Reading 66: Introduction to the Measurement of Interest Rate border, effective, computing, face

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LOS e, (Part 1): Distinguish among the alternative definitions of duration.

The goal of computing effective duration is to get a:

A) more accurate measure of the bond's price sensitivity when embedded options exist.

B) preliminary estimate of modified duration.

C) measure of duration that is effectively constant for the life of the bond.

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The point of effective duration is to consider expected changes in cash flow from features such as embedded options. When embedded options exist, the effective duration will give a better measure of the bond’s price sensitivity to interest rate changes.

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Effective duration is more appropriate than modified duration as a measure of a bond's price sensitivity to yield changes when:

A) the bond has a low coupon rate and a long maturity.

B) yield curve changes are not parallel.

C) the bond contains embedded options.

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Effective duration takes into consideration embedded options in the bond. Modified duration does not consider the effect of embedded options. For option-free bonds, modified duration will be similar to effective duration. Both duration measures are based on the value impact of a parallel shift in a flat yield curve.

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Which of the following statements about duration is most accurate?

A) Modified duration is the most appropriate measure of interest rate sensitivity for bonds with embedded options.

B) Effective duration accounts for changes in a bond’s cash flows resulting from interest rate changes.

C) Effective duration is calculated from past price changes in response to changes in yield.

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Neither Macaulay nor modified duration is an appropriate measure of interest rate risk for bonds with embedded options. Macaulay duration does not take the current YTM into account as modified duration does. Effective duration, however, explicitly takes into account changes in a bond’s cash flows due to interest rate changes and is calculated from expected price changes in response to a given increase or decrease in yield.

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Which of the following statements about duration is FALSE?

A) Effective duration is the exact change in price due to a 100 basis point change in rates.

B) For a specific bond, the effective duration formula results in a value of 8.80%. For a 50 basis point change in yield, the approximate change in price of the bond would be 4.40%.

C) The numerator of the effective duration formula assumes that market rates increase and decrease by the same number of basis points.

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Effective duration is an approximation because the duration calculation ignores the curvature in the price/yield graph.

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An investor gathered the following information on two U.S. corporate bonds:

• Bond J is callable with maturity of 5 years
• Bond J has a par value of $10,000
• Bond M is option-free with a maturity of 5 years
• Bond M has a par value of $1,000

For each bond, which duration calculation should be applied?

Bond J

Bond M

A) Modified Duration Effective Duration only

B) Effective Duration Modified Duration or Effective Duration

C) Effective Duration Effective Duration only

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The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.

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Which of the following explains why modified duration should least likely be used for bonds with call options? Modified duration assumes that the cash flows on the bond will:

A) not change.

B) change with the bond's embedded options.

C) be affected by a convertible bond.

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Modified duration assumes that the cash flows on the bond will not change (i.e., that we are dealing with non-callable bonds). This greatly differs from effective duration, which considers expected changes in cash flows that may occur for bonds with embedded options.

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Why should effective duration, rather than modified duration, be used when bonds contain embedded options?

A) Effective duration considers expected changes in cash flows.

B) Modified duration considers expected changes in cash flows.

C) Either could be used if the bond has embedded options.

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Modified duration assumes that the cash flows on the bond will not change (i.e., that we are dealing with non-callable bonds). This greatly differs from effective duration, which considers expected changes in cash flows that may occur for bonds with embedded options.

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Which of the following statements about modified duration and effective duration is FALSE?

A) Modified duration should be used for bonds with embedded options.

B) Effective duration should be used for bonds with embedded options.

C) The modified duration measure assumes that yield changes do not change the expected cash flows.

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Using modified duration as a measure of the price sensitivity of a security with embedded options to changes in yield would be misleading. With embedded options, yield changes may change the expected cash flows.

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A bond with an 8% semi-annual coupon and 10-year maturity is currently priced at $904.52 to yield 9.5%. If the yield declines to 9%, the bond’s price will increase to $934.96, and if the yield increases to 10%, the bond’s price will decrease to $875.38. Estimate the percentage price change for a 100 basis point change in rates.

A) 4.35%.

B) 2.13%.

C) 6.58%.

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The formula for the percentage price change is: (price when yields fall – price when yields rise) / 2 × (initial price) × 0.005 = ($934.96 – 875.38) / 2($904.52)(0.005) = $59.58 / $9.05 = 6.58%. Note that this formula is also referred to as the bond’s effective duration.

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When calculating duration, which of the following bonds would an investor least likely use effective duration on rather than modified duration?

A) Callable bond.

B) Option-free bond.

C) Convertible bond.

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The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.