medium · Quantitative Finance prob-stats
An analyst estimates the 1-day 99% Expected Shortfall (ES) for a portfolio with normal losses having mean μ_L and standard deviation σ_L.
Compared to the 99% Value-at-Risk (VaR), which of the following is true?
- ES is smaller than VaR because it is a conditional expectation which 'smooths' the extreme outliers.
- ES is equal to VaR for the normal distribution because the distribution is symmetric.
- ES cannot be compared to VaR because ES is not a subadditive measure.
- ES is always greater than VaR because it averages all losses in the tail beyond the VaR threshold.
Sign up free to see the explanation and track your rank →
More Quantitative Finance prob-stats practice
- What is the estimated OLS slope hatβ?
- Assuming 252 trading days in a year, what is the annualized historical volatility?
- If the correlation between two assets is ρ = 0.6, what is the R^2 of a linear regression o
- If the slope β is positive, what is the correlation coefficient ρ between x and y?
- What is the defining property of the 'Cumulative Distribution Function' F(x)?
- Which 'standardized moment' should they measure to quantify this?
- What is the probability the stock outperforms given the signal fired?
- Which statistical property describes a time series where the mean, variance, and autocorre