# Which bond is putable and which bond is callable ?

Hi Folks, Here is question from Fixed Income, I am not getting logical reasoning behind it. A bond dealer provides following info for fixed income securities: Par Value Market Value coupen Modified Effective Effective Convexity Duration Duration Convexity \$2mil 100 6.5% 8 8 154 \$3mil 93 5.5% 6 1 50 \$4mil 95 7% 8.5 8.5 130 \$1mil 103 8% 9 5 -70 Questions: 1> Which Bond(s) likely have no embedded option(Identify bonds with coupen) 2> Which bond(s) likely callable ? 3> Which bond(s) likely putable ? Can you explain the answer in each of these question ? How did u come up to that answer ? Your response will be appericiated. -Cheers

So through coupon we take care of the \$2mil, 100, 6.5% and then we have " Modified Effective Effective Convexity Duration Duration Convexity " describing 8, 8, 154 so working backwards that means 154 = convexity, 8 = duration, and then Modified Effective Effective Convexity Duration = 8. I guess I don’t know that term.

Bro guess what I am currently battling the very same problem. For question 1 Modified Duration can only be used when there are no expected changes in cash flow due to a change in yield as we all know that a change in yield can result in a change of cash flow eg prepayments,calling etc So, in situations where modified duration is equal to effective duration one can rightfully assume that there are no embedded options. cause effective duration actually takes the fact that their may be embedded options into consideration.

questions 2 and 3 are easier Call embedded options are a cost to the firm and remember that call embedded options exhibit negative convexity while put embedded options are a cost to the buyer i.e they are generally sold below par. any corrections will be sincerely appreciated.

The first and third have no options, the second is puttable, and the last is callable.

I think there is one too many Convexity in this sentence Par Value Market Value coupen Modified Effective Effective Convexity Duration Duration Convexity I think this should be interpreted as Par Value***Market Value***Coupon***Modified Duration***Effective Duration***Effective Convexity \$2mil***100***6.5%***8***8***154 \$3mil***93***5.5%***6***1***50 \$4mil***95***7%***8.5***8.5***130 \$1mil***103***8%***9***5***-70 Based on my interpretation above: Since -ve Convexity is displayed by the 8% bond – I think that is the one with the Callable option. Putable is possible Bond 1 with the 6.5% coupon. Am I way off the mark??? CP

Hello, How did u come with that answer ? Putable and callable both can have +ve and -ve convexitiy, so how did you determine, in this case, which was putable and which callable solely based on convexity, is there any other factor to consider while determining what type of callable bond ? Please explain the logic. -Thanks

I thot it was only callable bonds that have -ve convexity

wyantjs has this. Assuming cpk’s diagram is correct, Bond 1 has same effective duration as modified duration. If modified duration and effective duration are equal it is very likely that there are no embedded options (possible that there are offsetting options) because effective duration accounts for the effects of optionality and modified duration doesn’t. Bond 2 has shorter effective duration than modified duration but positive convexity. This one is ambiguous because the market value doesn’t really mean anything but what they are trying to say is that this bond is selling below par which means interest rates have increased. However as interest rates have increased the bond becomes less sensitive to further interest rate moves. The only reason this could happen is that the bond can be put back to the issuer so further increases in interest rates don’t matter much. Bond 3 same as 1 Bond 4 has negative convexity which is the hallmark of callable bonds. As interest rates decrease the price goes up but can’t exceed the call price (probably). That means the price-yield curve has to flatten out against the ceiling which makes it concave down thus having negative convexity. Puttable bonds don’t have negative convexity (try drawing it).

Joey thanks a million. you are worth your worth in gold

Thanks Joey, However I still have one question: Isn’t that true, callable and putable bond have +ve convexity(when become like option free bond) and -ve convexity, so based on interest rate, callable can have +ve covexity(when act like option free), so how can one say callable should only have -ve convexity, so in this case, how can you predict -ve convexity is related to callable ? Thanks in advance.

Callable bonds have a negative convexity its on the cover of your Schweser text book

Hello, Callable bond do exhibit +ve convexity, when interest rate goes up, so it has both -ve and +ve convesity ? Am I correct ? -Thanks,

I didn’t mean to imply that callable bonds always have negative convexity - only that callable bonds can sometimes have negative convexity. This happens when interest rates drop so that the price of the bond rises toward its call price. Puttable bonds never have negative convexity (unless there is also an embedded call or something).

cfa20089 Wrote: ------------------------------------------------------- > Hello, > > Callable bond do exhibit +ve convexity, when > interest rate goes up, so it has both -ve and +ve > convesity ? > > Am I correct ? > > -Thanks, Yes - in “most” situations a callable bond has positive convexity.

Hello, So when interest rate falls, callable bond has -ve convexity and when it rises, after certain level of yield, it has +ve convexity( act like option free) ? Putable bond has +ve convexity(act like option free), as interest rate rise and after certain level of yield, it has -ve convexity Am I right ? -Thanks

Putable bond never has -ve convexity as far as I remember. Always +ve convexity.

cfa20089 Wrote: ------------------------------------------------------- > Hello, > > So when interest rate falls, callable bond has -ve > convexity and when it rises, after certain level > of yield, it has +ve convexity( act like option > free) ? > > Putable bond has +ve convexity(act like option > free), as interest rate rise and after certain > level of yield, it has -ve convexity > > Am I right ? > > -Thanks Alas, it is not so symmetric. Puttable bonds just flatten out at the put price but always have positive convexity. (This is best shown by drawing the price/yield curve. You should do that so you understand it).