Consider the following two Treasury securities: Bond A is sold at $120 with modified duration = 5, and Bond B is sold at $80 with modified duration = 7. Which bond will have greater dollar price change for a 50-basis-point change in interest rates?

Question

BlackTom AI · Accepted Answer

Modified duration measures the approximate percentage price change for a small change in yield: ΔP/P ≈ −(Modified Duration) × Δy. Use Δy in decimal form (50 basis points = 0.005). The negative sign indicates price falls when yields rise; here we compare magnitudes.

Step-by-step calculations:

1) Convert the interest-rate change:
   - 50 basis points = 0.50% = 0.005 (decimal).

2) Bond A:
   - Modified duration = 5.
   - Approximate percentage price change = −5 × 0.005 = −0.025 = −2.5%.
   - Dollar price change = (percentage change) × (price) = 0.025 × $120 = $3.00 (price decreases by $3.00).

3) Bond B:
   - Modified duration = 7.
   - Approximate percentage price change = −7 × 0.005 = −0.035 = −3.5%.
   - Dollar price change = 0.035 × $80 = $2.80 (price decreases by $2.80).

Why Bond A is correct:
- Although Bond B has the higher modified duration (so a larger percentage sensitivity), Bond A’s higher price ($120 vs $80) produces the larger absolute (dollar) price change. $3.00 (Bond A) > $2.80 (Bond B), so Bond A experiences the greater dollar price change for a 50-basis-point move.

Why the other options are incorrect:
- “Bond B” is incorrect because its dollar change ($2.80) is smaller than Bond A’s ($3.00).
- “Both bonds will have the same dollar price change” is incorrect because the computed dollar changes differ.
- “Cannot be determined” is incorrect because modified duration and prices provide enough information for the approximation.

Conclusion: The bond with the greater dollar price change for a 50-basis-point move is Bond A, which matches the provided answer.

Consider the following two Treasury securities: Bond A is sold at $120 with modified duration = 5, and Bond B is sold at $80 with modified duration = 7. Which bond will have greater dollar price change for a 50-basis-point change in interest rates?单项选择题

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