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FRM Part II · FRM Exam Part II · VaR Mapping

Which situation would make single-index beta mapping least appropriate for measuring the VaR of an equity portfolio?

Beta mapping is least suitable for a concentrated 10-stock small-cap portfolio in one sector, because much of its risk is idiosyncratic or sector-driven and not explained by the market index. The mapped VaR would understate true risk, unlike a broad diversified portfolio.

  1. AA portfolio of 10 stocks concentrated in one small-cap sector with high idiosyncratic volatilityCorrect
  2. BA broad portfolio of 500 large-cap stocks tracking the index
  3. CA portfolio whose betas are stable and estimated with high R-squared
  4. DA well-diversified portfolio of large-cap stocks across sectors

Explanation

Beta mapping captures only systematic risk. A concentrated portfolio in one sector has large specific and sector-specific risk not explained by the market index, so VaR would be understated. Diversified, high R-squared portfolios are well represented by the index.

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