Kingpin804

An analyst is evaluating the following two statements about putable bonds:

Statement #1: As yields fall, the price of putable bonds will rise less quickly than similar option-free bonds (beyond a critical point) due to the decrease in value of the embedded put option.
Statement #2: As yields rise, the price of putable bonds will fall more quickly than similar option-free bonds (beyond a critical point) due to the increase in value of the embedded put option.

The analyst should:

A) disagree with both statements.

B) agree with both statements.

C) agree with only one statement.

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Both statements are false. As yields fall, the value of the embedded put option in a putable bond decreases and (beyond a critical point) the putable bond behaves much the same as an option-free bond. As yields rise, the value of the embedded put option increases and (beyond a critical point) the putable bond decreases in value less quickly than a similar option-free bond.

Kingpin804

At a market rate of 7%, a $1,000 callable par value bond is priced at $910, while a similar bond that is non-callable is priced at $960. What is the value of the embedded call option?

A) $40.

B) $50.

C) $30.

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The value of the embedded call option is simply stated as:  
value of the straight bond component – callable bond value = value of embedded call option.
$960 – $910 = $50

Kingpin804

Which of the following statements best describes the concept of negative convexity in bond prices? As interest rates:

A) fall, the bond's price increases at an increasing rate.

B) rise, the bond's price decreases at a decreasing rate.

C) fall, the bond's price increases at a decreasing rate.

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Negative convexity occurs with bonds that have prepayment/call features. As interest rates fall, the borrower/issuer is more likely to repay/call the bond, which causes the bond’s price to approach a maximum. As such, the bond’s price increases at a decreasing rate as interest rates decrease.

mouse123

Convexity is important because:

A) it measures the volatility of non-callable bonds.

B) the slope of the price/yield curve is not linear.

C) the slope of the callable bond price/yield curve is backward bending at high interest rates.

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Modified duration is a good approximation of price changes for an option-free bond only for relatively small changes in interest rates. As rate changes grow larger, the curvature of the bond price/yield relationship becomes more prevalent, meaning that a linear estimate of price changes will contain errors. The modified duration estimate is a linear estimate, as it assumes that the change is the same for each basis point change in required yield. The error in the estimate is due to the curvature of the actual price path. This is the degree of convexity. If we can generate a measure of this convexity, we can use this to improve our estimate of bond price changes.

mouse123

Negative convexity is most likely to be observed in:

A) callable bonds.

B) zero coupon bonds.

C) treasury bonds.

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All noncallable bonds exhibit the trait of being positively convex and callable bonds have a negative convexity.  Callable bonds have a negative convexity because once the yield falls below a certain point, as yields fall, prices will rise at a decreasing rate, thus giving the curve a negative convex shape.

mouse123

Which of the following is most accurate about a bond with positive convexity?

A) Positive changes in yield lead to positive changes in price.

B) Price increases and decreases at a faster rate than the change in yield.

C) Price increases when yields drop are greater than price decreases when yields rise by the same amount.

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A convex price/yield graph has a larger increase in price as yield decreases than the decrease in price when yields increase. This comes from the definition of a convex graph.

mouse123

Positive convexity in bond prices implies all but which of the following statements?

A) As yields increase, changes in yield have a smaller effect on bond prices.

B) Bond prices approach a ceiling as interest rates fall.

C) The price volatility of non-callable bonds is inversely related to the level of market yields.

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The convexity of bond prices means that bond prices as a function of interest rates approach a floor as interest rates rise.

mouse123

If a put feature expires on a bond so that it becomes option-free, then the curve depicting the price and yield relationship of the bond will become:

A) less convex.

B) more convex.

C) inversely convex.

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When the option expires, the prices at the lower end of the curve will become lower. This will make the curve less convex.

mouse123

Can a fixed income security have a negative convexity?

A) Only when the price/yield curve is linear.

B) No.

C) Yes.

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Yes, fixed income securities can have a negative security. The only type of fixed income security with a negative convexity will be callable bonds.  

mouse123

How does the price-yield relationship for a callable bond compare to the same relationship for an option-free bond? The price-yield relationship is:

A) concave for the callable bond and convex for an option-free bond.

B) concave for low yields for the callable bond and always convex for the option-free bond.

C) the same for both bond types.

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Since the issuer of a callable bond has an incentive to call the bond when interest rates are very low in order to get cheaper financing, this puts an upper limit on the bond price for low interest rates and thus introduces the concave relationship between yields and prices.