andytrader

With respect to an option-free bond, when interest-rate changes are large, the duration measure will overestimate the:

A) fall in a bond's price from a given increase in interest rates.

B) increase in a bond's price from a given increase in interest rates.

C) final bond price from a given increase in interest rates.

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When interest rates increase by 50-100 basis points or more, the duration measure overestimates the decrease in the bond’s price.

andytrader

For a given change in yields, the difference between the actual change in a bond’s price and that predicted using the duration measure will be greater for:

A) a bond with less convexity.

B) a bond with greater convexity.

C) a short-term bond.

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Duration is a linear measure of the relationship between a bond’s price and yield. The true relationship is not linear as measured by the convexity. When convexity is higher, duration will be less accurate in predicting a bond’s price for a given change in interest rates. Short-term bonds generally have low convexity.

andytrader

For a given bond, the duration is 8 and the convexity is 50. For a 60 basis point decrease in yield, what is the approximate percentage price change of the bond?

A) 4.98%.

B) 4.62%.

C) 2.52%.

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The estimated price change is -(duration)(∆y) + (convexity) × (∆y)2 = -8 × (-0.006) + 50 × (-0.0062) = +0.0498 or 4.98%.

andytrader

A bond has a duration of 10.62 and a convexity of 91.46. For a 200 basis point increase in yield, what is the approximate percentage price change of the bond?

A) -17.58%.

B) -24.90%.

C) -1.62%.

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The estimated price change is:
-(duration)(∆y) + (convexity) × (∆y)2 = -10.62 × 0.02 + 91.46 × (0.022) = -0.2124 + 0.0366 = -0.1758 or –17.58%.

andytrader

If a Treasury bond has a duration of 10.27 and a convexity of 71.51. Which of the following is closest to the estimated percentage price change in the bond for a 125 basis point increase in interest rates?

A) -13.956%.

B) -9.325%.

C) -11.718%.

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The estimated percentage price change = the duration effect plus the convexity effect.
The formula is:
[–duration × (Δy)] + [convexity × (Δy)2].
Therefore, the estimated percentage price change is:
[–(10.27)(1.25%)] + [(71.51)(0.0125)2] = –12.8375 + 1.120% = –11.7175%.

andytrader

An investor gathered the following information about an option-free U.S. corporate bond:

• Par Value of $10 million
• Convexity of 45
• Duration of 7

If interest rates increase 2% (200 basis points), the bond’s percentage price change is closest to:

A) -14.0%.

B) -12.2%.

C) -15.8%.

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Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration × (change in yields)] + [convexity × (change in yields)2] = [(-7)(0.02) + (45)(0.02)2] = -0.12 = -12.2%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.

andytrader

Assume that a straight bond has a duration of 1.89 and a convexity of 15.99. If interest rates decline by 1% what is the total estimated percentage price change of the bond?

A) 1.56%.

B) 2.05%.

C) 1.89%.

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The total percentage price change estimate is computed as follows:
Total estimated price change = -1.89 × (-0.01) × 100 + 15.99 × (-0.01)2 × 100 = 2.05%

andytrader

Which of the following statements about the market yield environment is most accurate?

A) As yields increase, bond prices rise, the price curve flattens, and further increases in yield have a smaller effect on bond prices.

B) For a given change in interest rates, bond price sensitivity is lowest when market yields are already high.

C) Positive convexity applies to the percentage price change, not the absolute dollar price change.

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The price volatility of noncallable (option-free) bonds is inversely related to the level of market yields. In other words, when the yield level is high, bond price volatility is low and vice versa.
The statement beginning with, As yields increase. . . should continue . . .bond prices fall. Positive convexity (bond prices increase faster than they decrease for a given change in yield) applies to both absolute dollar changes and percentage changes.

andytrader

Consider a bond with a duration of 5.61 and a convexity of 21.92. Which of the following is closest to the estimated percentage price change in the bond for a 75 basis point decrease in interest rates?

A) 4.33%.

B) 4.21%.

C) 4.12%.

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The estimated percentage price change is equal to the duration effect plus the convexity effect. The formula is: [–duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [–(5.61)(–0.0075)] + [(21.92)(-0.0075)2] = 0.042075 + 0.001233 = 0.043308 = 4.33%.

andytrader

A bond has a convexity of 25.72. What is the approximate percentage price change of the bond due to convexity if rates rise by 150 basis points?

A) 0.71%.

B) 0.26%.

C) 0.58%.

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The convexity effect, or the percentage price change due to convexity, formula is: convexity × (Δy)2. The percentage price change due to convexity is then: (25.72)(0.015)2 = 0.0058.