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

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

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

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

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

B) the market values of the bonds.

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.

andytrader

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.

andytrader

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

A) a nonparallel shift in the yield curve.

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

C) a parallel shift in the yield curve.

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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).

andytrader

How does the convexity of a bond influence the yield on the bond? All else the same, for a bond with high convexity investors will require:

A) a higher or lower yield depending on the bond's duration.

B) a higher yield.

C) a lower yield.

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Convexity is to the advantage of the bond holder because a high-convexity bond's price will decrease less when rates increase and will increase more when rates decrease than a low-convexity bond's price.

andytrader

Why is convexity a good thing for a bond holder? Because when compared to a low convexity bonds a high convexity bond:

A) is usually underpriced.

B) is more sensitive to interest rate changes, increasing the potential payoff.

C) has better price changes regardless of the direction of the yield change.

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Relative to a bonds with low convexity, the price of a bond with high convexity will increase more when rates decline and decrease less when rates rise.

andytrader

Convexity is more important when rates are:

A) high.

B) unstable.

C) low.

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Since interest rates and the price of bonds are inversely related, unstable interest rates will lead to larger price fluctuations in bonds. The larger the change in the price of a bond the more error will be introduced in determining the new price of the bond if only duration is used because duration assumes the price yield relationship is linear when in fact it is a curved convex line. If duration alone is used to price the bond, the curvature of the line magnifies the error introduced by yield changes, and makes the convexity adjustment even more important.

andytrader

A 7% coupon bond with semiannual coupons has a convexity in years of 80. The bond is currently priced at a yield to maturity (YTM) of 8.5%. If the YTM decreases to 8%, the predicted effect due to convexity on the percentage change in price would be:

A) +50 basis points.

B) +20 basis points.

C) +40 basis points.

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Convexity adjustment: +(Convexity)(change in i)2
Convexity adjustment = +(80)(-0.005)(-0.005) = +0.0020 or 0.20% or +20 basis points.