SoA6, Mortgage Negative Convexity

[OT]

SoA6, Negative Convexity
HBOFIS, Ch 24, Mortgages and Overview of Mortgage-Backed Securities,
Pre-payment Risk,

“The investor in a mortgage is exposed to negative convexity when interest rates decline below the loan’s contract rate.” from page 561.

What do they mean that the investor is exposed to negative convexity? I am thinking that the x-axis is interest rates and y-axis is value of security/mortgage. As environmental interest rates decline, the value of the security/mortgage goes up until it (environmental interest rates ) reaches the mortgage interest/contract rate. From this point the change in value takes on a negative convexity (as interest rates decrease) -- not necessarily negative slope, though -- because the it will likely be called/prepaid at par.

Any comments or questions would be greatly appreciated.

<font size=-1>[ This Message was edited by: OT on 2001-12-27 16:32 ]</font>

[MetsMan]

Remember that the actual slope is an indication of the duration and that it is the rate of change of the slope that indicates the convexity.

[Exam Slave]

You describe it well.

As you state, the investor is exposed to negative convexity when the prepayment option is "in the money." He is not when the option is "out of the money."

Back to the cotton fields.

[Enough Exams Already]

Convexity is also a measure of rate of change of duration. As environmental in terest rates decrease past the mortgage contract rate, prepayment becomes more likely since people have a good reason to refinance. That decreases the average number of years before a dollar of the mortgage is repaid. Thus the duration shrinks as market interest rates drop below the mortgage rate. Hence the mortgage shows negative convexity.

Hope this helps, OT.

[Brad Spirrison]

The simple mathematical explanation of negative convexity is a change in the curvature of the Price (y axis) vs. interest rate (x axis) curve. If convecity is positive, the slope of the curve will continue getting steeper as interest rates drop (bigger change in price). However, if a call option exists (or refinancing which is essentially the same thing) then the curve will have an inflection point (where convexity = 0) and then it will asymptotically approach the call price, with its slope getting flatter as the interest rate drops.

[OT]

“investor is exposed to negative convexity when the prepayment option is ‘in the money.’” By Exam Slave.

That’s right – now I remember. The option, in this case call option, is “in the money” when it is worth being used. In this case, it is basically when the environmental interest rates are below mortgage contract rates.

“However, if a call option exists (or refinancing which is essentially the same thing) then the curve will have an inflection point (where convexity = 0) and then it will asymptotically approach the call price, with its slope getting flatter as the interest rate drops.” By Tigernet.

Now I remember this also. I was thinking there was some kind of trend or behavior of the yield curve on the left of the inflection point.

Great thread so far, don't you think. Good luck to all of you. Much thanks to all of you and -- so as to seem to not close the thread -- to future posters.


<font size=-1>[ This Message was edited by: OT on 2001-12-28 14:15 ]</font>