatively affect duration on mortgage securities, ie. why does duration shorten when rates fall and lenghten when rates rise for mortgage securities?
when rates fall - the prepayment option that the issuer has sold the investor on the MBS is exercised (or has more chances of being exercised) - and once that happens - the entire principal gets repaid to the issuer - and mortgage gets refinanced.
hence duration falls when rates fall.
When rates rise - there is much less chance of the prepayment option being exercised. price drops on the MBS but not as much as on a regular treasury security. So the duration of the MBS rises (when compared to a regular t-bond) when rates rise.
Not sure if I am missing sth.
This happens only for low interest rates: when the prepayment option is in the money. It’s the region where the mortgage has negative convexity. If you draw a price vs. yield graph for a mortgage you’ll see it immediately: think of the duration as the (negative of) slope of the curve.
(Yes: I know that duration isn’t the (negative of the) slope of that curve, but for visualization it works quite well. Duration is the (negative of the) slope of the ln(price) vs. yield curve, but who’s really counting here?)
Try visualising the price vs yield curve for mortgage securities.
The LHS exhibits negative convexity where price increase is capped due to the embedded call option. Thus the amount of price increase (change) reduces per unit of yield change. Thus compared to an otherwise non callable bond, the duration of the mortgage security is shorter because of lesser interest rate sensitivity.
As the curve moves from LHS to RHS, it starts to behave more like a non callable bond (positive convexity). Thus for thta reason the duration increases as it becomes more sensitive to interest rates changes.
And lastly at the RHS, a mortgage security will be expected to behave like a non callable bond.
Draw a picture.