Baran

 

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

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

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

C) Price changes are the same for both increases and decreases in yields.

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

Baran

 

The correct answer is A

 

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.

Baran

 

10、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 low yields for the callable bond and always convex for the option-free bond.

B) the same for both bond types.

C) concave for an option-free bond and convex for a callable bond.  

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

Baran

 

The correct answer is A

 

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.

Baran

 

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

A) more convex at some yields for the putable bond than for the option-free bond.

B) the same for both bond types.

C) more convex for a putable bond than for an option-free bond.  

D) concave for an option-free bond and convex for a putable bond.

Baran

 

The correct answer is A

 

Since the holder of a putable has an incentive to exercise his put option if yields are high and the bond price is depressed, this puts a lower limit on the price of the bond when interest rates are high. The lower limit introduces a higher convexity of the putable bond compared to an option-free bond when yields are high.

Baran

 

12、Can a fixed income security have a negative convexity?

A) No.  

B) Yes. 

C) Need more information to answer question.

D) Yes, but only when the price yield curve is linear.

Baran

 

The correct answer is B

 

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

Baran

 

13、Negative convexity is most likely to be observed in:

A) zero coupon bonds.

B) municipal bonds.

C) callable bonds.

D) treasury bonds.

Baran

 

The correct answer is C

 

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.