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FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management

A manager considers adding a new position to a portfolio. She computes portfolio VaR before and after the addition and takes the difference. Which measure is this, and how does it relate to marginal VaR for a large trade?

This is incremental VaR, the change in portfolio VaR from adding the position. Marginal VaR times trade size approximates it only for small trades, because marginal VaR is a derivative; for large trades the nonlinear effect makes the approximation inaccurate.

  1. AIncremental VaR; it is approximated by marginal VaR times trade size only for small tradesCorrect
  2. BComponent VaR; it equals marginal VaR times trade size exactly
  3. CStand-alone VaR; it always exceeds marginal VaR
  4. DIncremental VaR; it always equals marginal VaR times trade size

Explanation

The before-and-after difference is incremental VaR. Marginal VaR is a first-order (derivative) measure, so marginal VaR times size approximates incremental VaR well only for small changes. For large trades, nonlinearity makes the approximation poor.

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