Value at Risk

Value at Risk (VaR) is a statistical technique used to measure the level of financial risk within an investment portfolio, over a specific timeframe. It measures in three variables—the amount of potential loss, the probability of the loss, and the timeframe.

As an example, a portfolio may have a 1-month 5 percent VaR of $1 million. This means that there is a 5 percent probability that the portfolio will fall in value by more than $1 million over a 1-month period. Likewise, it also means that a $1 million loss should be expected once every 20 months.

The most common means of measuring VaR is by calculating the volatility. There are three common means of calculating the volatility: using historical data, variance-covariance, and the Monte Carlo simulation. We will examine the variance-covariance method here, as there is a straightforward formulation for the VaR once you have historical returns.

VaR assumes that returns are normally distributed. The returns for a stock or portfolio...