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Home > Capital Markets Calculations > Value at Risk

Capital Markets Calculations

# Value at Risk

## What It Measures

Value at risk (VAR) is a useful tool for anyone looking to quantify the risk of a particular project or investment opportunity by measuring the potential loss that might be incurred over a certain period of time. VAR measures what is the most that an investor might lose, based on a specific level of confidence, over a specific period of time. For example, “What’s the most I can—with a 95% level of confidence—expect to lose over the next 12 months?”

## Why It Is Important

Most risk measurements focus on volatility whereas VAR focuses specifically on losses. It is commonly used to evaluate risk across a portfolio, but can also be applied to single indexes or anything that trades like a stock. VAR is important because it provides financial executives with a method of quantifying risk that is rigorous but also easily understood by nonfinancial executives.

## How It Works in Practice

The most common method of calculating VAR is the variance-covariance approach, sometimes referred to as “parametric VAR.” Parametric VAR is a percentile-based risk measure that measures the expected loss of a portfolio over a specific period of time, depending on the confidence. To calculate parametric VAR, use the following formula:

Value at risk = Mean × HPR + [Z-score × Std Dev × SQRT (HPR)]

where Mean is the average expected (or actual) rate of return, HPR is the holding period, Z-score is the probability, Std Dev is the standard deviation, and SQRT is the square root (of time).

To calculate the VAR of a portfolio worth \$1 million with an expected average annual return of 13%, a standard annual deviation of 20% (equal to a daily deviation of 1.26%), and a 95% confidence score, therefore, you would perform the following calculation:

13 × 1 + (95 × 1.26 × SQRT) = 6.037%

This results in a 10-day VAR of \$60,370. This means that your biggest potential loss over any 10-day period should not exceed \$60,370 more than 5% of the time, or approximately once a year.

• VAR is now increasingly accepted as the de facto standard for risk measurement. In 1993, when the Bank of International Settlements members met in Basel, they amended the Basel Accord to require banks to hold in reserve enough capital to cover 10 days of losses based on a 95% 10-day VAR.

• A simpler alternative approach to calculating VAR is using the historical method—this simply takes all empirical profit and loss history and puts the returns in order of size. If we had 100 historical returns, the VAR for a 99% confidence score would simply be the second largest loss. Critics argue that very few portfolios have enough historical data to make this approach reliable, however.

• A third approach to calculating VAR is the simulation or Monte Carlo method, which uses computerized simulation to generate thousands of possible returns from a parametric assumption, then ordering them in the same way as with an historical calculation.

• Although VAR is often described as the “maximum possible” loss, this only applies at a single percentage confidence score. It is always possible to lose more by applying a higher confidence level—this is known as the conditional value at risk (CVAR), expected shortfall, or extreme tail loss.

## Further reading on Value at Risk

### Books:

• Butler, Cormac. Mastering Value at Risk: A Step-by-Step Guide to Understanding and Applying VAR. London: FT Prentice Hall, 1999.
• Choudhry, Moorad. An Introduction to Value-at-Risk. 5th ed. Chichester, UK: Wiley, 2013.