Variance-Covariance Value at Risk

Article QuantStart

Summary

This article defines Value at Risk as a loss threshold for a portfolio over a specified time horizon and confidence level. It explains that VaR can be applied to an individual strategy or a larger portfolio, with the horizon chosen to reflect the time needed to liquidate positions. The featured calculation is the variance-covariance method: estimate historical mean and standard deviation of returns, assume a normal distribution, and use its quantile to estimate the loss threshold for a portfolio value. A worked example applies the method to daily returns for a large US equity position and reports a VaR estimate at a stated confidence level.

The article outlines VaR’s practical appeal: it is relatively simple to calculate, interpret, adjust by horizon, and use to constrain strategy or portfolio risk. Its limits are equally central. The standard method assumes normally distributed returns and relies on volatility and correlation estimates that change over time. VaR describes a threshold but not the size of losses beyond it, and it is not designed to capture extreme events or future regime shifts. The author recommends combining it with other risk controls and previews Monte Carlo, historical bootstrap, and Expected Shortfall methods.

Key ideas

VaR estimates a portfolio loss threshold for a chosen confidence level and time horizon.
The variance-covariance approach uses return mean and volatility with a normality assumption.
Historical volatility and correlations can change, limiting the reliability of the estimate.
VaR does not quantify losses beyond its threshold and does not capture extreme tail events well.
The article recommends using VaR alongside broader risk controls and other risk measures.

Variance-Covariance Value at Risk for Trading Portfolios

Summary

Key ideas

Tags