Question 97 of CFA mock 1 afternoon - driving me NUTS

If market rates rise, the price of a callable bond, compared to an otherwise identical option-free bond, will most likely decrease by: A.) less than option-free bond B.) more than option free bond C.)Same as option free bond *Answer is A I JUST finished reading schweser notes, and it clearly states that callable bonds will exhibit positive convexity similar or identical to that of option free bonds after yield increases to a certain point (right of *y on the graphs) , meaning prices fall at decreasing rates as yields rise. It seems this answer would be true for putable, since as yields rise prices drop and approach the put value, and likely will not go below that point. The explanation is even more confusing: A callable bond’s value is equal to an option-free bond’s value less the value of the call. As rates rise, the value of the call decreases by a decreasing amount relative to the straight bond. The option-free bond also declines in value as rates rise, but this is offset by the decline in the value of the call option. Therefore, the price of a callable bond decreases by less than a comparable option free bond. I know that calls and puts are less sensitive to rate changes than bonds, so i can understand why they have that answer, but I also understand that convexity becomes positive at high yields with callable bonds, so it’s like the argument is made either way? The only caveat I see that could be a possibility is where schweser says “similar OR identical” above.

Callable bond = Regular bond - Call option 90 = 100 - 10 rates down 93 = 110 - 17 or rates up: 85 = 90 - 5 rates further up: 79 = 80 - 1 (call value goes down with limit 0, when the value of call option stops decreasing, the bonds (regular and callable) have the same sensitivity to yield change) if we assume that there is a value of the call option that can still go down and moreover the question is “most likely”, only A is correct this is how I see it. hope it helps

I agree, but in that case it should state where on the graph it is (to the right of y would mean the call is basically useless). No? Look at the graph, price is on vertical, yield horizontal, there is negative convexity at low yields (left of y) and pos convexity at high yields (right of y)

i think to the right of y the call still has some value but is decreasing very slowly. this slow decrease subtracted from the decrease of the option free bond is what is making its decent slower as compared to a single standing option free bond. this coupled with what pfcfaataf has above is the best i can come up with. its not crystal clear in my head as to the exact relation but i can run with that

I guess the assumption (thanks for the clarity schweser dipshits) is that while at high yields it exhibits positive convexity such as a normal bond, the call decreases at a slower rate… what a bogus question.

I had problems with this question as well. Visualizing it through the positive convexity displayed by option free bonds and callable bonds at a yield greater than y* does not help. Callable bonds are option free bonds MINUS the call option so I can’t rationalize how a callable bond would decrease in price less than an option free bond when the call option is being subtracted from the option free bond to equate the callable bond’s price. I’m going to have to reread this section again tonight…

You won’t find answer in schweser, i can tell you that much. I Just re-read the whole thing.

what we all know: on the left side of the graph, the callable value is “very” below noncallable (the limit is call price). On the right side the callable price approaches the noncallable price from below and they meet when call option price is zero. The fact is that even when the convexity (curvature) becomes positive for callable bond, the slope matters …

the whole freakin’ fixed income section drives me nuts!

This is retarted. Stock and interest rates are postivily correlated. So when the the interest rate rises the underlying asset should go up ( increasing stock), which means the call is more in the money, which means it is more valuable. So when the a call is more in the money the probablity of it being excersised has increased. Therefore the yield on this callable bond needs will go up to compinsate the invester for the risk that is being taken for holding bond that might be called. So when price goes down on the bond yeild goes up. So if my logic is right and please tell me if it is wrong??? This stmt is nuts!!! “As rates rise, the value of the call decreases by a decreasing amount relative to the straight bond. The option-free bond also declines in value as rates rise, but this is offset by the decline in the value of the call option. Therefore, the price of a callable bond decreases by less than a comparable option free bond”

I am revisiting my last reply. It is all wrong. I was confused by markCFAIL and went on a late night tangent. Any way markCFAIL the page you need to look at is CFAI page 453-455 vol 5. Most noteablly exhibit 10,11,12 When int rates rise the price of the callable bond goes down slower than option-free because of the negative convexity. This negative convexity is caused by the value of the call option. The value of the call option is the chance that the interest rate will decline some time in the future. To sum it up callable are not as reactive to interest rates as option free bonds. p.s. embedded option on bonds do not act the same way as derivative options.

1. we are talking about bonds not stocks 2. Callable bond includes option to call a bond (owned by issuer, not bondholder) => option to buy a fixed rate bond sold by the bondholder (when I buy a callable bond, it is equivalent to buying a regular bond and selling option to buy a bond) 3. we can agree that Rates going down => the “underlying” regular fixed rate bond price goes up example: regular bond price = 100 option to buy this bond (say at 100) = 10 callable bond = regular bond - option price = 90 rates go down -> regular bond price = 110 option to buy this bond (say at 100) = 17 callable bond = 93

Pistan, you have reversed callable and putable bonds. There is no negative convexity when yields go up and prices down.