Skip to content

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

A portfolio has two assets with weights 60% and 40%, volatilities 20% and 10%, and correlation 0.5. Portfolio value is USD 100 million. Using z = 2.33 and a one-year horizon, what is the component VaR of the 40% asset, closest to?

Portfolio volatility is 14.42%. The second asset's covariance with the portfolio is 0.010, so component VaR is 0.4 x 0.010/0.1442 x 2.33 x 100, about USD 6.5 million, closest to USD 6.0 million. Stand-alone VaR of USD 9.3 million ignores diversification.

  1. AUSD 2.4 million
  2. BUSD 6.0 millionCorrect
  3. CUSD 9.3 million
  4. DUSD 5.0 million

Explanation

Variance = 0.36x0.04 + 0.16x0.01 + 2x0.6x0.4x0.5x0.2x0.1 = 0.0144+0.0016+0.0048 = 0.0208; sigma = 14.42%. Portfolio VaR = 2.33x0.1442x100 = 33.6m. Covariance of asset 2 with portfolio = 0.6x0.5x0.2x0.1 + 0.4x0.01 = 0.006+0.004 = 0.010. Component = 0.4 x 0.010/0.1442 x 2.33 x 100 = 6.46m. Closest option is 6.0 million. Stand-alone VaR would be 9.3 million, which ignores diversification.

Did you get it right without looking?

One question tells you little. A timed set on VaR and Risk Budgeting in Investment Management shows your real accuracy, how long you take and where you lose marks.

Practise VaR and Risk Budgeting in Investment ManagementFree diagnostic mock

More VaR and Risk Budgeting in Investment Management questions