LOS f, (Part 1): Compute the duration of a portfolio, given the duration of the bonds comprising the portfolio.

Q1. 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)   6.07.

B)   6.00.

C)   6.67.

Q2. 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.

Q3. Which of the following statements about portfolio duration is FALSE? 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.

Q4. Suppose you have a two-security portfolio containing bonds A and B. The book value of bond A is $20 and the market value is $35. The book value of bond B is $40 and the market value is $50. The duration of bond A is 4.7 and the duration of bond B is 5.9. Which of the following amounts is closest to the duration of the portfolio?

A)   5.5.

B)   5.3.

C)   5.4.

Q5. 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)   3.6

C)   0.4

[此贴子已经被作者于2009-3-5 11:27:50编辑过]

LOS f, (Part 1): Compute the duration of a portfolio, given the duration of the bonds comprising the portfolio.fficeffice" />

Q1. 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)   6.07.

B)   6.00.

C)   6.67.

Correct answer is A)

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.

Q2. 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.

Correct answer is C)        

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

Q3. Which of the following statements about portfolio duration is FALSE? 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.

Correct answer is B)

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

Q4. Suppose you have a two-security portfolio containing bonds A and B. The book value of bond A is $20 and the market value is $35. The book value of bond B is $40 and the market value is $50. The duration of bond A is 4.7 and the duration of bond B is 5.9. Which of the following amounts is closest to the duration of the portfolio?

A)   5.5.

B)   5.3.

C)   5.4.

Correct answer is C)

Market values (not book values) should be used to calculate effective portfolio duration.

(35/85 × 4.7) + (50/85 × 5.9) = 5.41

Q5. 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)   3.6

C)   0.4

Correct answer is B)

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.

[此贴子已经被作者于2009-3-5 11:29:25编辑过]

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