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LOS n: Explain how yield volatility affects the price of a bond with an embedded option and how changes in volatility affect the value of a callable bond and a putable bond.

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.

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.

Which of the following statements is CORRECT for both callable and putable bonds?

A)	When yield volatility increases, the value of the option increases.

B)	The value of the bond is equal to the value of a similar straight bond plus the value of the option.

C)	When yield volatility increases, the value of the bond increases.

To calculate the value of a putable bond, it is correct to add the option value to the value of a similar straight bond. However, to calculate the callable bond value, subtract the option value from that of a similar straight bond. As a result, when yield volatility increases (thus increasing the option value), the value of a callable bond decreases and the value of a putable bond increases.

Which of the following statements concerning the effects of interest rate volatility on bonds with embedded options is least accurate?

A)	A putable bond's value is its straight bond value plus the value of the embedded put option.

B)	As yield volatility increases, the value of callable bonds decreases.

C)	A callable bond's value is its straight bond value plus the value of the embedded call option.

A callable bond’s value is its straight bond value minus the value of the embedded call option. Since the bondholder is effectively short a call option, the value of the option is subtracted from the bond price. This is why the value of callable bonds decreases when yield volatility rises.

Which of the following statements about embedded options and yield volatility is NOT correct?

A)	As yield volatility increases, the value of the call option increases along with the value of the callable bond.

B)	Putable bondholders benefit from increases in yield volatility.

C)	A call option benefits the issuer and a put option benefits the holder.

As yield volatility increases, the value of the call option increases, and the value of the callable bond decreases and thus the bondholder loses. (As shown by the equation: Value of callable bond = Value of straight bond – Call option value.) The other choices are true. A holder of a put option benefits from increased yield volatility because the value of the put option increases, increasing the putable bond value. (Value of putable bond = Value of straight bond + Put option value.)

Simone Girard, CFA candidate, is studying yield volatility and the value of callable bonds. She has the following information: a callable bond with a call option value calculated at 1.25 (prices are quoted as a percent of par) and a straight bond similar in all other aspects priced at 98.5. Girard also wants to determine how the bond’s value will change if yield volatility increases. Which of the following choices is closest to what Girard calculates as the value for the callable bond and correctly describes the bond’s price behavior as yield volatility increases?

A)	97.25, price increases.

B)	99.75, price decreases.

C)	97.25, price decreases.

To calculate the callable bond value, use the following formula:

Value of callable bond = Value of straight bond – Call option value

Value of callable bond = 98.5 – 1.25 = 97.25.

Remember: The call option is subtracted from the bond value because the call option is of value to the issuer, not the holder.

As yield volatility increases, the value of the embedded option increases. The formula above shows that for a callable bond, an increase in the option value results in a decreased bond value.