FRM Part II · FRM Exam Part II · VaR Mapping
A risk manager wants to estimate the VaR of a well-diversified portfolio of 200 US equities. Rather than modelling each stock separately, she maps the portfolio to a broad market index using each position's beta. What is the main reason this mapping is used?
Beta mapping reduces dimensionality: many stock positions are replaced by exposure to a few risk factors such as a market index. This shrinks the covariance matrix needed for VaR. It does not remove specific risk or force VaRs to add up.
- AIt replaces many individual positions with exposure to a small number of risk factors, reducing the dimension of the risk problemCorrect
- BIt eliminates the idiosyncratic risk of the portfolio so the VaR becomes exactly zero for that component
- CIt guarantees that the portfolio VaR equals the sum of the individual stock VaRs
- DIt converts the portfolio from a nonlinear to a linear payoff by construction of the index
Explanation
Beta mapping represents each stock by its sensitivity to a market index, so the portfolio is described by a few risk factors rather than hundreds of positions and a large covariance matrix. Specific risk is not set to zero; it is ignored or treated separately and is small only when the portfolio is diversified. Summing individual VaRs would ignore diversification.
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