ETF Tracking Error: Tail Probability and VaR

Statistics · Easy · Free problem
The daily tracking error of an ETF (its return relative to its benchmark) is modeled as $X \sim N(0, \sigma^2)$ with $\sigma = 0.40\%$. (i) Compute $P(|X| > 1.00\%)$ in terms of the standard normal CDF $\Phi$. (ii) Compute the one-day 99% Value at Risk of $-X$ (i.e., the loss from the ETF underperforming its benchmark) and express the answer in basis points.

Open the full interactive solver, hints, and worked solution →