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Answer: The VaR estimated using the duration mapping approach replaces the portfolio with a zero-coupon bond whose maturity equals the duration of the portfolio.
**Explanation:** **B is correct.** The duration mapping approach simplifies the portfolio by replacing it with a single zero-coupon bond whose maturity equals the duration of the portfolio. This approach captures the interest rate sensitivity of the portfolio through duration. **A is incorrect** because principal mapping actually *overstates* the true risk of a portfolio. By ignoring coupon payments, principal mapping assumes all cash flows occur at maturity, which increases the portfolio's effective duration and thus overstates VaR. **C is incorrect** because the difference between principal mapping and duration mapping VaR estimates arises from the treatment of intervening cash flows, not from correlation adjustments. Principal mapping ignores intervening cash flows while duration mapping implicitly accounts for them. **D is incorrect** because cash-flow mapping is actually *more accurate* than duration mapping. Cash-flow mapping accounts for the timing of all cash flows and incorporates correlations between different maturity points, making it the most precise approach among the three mapping methods.
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An analyst at a fixed-income investment company is evaluating different ways the company uses to estimate the VaR of its corporate bond portfolios. The portfolios consist of a large number of bonds with a wide range of maturities. The analyst examines the possibility of using a mapping approach to simplify the estimation process. Which of the following statements would the analyst be correct to make regarding the approaches to mapping fixed-income portfolios?
A
The VaR estimated using the principal mapping approach understates the true risk of a portfolio since it ignores coupon payments and any risk associated with them.
B
The VaR estimated using the duration mapping approach replaces the portfolio with a zero-coupon bond whose maturity equals the duration of the portfolio.
C
The VaR estimated using the principal mapping approach differs from the undiversified VaR estimated using the duration mapping approach due to an adjustment made for correlations.
D
The VaR estimated using the cash-flow mapping approach is less accurate than the VaR estimated using the duration mapping approach since it does not account for the timing of cash flows.
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