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FRM Part II · FRM Exam Part II · VaR Mapping

A bank holds a USD 10 million zero-coupon cash flow due in 4 years. Vertices exist at 3 years and 5 years. Under cash-flow mapping that preserves present value and risk, which feature of the allocation is correct?

The present value of the cash flow is split between the 3-year and 5-year vertices, with weights chosen so the mapped position's variance matches that of the original 4-year cash flow. Both value and risk are preserved, and correlation between the vertices is used in the calculation.

  1. AThe present value is split between the 3-year and 5-year vertices so that the portfolio variance equals that of the original cash flowCorrect
  2. BThe full present value is placed at the nearer 3-year vertex to be conservative
  3. CThe undiscounted amount of USD 10 million is split equally between the vertices
  4. DThe allocation is chosen so the two vertex positions have equal volatility weights regardless of correlation

Explanation

RiskMetrics-style mapping allocates present value to the two adjacent vertices, with weights solved so that the variance of the mapped position equals the variance of the original cash flow (using interpolated volatility and the correlation). Splitting undiscounted amounts or ignoring correlation breaks this.

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