So after completing reading #26, I understand the impact options (particularly call options in this case) can have on price changes in response to changing interest rates. Due to the negative convexity caused by the option, price on a callable bond will increase less to falling rates and decrease more to rising rates then a comparable noncallable bond (assuming rates below coupon -obviously doesn’t really matter if well above the coupon).
However on page 61 of Schweswer, it says callable bonds will OUTPERFORM noncallable bonds when rates increase bc, it says, the negative convexity makes callable bonds respond less to higher rates and thus decrease in value less.
what nuance am I missing, don’t these contradict each other! I agree with the first statement bc with high rates there are fewer prepayments and thus duration increases causing greater sensitivity, therefore greater price declines!
Please refer to page 152 Volume 4, first paragraph . Mortgage securities display positive convexity which is usual in bonds when rates rise beyond (see page 154 first paragrpah also) . Treasuries decrease more to rising rates while MBS decrease less to rising rates. This is because of the compensation ( premium ) received by investors implicitly for the prepayment call option
So are you referring to the positive convexity side of the yield-price graph? That is, when rates are already above the coupon rate and an MBS acts like a noncallable bond?
The book says an MBS increases less to rate decreases and decreases more to rate increases - is this only true when rates are fluctuating and they’re well below the coupon - that is, on the negative convexity side of the yield-prie curve?
Value of callable bond = Value of Treasury - Value of call option
When the interest rates rise, it reduces the value of the treasury as well as the call option (as the option becomes far out of money). Hence the total reduction in value of callable bond will be less than that of the treasury security.
Due to this bonds with call options outperform treasury securities when interest rates rise ( in the positive convexity region).
To confirm, if rates are less than the coupon, the negative convexity side, an MBS will underperform a similar noncallable bond regardless? However, if we’re on the positive convexity side (rates > coupon), then an MBS can outperform the benchmark?
To clairfy your statement though, it’s not that the MBS value > than the treasury value, it’s just that it doesn’t fall as far in value as the treasury when rates increase (so smaller change in value)?
For a callable band, when interest rates are high its duration and convexity are pretty close to those of a similar, option-free bond, so it will neither underperform nor outperform (i.e., lose about the same amount in price as) an option-free bond when interest rates increase. When interest rates are low, the callable bond will have a lower duration than that of a similar, option-free bond, so the callable will outperform (i.e., not lose as much in price as) the option-free when interest rates rise.
Note too that the inflection point in the price vs. yield curve (the point where the convexity changes from positive to negative) is not necessarily where the yield equals the coupon rate. For a bond callable (or prepayable) at par, the convexity will be less than that of an option-free bond at yields well above the coupon rate, but where, exactly, it goes from positive to negative is anyone’s guess.
I’m confused now. Referring back to my original post (1st paragraph), the text says when rates rise, the MBS will decrease more in value than a similar option-free bond - So MBS gains less from rate decreases but loses more from rate increases (lose-lose, seemingly). However, that does not line up with your last post, S2000 - you say it decreases less.
I guess i was under the impression and conclusion from the thread that when rates are below CPN (towards the negative convexity side) that it’s almost as if duration on the MBS is more sensitive such that lower rates don’t help the MBS as much but, as soon as rates increase, it quickly recovers with higher duration meaning it loses more in value. However, you are tending to agree with my original 2nd paragraph which i did not understand bc it contradicts the first.
I was comfortable thinking, and in agreement with anks, that MBS does decrease in value less but only when rates increase an we’re on the positive convexity side, no?
issuer has sold a prepayment option on the MBS to the investor. When rates drop - the prepayment option becomes more valuable, will be exercised. So instead of rising in value as much as a treasury bond would under the same circumstances - the value of the MBS would be capped. This causes the negative convexity region for the MBS. rate drops - value also falls
When rates increase - the value of the MBS does not fall as much as a treasury bond would. Here the prepayment option becomes less valuable.
MBS = Treasury Bond - Prepayment Option (Call option)
When rates rise - the treasury bond component portion of the MBS falls in value. But the prepayment option does not fall as much. As a result MBS drops in value less that a Treasury bond would. This causes the positive convexity region for the MBS - where rates rise and value of the MBS also rise.
Are you referring to price decreasing less when rates > coupon and on the positive convexity side? I understood it that if rates are below the coupon, that the MBS will underperform if rates increase or decrease. And that MBS will only outperform when rates are above the coupon, that’s when price will decrease less for the MBS.
The text in the MBS reading says MBS (due to its negative convexity) will incur less price appreciation when rates drop and greater price decrease as rates increase - this doesn’t gel with what you’re saying, which harks back on my initial post and reference to page 61 on schweser which does agree with your post.
it’s on page 116 of Schweser. they state: ``the smaller appreciation and larger depreciation in price for a given change in rates is called negative duration". I think this is a confusing issue. If you look at the graph on p117 (figure2), which is also on p152 of the CFA book, you can see there are clearly parts where negative convexity securities outperform (ie lose less money as rates rise), and parts where they underperform.
It seems we all agree on what happens when interest rates drop: callable securities underperform.
So what we’re trying to work out, is what happens when rates rise. I understand the logic for outperformance (ie the value of the prepayment option declines, reducing the losses for the investors). And the CFA book says this very clearly, so it must be right! But I don’t understand how this relates to the duration and convexity formula: ie: Price change = (duration * yield change) + (convexity * (yield change squared))
The formula implies that if convexity is negative, it’s always going to make the % price change worse (ie they will gain less when rates fall, and lose more when they rise).
The only explanation I can think of is that callable and non-callable securities would ‘start’ at different prices, ie non-callable would be worth more prior to the rate rise. So although its price may drop less in % terms, it could drop more in absolute terms ($), leading to the outperformance of callables? very keen to hear other peoples’ thoughts on this. thanks!
Wow, KiaKaha…that’s the exact line and page # I was referring to. Nice call, I was worried that I was alone with this. Seems like an obvious point of contradiction within the text, surprised it hasn’t been brought up before…sometimes I wonder if i’m too detail oriented and letting matters like this slow me down. Nevertheless…
I still have no conclusion. Not sure where you got that formula, Kia…CFAI? Worries me bc Schweser doesn’t show it. I can convince myself of both Views. I would initially agree with S2000 and the page 61 statement bc it makes intuitive sense that if the MBS price is lower, than rates increase, that it would not fall as much in absolute dollar terms (although as a smaller number, I would think it would decrease more in percentage terms).
On the other hand, I assumed what the text was saying was that as rates increase (due to its negative convexity), an MBS’s duration increases at a faster rate and becomes more sensitive to increasing rates than an option free bond - thus it’s price will decrease more rate increases.
Alas, I can’t rationalize which is right. I finally accepted that perhaps page 61 is correct but only when rates exceed the coupon on the positive convexity side. And that everything on the negative convexity side (rates < coupon), results in an MBS underperforming regardless of the change in rates (increase or decrease).
Having read the offending sentence on p. 116, I believe I understand what’s going on here.
It’s a misunderstanding, mainly from an ambiguously written sentence.
When it uses the expressions “smaller appreciation” and “larger depreciation”, it is not comparing the appreciation and depreciation to those of an option-free bond; _ it’s comparing them to each other _. All that sentence means is that, for example, a 0.5% decrease in yield will lead to a 1% increase in the price of the MBS, while a 0.5% increase in yield will lead to a 2% decrease in price; it’s saying that 1% is smaller than 2%, and 2% is larger than 1%. It could very well be that for the option-free bond a 0.5% decrease in yield would lead to a 3% increase in price, while a 0.5% increase in yield would lead to a 2.5% decrease in price: the MBS has less price appreciation and less price depreciation than the option-free bond.
So, no contradiction: p. 61 is correct, and p.116 is correct; you just have to understand what the author intended on p. 116, which admittedly isn’t clear.
Awesome. So to sum up, (speaking to the negative convexity side because an MBS and an option free bond act essentially the same on the positive side) an MBS will appreciate less from a decrease in rates compared to an option-free bond (due to its negative convexity and lower duration at lower rates). But, an MBS will depreciate less in value than an option-free bond when rates increase.
Why is the second part true exactly?
That’s all i have. Thank you again, many many thanks!
Take a look at the top graph on p. 117: in the area where the convexity is negative, the duration of the MBS is less than the duraton of the option-free bond.
(Note, too, that the straight line they’re describing as duration is good for visualization, but it’s technically incorrect. Don’t worry about that.)
But I don’t understand how this relates to the duration and convexity formula: ie: Price change = (duration * yield change) + (convexity * (yield change squared))