# FI - option and interest risk

I would like to discuss this practice question Which of the following bonds has the greatest interest rate risk ? A- 5% 10Y callable bond B- 5% 10Y putable bond C- 5% 10Y option free bond The answer given by the book is : C, saying that options are reducing interest rate risk For me, I would have responsed A. A bondholder holding an option free bond is subject to increase and decrease in interest rate. She could win or lose But with a callable bond, she is only subject to increase in interest rate (then decrease in bond price). If there is a decrease in interest rate (then increase in bond price), the bond issuer is likely to call the bond. For me it’s risker for a bondholder to have a callable bond than an option free bond. thanks for your help on this matter

An increase in price of a callable bond is limited to the call price in case of decrease in interest rates. hence callable bond is less sensitive to interest rate risk than a option free bond. A decrease in price of a putable bond is limited to the put price in case of increase in interest rates. hence putable bond is less sensitive to interest rate risk than a option free bond. hence the correct option is C.

callble/puttable bond will always have a lower duration than an identical non callable bond

In case of callable bond - bondholder cannot take advantage of a favorable interest rate change, since the bondissuer will use the call option - bondholder will bear adverse interest rate change In case of option free bond - bondholder will take advantage of a favorable interest rate change - bondholder will bear adverse interest rate change so, there is more risk for bondholder with a callable bond … Thanks for your help

surely this is just a duration question…?

My understanding: Callable bond- Bond issuer is at a better position. Putable bond- Bond holder is at a better position. Option free bond- both are not in a better position- since they are locked in the bond interest rate until the bond matures. the bond is not sensitive to interest rate change. hence is more risky. So the answer is C. Buzz

You have to remember the price/yield relationship for a bond. if price is the y axis and interest rate is the x axis. the graph will be convex towards the origin. when price is high, interest rates will be low. when price is low, rates will be high. now consider a bond with a call option. as yield increases the bond becomes less valuable for the holder, and a seller will be less likely to call the bond, so the price of a callable bond when the interest rate is high will be similar to that of an option free bond. now when the yield decreases it raises the price of a call option, and the bond will be worth less (price with call option = price of option free - call option price). so with a call option the price is always less than or equal to the price of an option free bond. a call option reduces interest rate risk because there is less price movement area. now for a put. if the rates are low, the bond will be worth more, so the put will be almost worthless. so when rates are low the price of a putable bond is roughly equal to that of an option free bond. now when rates are high, bond prices fall, and the put option is worth more. but recall: price putable bond = price option free + price of put. so the putable bond will always be worth more than the price of an option free bond, prices wont decrease as much as they would with an option free bond. you have to consider these two equations: price of a callable bond = price option free - call option price price of putable bond = price option free + price of put and then consider what happens with interest rate changes.