# Bond question no one can answer ?

V5- 97 If market interest rates rise, the price of a callable bond, compared to an otherwise identical option-free bond, will most likely: Select exactly 1 answer(s) from the following: A. increase by less than the option-free bond. B. decrease by less than the option-free bond. C. decrease by more than the option-free bond. D. decrease by the same amount as the option-free bond. I SAID B

I said B b/c for a normal bond, higher rates = lower price however, for a callable, a higher rate DECREASES the chances of the bond getting called, so it should see its value diminish at a less violent rate than the normal bond. NEED HELP HERE, FELLAS

As previously explained in the other post (by Joey). It is B. This is due to the fact that: Callable bond= bond + call option. If intererest rate rise, it will be not convinient for the issuer to call the bond (as it would be more expensive to borrow funds in the market). Therefore, due to the inverse relationship Price-Yield, the price of both callable bond and option free bond will fall, however due to the callable feature, the price of the callable will decrease less than the option-free bond. Note: This effect can be explained by the fact that the call option will have a delta (measures the sensitivity to changes in the price of the underlying asset), less then one. Thanks Joey.

It is B.

strangedays Wrote: ------------------------------------------------------- > As previously explained in the other post (by > Joey). It is B. > > This is due to the fact that: > > Callable bond= bond + call option. > > If intererest rate rise, it will be not convinient > for the issuer to call the bond (as it would be > more expensive to borrow funds in the market). > Therefore, due to the inverse relationship > Price-Yield, the price of both callable bond and > option free bond will fall, however due to the > callable feature, the price of the callable will > decrease less than the option-free bond. > > Note: This effect can be explained by the fact > that the call option will have a delta (measures > the sensitivity to changes in the price of the > underlying asset), less then one. > > Thanks Joey. shouldn’t callable bond = option free - call option? as callable bond is more risky to the investor, he will pay less for it than for otherwise bond without the call option.

Yes pepp, typo. It is: Pcallable= PnonBond - CallOption Pputable=PnonBond + PutOption Everthing else it is fine. Thanks to note it.

so can we conclude that irrespective of price increase/decrease, the decrease/inrease is less for callable bonds compared to option free bonds ?

if u understand convexity, this should be no prob. negative convex for callable bonds. price increase in a decreasing rate compared to option free. u might wana revisit convex

thunder, that is correct. remember price of option < price of the option free bond. if the price of option free bond < price of option, then everyone should simply buy option free bond. less risk and low price. wow. i hit jackpot. arbitrage.

This is the final result (reported as bullet point to remember): A) The buyer of a callable bond is: - long a noncallable bond with the same maturity as the callable one - short a call option on this bond B) Price of a callable bond P(callable) = P(non-call) - Call Option C) Interest rate delta (which measure the sensitivity of the price of the call option to small variation of the interest rates) of a callable bond is equal to the delta of the noncallable minus the delta on the option and as a result: CALLABLE BOND HAS LESS INTEREST RATE SENSITIVITY THAN THE NONCALLABLE.

Strange, there is no need to get in those results, I agree all what you said is correct but conceptually expects you to know: a) a risky asset should be priced lower than otherwise non-risky asset. if this was not the case, then everyone would buy non-risky asset ONLY. b) as you reduce the riskiness of the risky asset, the price of the risky asset will converge to the non-risky asset. and if you completely eliminate the risk of the risky asset, you’ll end up with the same price that of non-risky asset. I feel I am very glad that I am able to understand the above concept without getting into the technicals of interest rate volatility etc.

"shouldn’t callable bond = option free - call option? " NO – the CB = NCB + attached option note that MBS is also considered a bond with an option attached, as are convertibles and reverse convertibles. RCs have a put feature CBs have a call feature

That’s wrong daj. It is exactly what strangedays said: Pcallable= PnonBond - Option Pputable=PnonBond + Option Think negative in terms of a callable bond because the issuer has the advantage and add the option on a putable lond because it is an advantage to the holder.

I would say D because at rising interest rate a callable bond will behave like option free/noncallable bond.

D is only true of interest rates are extremely high. It is in Vol. 5 of CFAi, I forget the page numbers.

I thought someone would give me credit for the below explanation. pepp Wrote: ------------------------------------------------------- > Strange, > > there is no need to get in those results, I agree > all what you said is correct but conceptually > expects you to know: > > a) a risky asset should be priced lower than > otherwise non-risky asset. if this was not the > case, then everyone would buy non-risky asset > ONLY. > > b) as you reduce the riskiness of the risky asset, > the price of the risky asset will converge to the > non-risky asset. and if you completely eliminate > the risk of the risky asset, you’ll end up with > the same price that of non-risky asset. > > > I feel I am very glad that I am able to understand > the above concept without getting into the > technicals of interest rate volatility etc.

<<< That’s wrong daj. It is exactly what strangedays said: Pcallable= PnonBond - Option Pputable=PnonBond + Option Think negative in terms of a callable bond because the issuer has the advantage and add the option on a putable lond because it is an advantage to the holder. >> YES YOU ARE RIGHT, MY BAD. THANKS : )

These type of problems are most easily solved by drawing a price-yield curve for the bond specified.