Reading 66: Introduction to the Measurement of Interest Rate 2010, different, between, effective

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LOS h: Differentiate between modified convexity and effective convexity.

The distinction between modified convexity and effective convexity is that:

A) different dealers may calculate modified convexity differently, but there is only one formula for effective convexity.

B) modified convexity becomes less accurate as the change in yield increases, but effective convexity corrects for this.

C) effective convexity accounts for changes in cash flows due to embedded options, while modified convexity does not.

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Effective convexity is the appropriate measure to use for bonds with embedded options because it takes into account the effect of the embedded options on the bond’s cash flows.

 

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One major difference between standard convexity and effective convexity is:

A) effective convexity reflects any change in estimated cash flows due to embedded bond options.

B) effective convexity is Macaulay's duration divided by [1 + yield/2].

C) standard convexity reflects any change in estimated cash flows due to embedded options.

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The calculation of effective convexity requires an adjustment in the estimated bond values to reflect any change in estimated cash flows due to the presence of embedded options. Note that this is the same process used to calculate effective duration.

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Which of the following statements is most accurate concerning the differences between modified convexity and effective convexity?

A) Modified convexity takes into account changes in cash flows due to embedded options, while effective convexity does not.

B) For an option-free bond, modified convexity is slightly greater than effective convexity.

C) Effective convexity is most appropriate for bonds with embedded options.

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Effective convexity is most appropriate for bonds with embedded options because it takes into account changes in cash flows due to changes in yield, while modified convexity does not. For an option-free bond, modified convexity and effective convexity should be very nearly equal.

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William Morgan, CFA, manages a fixed-income portfolio that contains several bonds with embedded options. Morgan would like to evaluate the sensitivity of his portfolio to large interest rate changes and will therefore use a convexity measure in addition to duration. The convexity measure that will best estimate the price sensitivity of Morgan’s portfolio is:

A) modified convexity.

B) effective convexity.

C) either effective or modified convexity.

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Effective convexity is the appropriate measure because it takes into account changes in cash flows due to embedded options, while modified convexity does not.