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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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) more convex.

B) inversely convex.

C) less 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.

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

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

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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.

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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.

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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 a decreasing rate.

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

C) rise, the bond's price decreases 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.

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Positive convexity means that:

A) the graph of a callable bond flattens out as the market value approaches the call price.

B) as interest rates change, bond prices will increase at an increasing rate and decrease at a decreasing rate.

C) the price of a fixed-coupon bond is inversely related to changes in interest rates.

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Positive convexity refers to the principle that for a given change in market yields, bond price sensitivity is lowest when market yields are high and highest when market yields are low.

Although the statements that begin, the graph of a callable bond . . . and the price of a fixed-coupon bond . . . are true, they are not the best choices to describe positive convexity.

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Consider two bonds, A and B. Both bonds are presently selling at par. Each pays interest of $120 annually. Bond A will mature in 5 years while bond B will mature in 6 years. If the yields to maturity on the two bonds change from 12% to 10%, both bonds will:

A) increase in value, but bond A will increase more than bond B.

B) increase in value, but bond B will increase more than bond A.

C) decrease in value, but bond B will decrease more than bond A.

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There are three features that determine the magnitude of the bond price volatility: 

    (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.

Since both of these bonds are the same with the exception of the term to maturity, the bond with the longer term to maturity will have a greater price volatility.  Since bond value has an inverse relationship with interest rates, when interest rates decrease bond value increases. 

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Which of the following bonds may have negative convexity?

A) Both of these choices are correct.

B) Mortgage backed securities.

C) Callable bonds.

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Negative convexity is the idea that as interest rates decrease they get to a certain point where the value of certain bonds (bonds with negative convexity) will start to increase in value at a decreasing rate.  

Interest rate risk is the risk of having to reinvest at rates that are lower than what an investor is currently receiving.

Mortgage backed securities (MBS) may have negative convexity because when interest rates fall mortgage owners will refinance for lower rates, thus prepaying the outstanding principle and increasing the interest rate risk that investors of MBS may incur.

Callable bonds are similar to MBS because of the possibility that the principle is being returned to the investor sooner than expected if the bond is called causing a higher level of interest rate risk.

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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.