# Value at Risk

Value-at-risk (VaR) is the minimum loss that would be expected a certain percentage of the time over a certain period of time given the assumed market conditions. It can be expressed in either currency units or as a percentage of portfolio value. VaR can be viewed as a probabilistic measure of the range of values a firm’s portfolio could lose due to market volatility. This volatility includes effects from changes in interest rates, exchange rates, commodities prices, and other general market risks.

A typical reporting of VAR would be the following statement:

The 5% VaR of a portfolio is \$2 million over a one-day period.

The following three points are important in understanding the concept of VaR:

– VaR can be measured in either currency units (in this example, the USD) or in percentage terms. In this example, if the portfolio value is \$100 million, the VaR expressed in percentage terms would be 2% (\$2 million/\$100 million = 0.02).

– VaR is a minimum loss. This point cannot be emphasized enough. VaR is often mistakenly assumed to represent how much one can lose. If the question is, “how much can one lose?” there is only one answer: the entire portfolio. In a \$100 million portfolio, assuming no leverage, the most one can lose is \$100 million.

– A VaR statement references a time horizon: losses that would be expected to occur over a given period of time. In this example, that period of time is one day. (If VaR is measured on a daily basis, and a typical month has 20–22 business days, then 5% of the days equates to about one day per month.)

These are the three explicit elements of a VaR statement—the frequency of losses of a given minimum magnitude expressed either in currency or percentage terms. Thus, the VaR statement can be rephrased as follows: A loss of at least \$2 million would be expected to occur about once every month.

A 5% VaR is often expressed as its complement—a 95% level of confidence. Commonly, the notion, the 5% VaR, is used, but we should be mindful that it does imply a 95% level of confidence.

## History

J.P. Morgan Chairman Dennis Weatherstone demanded a simple report at the end of each day on how the firm’s position could change due to market risk. Morgan analysts came up with VAR as this measure and incorporated it into what became known as the 4:15 report, the report was given to Weatherstone daily at that time to summarize the day’s market events.

The Washington-based Group of Thirty, in a 1993 study headed by Weatherstone, Derivatives: Practices and Principles, recommended using VAR as a means of identifying a firm’s overall market risk. Since then, VAR has skyrocketed in popularity and there are few financial institutions which do not envisage making it part of their day-to-day reporting. In fact, many financial regulators, such as the European Economic and Monetary Union, require banks to report their VARs on a regular basis.

Because there are a variety of ways to calculate VAR, J.P. Morgan sought to make its method the industry standard. In 1994 it began giving away copies of RiskMetrics, a program it developed to calculate VAR. Morgan’s Internet web site includes a RiskMetrics section, where individuals or firms can download parts of the program. This initial move into the VAR market did not stop other investment banks from creating their own VAR calculation programs and peddling them to other financial organizations. Many of these programs differ from RiskMetrics, and while RiskMetrics is widely recognized in VAR measurement, the industry has yet to settle on a single calculation method.