Reading 66: Introduction to the Measurement of Interest Rate 2010, face, percentage, currently, change

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LOS g: Describe the convexity measure of a bond.

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.

 

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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) decrease by 7.5%.

C) increase by 7.5%.

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Percentage Price Change = –(duration) (?i) + convexity (?i)²

therefore

 ercentage Price Change = –(7) (–0.01) + (50) (–0.01)²=7.5%.

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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) 1.89%.

C) 2.05%.

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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%

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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.

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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) down 1.46%.

C) up 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%

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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.

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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 15.00%.

C) down 1.46%.

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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

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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) -4.06%.

B) -4.50%.

C) -4.94%.

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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.

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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) -12.2%.

B) -14.0%.

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.

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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%.