Value at Risk (VaR) & Expected Shortfall (CVaR)
Historical simulation Β· 1-year lookback
VaR (Value at Risk) = the loss you should NOT exceed with a given confidence level. At 95% confidence, 1-day VaR of 3% means: on 19 out of 20 days, you won't lose more than 3% β but on 1 day you might.
CVaR (Expected Shortfall) = the average loss in the worst scenarios that break through the VaR threshold. CVaR is a more complete picture of tail risk because it asks "when VaR is breached, how bad does it actually get?"
Method: Historical simulation using actual daily returns β no normality assumption. Multi-day figures use overlapping return windows.
CVaR (Expected Shortfall) = the average loss in the worst scenarios that break through the VaR threshold. CVaR is a more complete picture of tail risk because it asks "when VaR is breached, how bad does it actually get?"
Method: Historical simulation using actual daily returns β no normality assumption. Multi-day figures use overlapping return windows.
Rolling 1-Day 95% VaR (3-month window)
Return Distribution (daily log returns)
Return Distribution Statistics
Skewness: Negative skew = left tail is fatter (more chance of large losses than large gains β typical for stocks). Positive skew = right tail fatter (lottery-like payoff).
Kurtosis (excess): > 0 means fatter tails than a normal distribution β extreme moves happen more often than models predict. Most stocks have positive kurtosis ("leptokurtosis"). This is why VaR based on normality is dangerously optimistic.
Fat tail %: Days with |return| > 2 standard deviations. Under normality, this should be ~4.55%. Higher = fatter tails.
Return Percentile Table