# Positive Convexity ?

It was my understanding that positive convexity would be noticeable or would manifest when prices are above par, and/or the yield on the FI security is below market yields which would encourage prepayment (or call option execution) and would shift away from the typical negative convexity curve to the positive backward bending positive convexity curve on a price-yield graph; while if the price is below par and the yield is greater than the market yield, then the FI security will behave more like a typical bullet and exhibit negative convexity. A little help deciphering this question and my logic??? ---- A mortgage security is most likely to exhibit positive convexity if: A) the price is below par. B) the yield curve has a parallel downward shift. C) the price is above par. Your answer: C was incorrect. The correct answer was A) the price is below par. If the price is below par, the market yield must be higher than the yield on the underlying mortgages, and the prepayment rate will be lower. This means the instrument is more likely to exhibit positive convexity.

Yield vs interest rate trade-off. If interest goes sky high, mortgage securities are less likely to be prepaid so the call option is almost zero. That means positive convexity. Now with interest rates higher than the rate on the mortgage security, you can expect the price to be below par. So A.

Sorry, but this still doesn’t make sense to me…If interest rates go sky high and the call option becomes essentially worthless as you described, doesn’t that mean we are on the far right of the price-yield curve indicating negative convexity?? What am I not understanding here??

The far right of the Price/Yield curve would be positive convexity. Think about the Price/Yield curve for a regular coupon bond as compared to the mortgage sec. The right side of the curve is identical for each (postive convexity). The left side bends towards the call price for the MBS indicating negative convexity.

I think I may be an idiot…I think I just misinterpreted the two! The de-facto standard on a bond is positive convexity, implying an add-on to the duration estimate which is a linear interpolation and requires a greater add-on as the change in yield (pos or neg) increases. With the call option or prepayment introduced, the backward bending on the left side of the price-yield curve leads to negative convexity…I am moron. Not sure how I got into the trance of thinking the norm was negative convexity…Damn Dec Mullarkey and his boring teachings!

ebiegs327, Look at the price yield curve for the MBS. you can see that it will have positive convexity if yield > coupon. If yield > coupon, price is below par.

I have one question - is the par always equal to the coupon rate? Because my understanding is where yield is below the coupon rate, the callable bond/ MBS would be most likely to exhibit negative convexity due to the incentive to refinance at a lower rate.

Yes. If market rates are at issue rates then the bond will be discounted by the same rate that it is paying. That means it will be trading for par or 1000.

mwvt9 Wrote: ------------------------------------------------------- > Yes. If market rates are at issue rates then the > bond will be discounted by the same rate that it > is paying. That means it will be trading for par > or 1000. Thanks mwvt9.