convexity of puttable bond

always positive… with less convexity in very high int rate environments (i.e the price of the bond does not decrease as much as rates rise)
 
By definition, the bond yield curve becomes a horizontal line at high interest rate, hence no convexity?
 
i wouldn’t say that, just because a bond has a put price at 80 cents on the dollar doesn’t mean the price/yield curve is asymptotic and approaching 80… if rates are high and there is concern with the borrowers ability to refinance (because of credit issues or lack of financing options) then that bond will certainly trade below 80… just as callable bonds can trade higher then their call price.
 
Char-Lee Wrote:
——————————————————-
> i wouldn’t say that, just because a bond has a put
> price at 80 cents on the dollar doesn’t mean the
> price/yield curve is asymptotic and approaching
> 80… if rates are high and there is concern with
> the borrowers ability to refinance (because of
> credit issues or lack of financing options) then
> that bond will certainly trade below 80… just as
> callable bonds can trade higher then their call
> price.
Yeah but that assumes credit risk. A callable bond that has an american call (continuous) in a default free low transaction cost environment, a callable would very rarely trade above call unless there was a good reason why the market thought the bond would not be called (maybe the market knows the issuer has a hedge behind). A callable will trade above par if the call structure is one time or discrete, at which point the market can trade a bond at the yield to call or yield to next call.
Assume you had a continuously putable default free bond with a put price of 100. Assuming a rational market, if anyone offered the bond at less than par, a trader could instantly buy the bond and exercise the put for an arbitrage profit. Therefore the floor price of the bond is the put price. Graphically, this represents more POSITIVE convexity than a non callable non putable bond as the price curve is more convex.
 
1morelevel Wrote:
——————————————————-
>
>
> Yeah but that assumes credit risk.
***no it doesn’t, if there is no access to financing then good luck putting your bonds (think how much a put option was worth in late 08 on the most credit worthy borrowers. Also, perhaps you (the bond holder) have been primed by new bank debt with certain covenants against certain finance actions, then once again good luck.
> A callable
> bond that has an american call (continuous) in a
> default free low transaction cost environment, a
> callable would very rarely trade above call unless
> there was a good reason why the market thought the
> bond would not be called (maybe the market knows
> the issuer has a hedge behind).
*** again not true, refinancing cost (i.e legal and underwriting fees) can be high enough to deter a borrower from refinancing at a lower rate. Or the borrower could be unsophisticated and just not call bonds (sometimes for many years, even though it’s economic to do so) OR the coupon is so high that even a “continuously” callable bond would trade at a premium because the yield to the next call date (at the earliest 30 days, but typically ~6mo from first call) is still positive… and there are a half dozen other examples but i’ll stop here
> A callable will
> trade above par if the call structure is one time
> or discrete, at which point the market can trade a
> bond at the yield to call or yield to next call.
>
> Assume you had a continuously putable default free
> bond with a put price of 100.
*** doesn’t exist
> Assuming a rational
> market, if anyone offered the bond at less than
> par, a trader could instantly buy the bond and
> exercise the put for an arbitrage profit.
*** let’s be clear here, bond options are not like what trades in Chicago, they are tied to the bond so you don’t just “exercise” you put options instantly, sorry, not even theoretically.
> Therefore the floor price of the bond is the put
> price. Graphically, this represents more POSITIVE
> convexity than a non callable non putable bond as
> the price curve is more convex.
*** just simply wrong… draw your option free bond line then the putable bond line… true there are inflection points as you approach the put price, but over all the putable bond price curve has LESS convexity at higher rates (just like a steeply discounted option free bond), at higher rates the option value increase at a faster pace then the underlying bond discounts, causing the line to flatten sooner
some of this is outside the CFA curriculum, but i had to correct the comments above
 
Dude did you even read my comments all the way through?
This discussion is about theoritical pricing, model pricing, intrinsic value. I am well aware that a putable default free bond doesn’t exist. I am describing the theoretical price. Doesn’t that make a lot more sense to use default free for the theory than saying assume a putable bond on a B- rated bank in Uruguay? I dont get your “doesn’t exist” reference. Neither do the Ingers. Neither does Country A. Whats your point?
First, the graph of putable vs bullet. At all points, the price of the putable is above the bullet as the option has value. The option is deep out of money at low interest rates, so difference is small. At left side of graph, the bullet curve and putable are nearly the same. As rates go higher, the put gains value and the lines diverge. The putable has a horizontal floor at the put strike and has positive convexity to a greater degree than the bullet bond. For verification, see Fabozzi, “Corporate Bond Portfolio Mgmt” Pg 83 or Fabozzi “Duration, convexity, and other bond risk measures ” I’m sure you can find it in several Fabozzi sources but that is what came up in a quick google search.
“let’s be clear here, bond options are not like what trades in Chicago, they are tied to the bond so you don’t just “exercise” you put options instantly, sorry, not even theoretically.” -
Did you read where I said “Assume you had a continuously putable default free bond with a put price of 100. “?
*** again not true, refinancing cost (i.e legal and underwriting fees) can be high enough to deter a borrower from refinancing at a lower rate. Or the borrower could be unsophisticated and just not call bonds (sometimes for many years, even though it’s economic to do so) OR the coupon is so high that even a “continuously” callable bond would trade at a premium because the yield to the next call date (at the earliest 30 days, but typically ~6mo from first call) is still positive… and there are a half dozen other examples but i’ll stop here”
Sorry, left out “efficient”. I thought a “default free, low transaction cost” qualfier was enough to imply we were talking about efficient markets. Why are you trying to point out how something could be priced in inneficient, illiquid markets with unsophisticated participants? Sure, it could trade at ANY price in that market. I think the CFA curriculum is more focused on intrinsic value, arbitrage principals etc that your hypothetical situations in obscure markets.
 
now you’re just being obnoxious at best and giving false information to people not as strong in this material at worst.
nothing i said is in “obscure” markets, they happen every day in well functioning markets. These aren’t one off events, in fact some are even the result of well functioning markets such as underwriting costs being a hurdle to call option exercise and high coupons vs ytc rates causing callable bonds to trade at premiums…
read the original question(s), then reread your ridiculous responses and tell me if you answered the question or not… the biggest problem people have passing these exams are making assumptions (like the dozen or so you did to justify your response, such as the market guessing there is a hedge behind (whatever that means), the existence of risk free puttable bonds, choosing continuous vs discrete options, low transaction costs, etc etc)… when CFA asks you what is 1+2 do you say 4 because I live in an alternate universe where 2 was not invented and all arithmetic questions must have even number answers???
For everyone else
“convexity of puttable bond - is it negative for high int, positive for low int?”
always positive, never negative
“By definition, the bond yield curve becomes a horizontal line at high interest rate, hence no convexity?”
close to horizontal but still has convexity.
 
“These aren’t one off events”
-An unsophisticated borrower that doesn’t call their bonds isn’t a one off?
Hypothetical CFA question:
UBC Nation issued 5 year callable bonds in March of 2006 with a yield if 5%. It is now March of 2008 and the yield curve has shifted downward. What should ABC do? Ignore transaction costs.
Answer choices:
A. Nothing, the treasurer is unsophisticated.
B. UBC Nation does not exist so the question is irrelevant
C. Continuously callable bonds require at a minimum of 30 days notice
D. Putable bonds do not have more positive convexity than a bullet
Which of your statements would you choose?
 
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