LOS g, (Part 2): Estimate a bond's percentage price change, given the bond's duration and convexity and a specified change in interest rates.

Q1. 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%.

Q2. 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)   -24.90%.

B)   -1.62%.

C)   -17.58%.

Q3. 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)   -11.718%.

B)   -13.956%.

C)   -9.325%.

Q4. 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%.

Q5. 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)   0.58%.

C)   0.26%.

LOS g, (Part 2): Estimate a bond's percentage price change, given the bond's duration and convexity and a specified change in interest rates.fficeffice" />

Q1. 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%.

Correct answer is A)

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

Q2. 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)   -24.90%.

B)   -1.62%.

C)   -17.58%.

Correct answer is C)

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%.

Q3. 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)   -11.718%.

B)   -13.956%.

C)   -9.325%.

Correct answer is A)

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%.

Q4. 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%.

Correct answer is A)

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%.

Q5. 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)   0.58%.

C)   0.26%.

Correct answer is B)

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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