Reading 66: Introduction to the Measurement of Interest Rate relation, positive, important, 2010

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LOS c: Describe positive convexity, negative convexity, and their relation to bond price and yield.

Negative convexity for a callable bond is most likely to be important when the:

A) bond is first issued.

B) market interest rate rises above the bond's coupon rate.

C) price of the bond approaches the call price.

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Negative convexity illustrates how the relationship between the price of a bond and market yields changes as the bond price rises and approaches the call price. The convex curve that we generally see for non-callable bonds bends backward to become concave (i.e., exhibit negative convexity) as the bond approaches the call price.

 

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Jayce Arnold, a CFA candidate, is studying how the market yield environment affects bond prices. She considers a $1,000 face value, option-free bond issued at par. Which of the following statements about the bond’s dollar price behavior is most likely accurate when yields rise and fall by 200 basis points, respectively? Price will:

A) decrease by $124, price will increase by $149.

B) increase by $149, price will decrease by $124.

C) decrease by $149, price will increase by $124.

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As yields increase, bond prices fall, the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, the price curve gets steeper, and changes in yield have a larger effect on bond prices. Thus, the price increase when interest rates decline must be greater than the price decrease when interest rates rise (for the same basis point change). Remember that this applies to percentage changes as well.

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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) the same for both bond types.

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

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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.

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

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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.

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

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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.

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Which of the following bonds bears the greatest price impact if its yield declines by one percent? A bond with:

A) 30-year maturity and selling at 100.

B) 30-year maturity and selling at 70.

C) 10-year maturity and selling at 70.

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There are three features that determine the magnitude of duration:

(1) The lower the coupon, the greater the bond price volatility.
(2) The longer the term to maturity, the greater the price volatility.
(3) The lower the initial yield, the greater the price volatility.

The bond with the 30-year maturity will have a greater price impact than the 10-year maturity. The bond selling at the greatest discount will have a large price impact, a discount means that the coupon payments are low or the initial yield is low. So, the bond with the 30-year maturity and selling at 70 will have the greatest price volatility.

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Non-callable bond prices go up faster than they go down. This is referred to as:

A) negative convexity.

B) inverse features.

C) positive convexity.

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When bond prices go up faster than they go down, it is called positive convexity.

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Non-callable bond prices go up faster than they go down. This is referred to as:

A) negative convexity.

B) inverse features.

C) positive convexity.

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When bond prices go up faster than they go down, it is called positive convexity.

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Can a fixed income security have a negative convexity?

A) Yes.

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

C) No.

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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. 

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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.