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FRM Part II · FRM Exam Part II · VaR Mapping

A portfolio manager holds a single zero-coupon bond maturing in 6 years. The risk system has vertices only at 5 and 7 years. Under the principle of mapping that preserves the market value and the risk (variance) of the original position, how should the bond's present value be allocated?

The present value should be split between the 5- and 7-year vertices using weights that preserve both the market value and the variance of the original cash flow. This uses interpolated volatility and the vertices' correlation, rather than an arbitrary equal split or mapping to one vertex.

  1. AEntirely to the 5-year vertex because it is the nearest below the maturity
  2. BSplit between the 5- and 7-year vertices with weights chosen so that the total value is preserved and the mapped position's variance equals that of the original cash flowCorrect
  3. CSplit 50/50 between the vertices regardless of volatilities, since 6 is the midpoint
  4. DAllocated to the 7-year vertex only, to be conservative

Explanation

Variance-preserving (cash-flow) mapping chooses weights so that the sum of mapped values equals the original present value and the variance of the mapped position equals the variance of the original cash flow, using interpolated volatility and the vertex correlation. A simple 50/50 split ignores volatility differences, and single-vertex mapping misstates risk.

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