Variance-Covariance Value at Risk for Trading Portfolios

Summary

The document explains Value at Risk (VaR) as a loss threshold for a portfolio over a specified period at a chosen confidence level. It outlines common uses, including setting risk limits for individual strategies and portfolios, comparing risk across instruments, and communicating potential losses. It introduces three calculation approaches: variance-covariance, Monte Carlo, and historical bootstrapping, then focuses on variance-covariance VaR. This method estimates a return quantile using the historical mean and standard deviation under a normal-distribution assumption, then scales the result by portfolio value. An example uses historical daily returns for a large US bank stock to illustrate the calculation.

The article cautions that VaR does not describe losses beyond its threshold and that standard estimates rely on typical market conditions, stable estimates of volatility and correlation, and normally distributed returns. Historical inputs may miss regime changes. It recommends combining VaR with other risk controls; alternative VaR methods and Expected Shortfall are mentioned but not developed.

Key ideas

• VaR estimates a portfolio loss threshold for a chosen confidence level and time horizon.
• The variance-covariance approach uses estimated mean and volatility under a normality assumption.
• VaR can support risk limits at the strategy, instrument, or portfolio level.
• VaR does not indicate how severe losses beyond its threshold may be.
• Historical estimates can fail during extreme events or changing market regimes.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.