I’m a little confused with this very simple question Tina Donaldson, CFA candidate, is studying yield volatility and the value of putable bonds. She has the following information: a putable bond with a put option value calculated at 0.75 (prices are quoted as a percent of par) and a straight bond similar in all other aspects priced at 99.0. Donaldson also wants to determine how the bond’s value will change if yield volatility decreases. Which of the following choices is closest to what Donaldson calculates as the value for the putable bond and correctly describes the bond’s price behavior as yield volatility decreases? A) 99.75, price increases. B) 99.75, price decreases. C) 98.25, price decreases. D) 98.25, price increases. The correct answer was B) 99.75, price decreases. To calculate the putable bond value, use the following formula: Value of putable bond = Value of straight bond + Put option value Value of putable bond = 99.0 + 0.75 = 99.75. Remember: The put option is added to the bond value because the put option is of value to the bondholder, not the issuer. As yield volatility decreases, the value of the embedded option decreases. The formula above shows that for a putable bond, a decrease in the option value results in a decreased bond value. I understand that if yield volatility decreases that the value of the embedded option decreases, which therefore ultimately decreases the bond value but what happens to the value of the straight bond when yield volatility decreases. Would that lead to an increase in price of the straight bond, which would lead to an increase in bond value. Maybe I need to go back and read over Fixed Income. Any assistance would be greatly appreciated.

Where did you get this question ? Straight Bond: When yield volatility decreases the required rate of return (and hence the required yield) will decrease too and hence increase in price of the bond.

When Interest rates fall, the price of a straight bond would increase, but that of a bond with an embedded option would increase at a slower pace. The Put Option itself loses value. So, in all, net effect is that the Price of the Option embedded put bond is lower, when the interest rates decrease.

CPK - But in the above question it states “yield volatility” decreases which in itself doesn’t explicitly mean decrease in yield on bond. ??

Go back to the fixed income chapter 68 and read up on the zero volatility spread and option adjusted spread (OAS). Remeber, the Z-spread is a the spread that applies to the entire term structure of treasury yields, and incorporates liquidity risk, credit risk, and embedded options. The OAS excludes the latter. The difference between these two spreads represent the option cost. Where am going with this? Yield volatility affects the embedded option value. Drop the embedded option, and you have the z-spread equaling the option-adjusted spread. The OAS excludes yield volatility. On a straight bond, you have no embedded option, so the z-spread equals OAS. So yield volatility (while definitely a viable concept in general) doesn’t explain much in the pricing of a straight bond. Volatility is measured by dispersion, or variation–risk in other words–of yields. That uncertainty in yields doesn’t translate into much with a straight bond. Rather, a straight bond is simply concerned with the overall level of yields–along with other sundry risk factors such as credit, liquidity, regulatory, etc. Volatility, however, is important in the value of an embedded option. Think of the option on a stock with market price X and strike price X. In a stable market, does that option really mean much to the investor? Not really. By the way, the key to answering questions like the one you posted is to break down the answers into parts: first answer, what’s the value of the putable bond? Then answer the question, does the price increase or decrease with yield volatility? The order in which you answer these questions doesn’t really matter. As long as you narrow your selection down to two choices.

"Volatility, however, is important in the value of an embedded option. Think of the option on a stock with market price X and strike price X. In a stable market, does that option really mean much to the investor? Not really. " Let me know when you are ready to start giving those away when they don’t mean much. “Yes, well I know that gamma is approximately infinity, but these options don’t mean much in this stable market environment”.

thunderanalyst Wrote: ------------------------------------------------------- > CPK - But in the above question it states “yield > volatility” decreases which in itself doesn’t > explicitly mean decrease in yield on bond. > > ?? I think volatility risk is specific to bond options (callable or putable), and option-free bond itself will not change. Anyone?

In an ideal world, the price of an option free, risk free bond doesn’t depend on yield volatility. The price of the bond is just the discounted cash flows from the bond. In real-life, yield vol causes a premium on convexity and can filter over into all kinds of credit spread, currency, risk premium, etc. issues. At least for L I, assume that yield vol affects only bonds with options (maybe you should know about convexity too).

JoeyDVivre Wrote: ------------------------------------------------------- > "Volatility, however, is important in the value of > an embedded option. Think of the option on a stock > with market price X and strike price X. In a > stable market, does that option really mean much > to the investor? Not really. " > > Let me know when you are ready to start giving > those away when they don’t mean much. “Yes, well > I know that gamma is approximately infinity, but > these options don’t mean much in this stable > market environment”. Where have you been? I had a major clearance sale last Saturday–and I’m all out of stock. But seriously, I don’t doubt that options have a purpose. It’s like insurance on your car. If you get into an accident, that policy looks very meaningful. If you’re a safe driver and pay your premium every year but never file a single claim, you end up cursing the insurance company for making money on you. It’s all relative I guess.