risk-metrics-calculation

Create a RiskMetrics instance with a pandas Series of periodic returns, then call var_historical(confidence) for historical VaR and cvar(confidence) for expected shortfall. Parametric and Cornish-Fisher VaR variants are also available for different distribution assumptions.

Use the PortfolioRisk class with a DataFrame of asset returns and call risk_parity_weights(). It minimizes the squared difference between each asset's risk contribution and an equal risk budget using scipy's SLSQP optimizer with weights constrained to sum to one.

The Sharpe ratio divides excess return over the risk-free rate by total volatility, while the Sortino ratio divides it by downside deviation only. Sortino penalizes only harmful volatility below a threshold, making it preferable when return distributions are asymmetric.

No, historical VaR uses empirical percentiles of the return series and makes no distribution assumption. The parametric VaR method assumes normality, while the Cornish-Fisher variant adjusts for skewness and kurtosis in the data.

VaR gives only a loss threshold at a confidence level and says nothing about losses beyond it. CVaR (expected shortfall) averages losses in the tail, and stress testing against historical crises captures regime behavior that VaR misses.