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FRM Part II · FRM Exam Part II · VaR Mapping

A portfolio manager compares the VaR of a 10-year coupon bond under principal mapping and under cash flow mapping, with all else equal and imperfectly correlated vertices. Which outcome is most likely?

Principal mapping typically gives a higher VaR. It places the full bond value at the long-maturity vertex, which has higher price volatility, ignoring that coupons arrive earlier and that cash flows at different vertices are imperfectly correlated, as cash flow mapping captures.

  1. APrincipal mapping gives a lower VaR because it ignores the coupons
  2. BPrincipal mapping gives a higher VaR because it treats the whole value as exposed to the long-maturity vertexCorrect
  3. CBoth give identical VaR because market value is the same
  4. DCash flow mapping gives a higher VaR because of diversification losses

Explanation

A coupon bond has duration well below its maturity, with much of its value in earlier cash flows. Principal mapping puts all value at the 10-year vertex, which has the highest volatility, so risk is overstated. Cash flow mapping reflects shorter cash flows and imperfect correlation.

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