MediumPortfolio & Risk

Value at Risk (Normal)

Goldman SachsMorgan StanleyMillennium Management

A portfolio’s daily return is Normal with mean 0 and standard deviation 2%. What is the 1-day 95% Value at Risk, expressed as a percent of portfolio value? (e.g. 3.29)

Approach

The 95% quantile of a standard normal is ≈ 1.645.

VaR (mean 0) = z · σ.