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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A portfolio's VaR is $10 million. Position X has a component VaR of $6 million and a standalone VaR of $5 million. Which conclusion is most supported?

Position X contributes more risk inside the portfolio than it would alone, which happens when it is highly correlated with the portfolio, which is the more volatile whole. A hedge would show a negative component VaR, and component VaR may legitimately exceed standalone VaR.

  1. APosition X is positively correlated enough with the rest of the portfolio that it contributes more risk than if held aloneCorrect
  2. BPosition X is a hedge against the rest of the portfolio
  3. CPosition X has a negative marginal VaR
  4. DPosition X's component VaR is inconsistent, as it must be below standalone VaR

Explanation

Component VaR equals standalone VaR times the correlation of X with the portfolio times a ratio of volatilities, so it exceeds standalone VaR when the position's correlation with the portfolio times portfolio-to-position vol ratio is above one. Here 6/5 exceeds 1, so X adds more than alone, which is possible when portfolio volatility is larger than X's and correlation is high. A hedge would have a negative component.

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