Investor A manages a portfolio of bonds with duration of 10 years. Investor B manages a portfolio of bonds with duration of 20 years. In all other dimensions, the two portfolios are identical. If interest rates go up next year (and nothing else changes), what will happen to the value of these portfolios:

Question

BlackTom AI · Accepted Answer

Duration measures approximate interest-rate sensitivity: the (modified) duration gives the percent change in bond/portfolio price for a 1 percentage-point (100 basis point) parallel change in yields. The sign is negative: when yields rise, prices fall. Thus percentage price change ≈ −Duration × Δy (with Δy expressed in decimal form).

Step-by-step reasoning with calculations:
1. Write the approximation: ΔP/P ≈ −D × Δy.
2. For Investor A (D = 10 years) and a 1.00% rise in rates (Δy = +0.01):
   ΔP/P ≈ −10 × 0.01 = −0.10 = −10.0% (price falls about 10%).
3. For Investor B (D = 20 years) with the same 1.00% rise:
   ΔP/P ≈ −20 × 0.01 = −0.20 = −20.0% (price falls about 20%).
4. For smaller moves (e.g., Δy = +0.005 or 0.5%), A loses ≈ −5% and B loses ≈ −10% — the proportional relationship holds.

Why this is correct: Duration is a linear sensitivity measure; all else equal, a longer-duration portfolio exhibits greater percentage price sensitivity to interest-rate changes. Since B’s duration (20) is twice A’s (10), B’s percentage loss from the same rise in rates will be roughly twice as large.

Other options that might be offered are incorrect for these reasons:
- “Both portfolios will suffer but A declines more” contradicts the duration rule (longer duration → greater sensitivity).
- “Only one loses value” is wrong because rising yields lower the value of any bond (or bond portfolio) with positive duration.
- “No change” is wrong because a change in yields directly affects present values via discounting.

Conclusion: Both portfolios will suffer a loss and the percentage decline in value will be stronger for portfolio B, which matches the provided correct answer.

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