andytrader

A bond portfolio consists of a AAA bond, a AA bond, and an A bond. The prices of the bonds are $1,050, $1,000, and $950 respectively. The durations are 8, 6, and 4 respectively. What is the duration of the portfolio?

A) 6.00.

B) 6.07.

C) 6.67.

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The duration of a bond portfolio is the weighted average of the durations of the bonds in the portfolio. The weights are the value of each bond divided by the value of the portfolio:

portfolio duration = 8 × (1050 / 3000) + 6 × (1000 / 3000) + 4 × (950 / 3000) = 2.8 + 2 + 1.27 = 6.07.

andytrader

Suppose you have a three-security portfolio containing bonds A, B and C. The effective portfolio duration is 5.9. The market values of bonds A, B and C are $60, $25 and $80, respectively. The durations of bonds A and C are 4.2 and 6.2, respectively. Which of the following amounts is closest to the duration of bond B?

A) 7.4.

B) 1.4.

C) 9.0.

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Plug all the known figures and then solve for the one unknown figure, the duration of bond B.
Proof: (60/165 × 4.2) + (25/165 × 9.0) + (80/165 × 6.2) = 5.9

andytrader

Which of the following statements about portfolio duration is NOT correct? It is:

A) a measure of interest rate risk.

B) a simple average of the duration estimates of the securities in the portfolio.

C) the weighted average of the duration estimates of the securities in the portfolio.

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Portfolio duration uses a weighted average figure, not a simple average.

andytrader

Vijay Ranjin, CFA, is a portfolio manager with Golson Investment Group. He manages a fixed-coupon bond portfolio with a face value of $120.75 million and a current market value of $116.46 million. Golson’s economics department has forecast that interest rates are going to change by 50 basis points. Based on this forecast, Ranjin estimates that the portfolio’s value will increase by $2.12 million if interest rates fall and will decrease by $2.07 million if interest rates rise. Which of the following choices is closest to the portfolio’s effective duration?

A) 4.3.

B) 0.4.

C) 3.6.

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Effective duration = (price when interest rates fall − price when interest rates rise) / (2 × initial price × basis point change)
= (118.58 – 114.39) / (2 × 116.46 × 0.005) = 3.60.

andytrader

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.

andytrader

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.

andytrader

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

A) Modified duration considers expected changes in cash flows.

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

C) Effective duration considers expected changes in cash flows.

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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.

andytrader

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) change with the bond's embedded options.

B) be affected by a convertible bond.

C) not change.

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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.

andytrader

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 Effective Duration only

C) Effective Duration Modified Duration or Effective Duration

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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.

andytrader

The goal of computing effective duration is to get a:

A) preliminary estimate of modified duration.

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

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.