andytrader

A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes:

A) down 15.00%.

B) up 1.46%.

C) down 1.46%.

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∆P = [(-MD × ∆y) + (convexity) × (∆y)2] × 100
∆P = [(-6 × 0.0025) + (62.5) × (0.0025)2] × 100 = -1.461%

andytrader

A bond has a modified duration of 7 and convexity of 50. If interest rates decrease by 1%, the price of the bond will most likely:

A) increase by 6.5%.

B) increase by 7.5%.

C) decrease by 7.5%.

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Percentage Price Change = –(duration) (∆i) + convexity (∆i)2
therefore
Percentage Price Change = –(7) (–0.01) + (50) (–0.01)2=7.5%.

andytrader

A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes:

A) up 4.00%.

B) down 1.46%.

C) down 15.00%.

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ΔP/P = (-)(MD)(Δi) +(C) (Δi)2
= (-)(6)(0.0025) + (62.5) (0.0025)2 = -0.015 + 0.00039 = - 0.01461

andytrader

A bond’s duration is 4.5 and its convexity is 43.6. If interest rates rise 100 basis points, the bond’s percentage price change is closest to:

A) -4.50%.

B) -4.94%.

C) -4.06%.

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Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration × (change in yields)] + [convexity × (change in yields)2] = (-4.5)(0.01) + (43.6)(0.01)2 = -4.06%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.

andytrader

If a bond has a convexity of 120 and a modified duration of 10, what is the convexity adjustment associated with a 25 basis point interest rate decline?

A) -2.875%.

B) +0.075%.

C) -2.125%.

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Convexity adjustment: +(C) (Δi)2
Con adj = +(120)(-0.0025)(-0.0025) = +0.000750 or 0.075%

andytrader

One major difference between standard convexity and effective convexity is:

A) effective convexity is Macaulay's duration divided by [1 + yield/2].

B) effective convexity reflects any change in estimated cash flows due to embedded bond options.

C) standard convexity reflects any change in estimated cash flows due to embedded options.

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The calculation of effective convexity requires an adjustment in the estimated bond values to reflect any change in estimated cash flows due to the presence of embedded options. Note that this is the same process used to calculate effective duration.

andytrader

William Morgan, CFA, manages a fixed-income portfolio that contains several bonds with embedded options. Morgan would like to evaluate the sensitivity of his portfolio to large interest rate changes and will therefore use a convexity measure in addition to duration. The convexity measure that will best estimate the price sensitivity of Morgan’s portfolio is:

A) modified convexity.

B) either effective or modified convexity.

C) effective convexity.

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Effective convexity is the appropriate measure because it takes into account changes in cash flows due to embedded options, while modified convexity does not.

andytrader

The distinction between modified convexity and effective convexity is that:

A) effective convexity accounts for changes in cash flows due to embedded options, while modified convexity does not.

B) different dealers may calculate modified convexity differently, but there is only one formula for effective convexity.

C) modified convexity becomes less accurate as the change in yield increases, but effective convexity corrects for this.

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Effective convexity is the appropriate measure to use for bonds with embedded options because it takes into account the effect of the embedded options on the bond’s cash flows.

andytrader

Which of the following statements is most accurate concerning the differences between modified convexity and effective convexity?

A) Modified convexity takes into account changes in cash flows due to embedded options, while effective convexity does not.

B) For an option-free bond, modified convexity is slightly greater than effective convexity.

C) Effective convexity is most appropriate for bonds with embedded options.

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Effective convexity is most appropriate for bonds with embedded options because it takes into account changes in cash flows due to changes in yield, while modified convexity does not. For an option-free bond, modified convexity and effective convexity should be very nearly equal.

andytrader

The price value of a basis point (PVBP) for a 7-year, 10% semiannual pay bond with a par value of $1,000 and yield of 6% is closest to:

A) $0.92.

B) $0.28.

C) $0.64.

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PVBP = initial price – price if yield changed by 1 bps.

Initial price:	Price with change:
FV = 1000	FV = 1000
PMT = 50	PMT = 50
N = 14	N = 14
I/Y = 3%	I/Y = 3.005
CPT PV = 1225.92	CPT PV = 1225.28

PVBP = 1,225.92 – 1,225.28 = 0.64
PVBP is always the absolute value.