Reading 69: Introduction to the Measurement of Interest R points, interest, black, price

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6.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 4.00%.

C)   up 1.46%.

D)   down 1.46%.

7.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)   0.26%.

B)   0.71%.

C)   0.58%.

D)   1.21%.

8.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)   4.2092%.

B)   4.3275%.

C)   0.0433%.

D)   4.1214%.

9.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)   12.736%.

C)   -11.718%.

D)   -9.325%.

10.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)   -1.62%.

B)   -2.04%.

C)   -17.58%.

D)   -24.90%.

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答案和详解如下：

6.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 4.00%.

C)   up 1.46%.

D)   down 1.46%.

The correct answer was D)

ΔP/P = (-)(MD)(Δi) +(C) (Δi)²

= (-)(6)(0.0025) +(62.5) (0.0025)² = - 0.015 + 0.00039 = - 0.01461

7.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)   0.26%.

B)   0.71%.

C)   0.58%.

D)   1.21%.

The correct answer was C)

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.

8.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)   4.2092%.

B)   4.3275%.

C)   0.0433%.

D)   4.1214%.

The correct answer was B)

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:  [–(5.61)(–0.75%)] + [(21.92)(0.0075)²] = 4.2075% + 0.12% = 4.3275%.

9.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)   12.736%.

C)   -11.718%.

D)   -9.325%.

The correct answer was C)

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%.

10.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)   -1.62%.

B)   -2.04%.

C)   -17.58%.

D)   -24.90%.

The correct answer was C)

The estimated price change is

–(duration)(∆y)+(convexity)*(∆y)² = -10.62*.02+91.46*(0.02²) = -0.2124+0.0366 = -0.1758 or –17.58%.