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FRM Part II · FRM Exam Part II · VaR Mapping

A 3-year zero-coupon cash flow of 1,000,000 (present value) must be mapped to vertices at 2 years and 5 years under the cash-flow mapping approach, preserving present value and risk (variance). The 2-year vertex has volatility (VaR rate) 0.60% and the 5-year vertex 1.50%, both with correlation 1. The 3-year volatility is interpolated linearly: 0.60% + (1/3)(0.90%) = 0.90%. What is the amount mapped to the 2-year vertex?

The amount mapped to the 2-year vertex is 666,667. With correlation of 1, risk is additive, so solving w×0.60% + (1−w)×1.50% = 0.90% gives w = 2/3 of the 1,000,000 present value, with the remaining 333,333 at the 5-year vertex.

  1. A400,000
  2. B600,000Correct
  3. C500,000
  4. D666,667

Explanation

With correlation 1, volatilities are additive: w·0.60 + (1−w)·1.50 = 0.90, so 1.50 − 0.90w = 0.90, giving w = 0.6667?? Check: 1.50 − 0.90w = 0.90 → w = 0.6667. Mapped to the 2-year vertex is 666,667, which is option 3, not 600,000.

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