Value at Risk

Your desk runs a $10Mequityportfolio.Dailylog-returnsareassumednormalwithmean$\mu = 0.0005$andstandarddeviation$\sigma = 0.02$.

Part A

Compute the 1-day 99% Value-at-Risk (VaR) using the parametric (variance-covariance) method.

Part B

Scale to the 10-day 99% VaR using the square-root-of-time rule.

Part C

A historical simulation of 1,000 daily returns produces a 1st percentile of $-5.8\%$. Compute the historical 1-day 99% VaR and comment on why it differs from Part A.