Reading 66: Introduction to the Measurement of Interest Rate 2010, face, border, style, given

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LOS f: Compute the duration of a portfolio, given the duration of the bonds comprising the portfolio.

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) 6.67.

C) 6.07.

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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.

 

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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) 3.6

B) 4.3

C) 0.4

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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.

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Which of the following is a limitation of the portfolio duration measure? Portfolio duration only considers:

A) the market values of the bonds.

B) a linear approximation of the actual price-yield function for the portfolio.

C) a nonparallel shift in the yield curve.

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Duration is a linear approximation of a nonlinear function. The use of market values has no direct effect on the inherent limitation of the portfolio duration measure. Duration assumes a parallel shift in the yield curve, and this is an additional limitation.

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Which of the following is NOT a limitation of the portfolio duration measure?

A) It is subject to huge swings in value since book values may change over time.

B) It assumes that the yield for all maturities changes by the same amount.

C) It is subject to huge swings in value since market values may change over time.

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Bond duration is calculated using market values; changes in book values are irrelevant.

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Which of the following is the most significant limitation of the portfolio duration measure? The assumption of:

A) a parallel shift in the yield curve.

B) a nonparallel shift in the yield curve.

C) a linear approximation of the actual price-yield function.

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The most significant limitation of portfolio duration is the assumption that the yield for all maturities changes by the same amount (a parallel shift in the yield curve).

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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

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Which of the following statements about portfolio duration is FALSE? It is:

A) a measure of interest rate risk.

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

C) a simple 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.

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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) 5.4.

B) 5.5.

C) 5.3.

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

(35/85 × 4.7) + (50/85 × 5.9) = 5.41