I’m not sure where I read this in the notes but it confuses me: negative convexity in a CMBS security means that the price of the security doesn’t go up as fast as it goes down when there is change in interest rates. (I’m paraphrasing what I rememenber reading here) I undestand that the curve shows negative convexity which means duration isnt very good at predicting the change in value but the curve remains the same for an increase or decrease in interest rates so if rates where to go up 1% one month and back down 1% the other I would figure the value to be recaptured. Anyone care to explain?
Look at graph #3 on this site: http://www.investopedia.com/university/advancedbond/advancedbond6.asp that helped me (just a little bit…) to visualize the convexity issue for bonds with callable options.
Do you remember a picture of a callable bond? MBS has a very similar chart.
Duration is a linear measure, so any curve (positive or negative convexity) isn’t captured by duration. That is why it is only useful for small moves, as the “curve error” isn’t that big yet. Most bonds show positive convexity, which is a good thing. It means that the security price drops less for a rise in interest rates than it falls for an equal drop in rates. In the case of a CMBS the price doesn’t go up as fast as a tradtional bond showing positive convexity for a given drop in interest rates due to the embedded option in the bond. I think the key to seeing this is that in order for the change to be symmetric the line would graph would be straingt (and duration would capture all the move). To convince yourself of this draw the graph and plot a couple of moves (I had to last year). If you draw a postive convexity line you will see that it ALWAYS benefits you. Negative convexity is not good. I am not sure I am actually answering your question though because I don’t know exactly where you are having the problem. I hope this helps.
Sims If you want to keep simple, you just need to know as mwvt9 put it. The only reason that you got this negative convexity is because homeowner will excise the option when interest rate decline. Therefore, your increase will be less that what you will get from a treasury because this one has only positive convexity since it is not callable. One think you can do is buying future to incrrease you porfolio duration so that you can make more money and pay some good bonus:)
thanks guys. I read up some more and I found a good piece explaining the unwanted effect of negative convexity. For any of you interested here it is: http://www.tiff.org/TEF/glossary/convexity.html I was looking at it that if rate go from B to C and then from C to B then there are no effects but that is not the right way to look at things.
If you hold a bond without options, a decline in rates results in a increase in price slightly greater than the decline in price when rates rise. Now if your bond cash flows are made using mortgage payments, what’s going to happen? When rates fall the mortgage holders will start to refinance their mortgages and you will start receiving prepays, so the price increase isn’t what it would have been if you were holding an option free instrument and you’ll have to reinvest the cash flows at the prevailing lower rate. If rates rise prepays will stay at their normal level or may rise somewhat. So, thinking of it conceptually, as a bond holder you want rates to fall, but when rates do fall you get more prepays (less increase in MV) and that is negative convexity.
Bankin’ Wrote: ------------------------------------------------------- > If you hold a bond without options, a decline in > rates results in a increase in price slightly > greater than the decline in price when rates > rise. > > Now if your bond cash flows are made using > mortgage payments, what’s going to happen? When > rates fall the mortgage holders will start to > refinance their mortgages and you will start > receiving prepays, so the price increase isn’t > what it would have been if you were holding an > option free instrument and you’ll have to reinvest > the cash flows at the prevailing lower rate. If > rates rise prepays will stay at their normal level > or may rise somewhat. > > So, thinking of it conceptually, as a bond holder > you want rates to fall, but when rates do fall you > get more prepays (less increase in MV) and that is > negative convexity. Would it be right to say that the upside (rates go down) is curtailed by greater prepayments and that downside (rates go up) is exacerbated by extension risk?
Sims Wrote: ------------------------------------------------------- > Bankin’ Wrote: > -------------------------------------------------- > ----- > > If you hold a bond without options, a decline > in > > rates results in a increase in price slightly > > greater than the decline in price when rates > > rise. > > > > Now if your bond cash flows are made using > > mortgage payments, what’s going to happen? > When > > rates fall the mortgage holders will start to > > refinance their mortgages and you will start > > receiving prepays, so the price increase isn’t > > what it would have been if you were holding an > > option free instrument and you’ll have to > reinvest > > the cash flows at the prevailing lower rate. > If > > rates rise prepays will stay at their normal > level > > or may rise somewhat. > > > > So, thinking of it conceptually, as a bond > holder > > you want rates to fall, but when rates do fall > you > > get more prepays (less increase in MV) and that > is > > negative convexity. > > > Would it be right to say that the upside (rates go > down) is curtailed by greater prepayments and that > downside (rates go up) is exacerbated by extension > risk? The first part is correct. I agree with the second part, because if rates went up by 500 bps overnight people would be more reluctant to move, but I believe that Schweser’s notes say that when rates go up they behave normally. I don’t have my notes to confirm this, so I could be wrong, but I think for test purposes they behave normally in up scenarios and display negative convexity in down.