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# What Is a Conditional Value-At-Risk?

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• Written By: Alex Newth
• Edited By: Angela B.
2003-2018
Conjecture Corporation
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Conditional value-at-risk (CVaR) is a math equation that helps investors and businesses understand the maximum amount of risk and loss that can be incurred before devastating losses occur. With the conditional value-at-risk formula, maximum loss is defined as when the loss is more than the value being assessed. Though the equation can be adjusted, this commonly is made for a 95 percent confidence level and generally is very accurate. Unlike the value-at-risk (VaR) equation, this formula gives an exact figure of loss. This also shows a range of loss, from minimal loss to maximum.

One of the worst things that can happen to an investor or business is to encounter maximum loss, which means the value that is being held has already been lost. For example, if an investor is holding an investment of \$1,000 US Dollars (USD), but he or she has already lost \$1,000 USD or more, then maximum loss has occurred and he or she has lost the entire investment. This typically continues to trend downward, to further loss, and conditional value-at-risk helps an investor or business understand when to let go of investments or deals before they cause this massive loss.

When it comes to complex equations with finances and other subjects, most formulas are not 100 percent accurate and a confidence level is used to let the business or investor know how much he or she should be vested in the equation. While the conditional value-at-risk formula can have a lower confidence level for a broader result, the common confidence is 95 percent. This tends to make rather accurate risk estimates. CVaR is typically the mean of VaR plus the maximum loss a business or investor can tolerate.

The VaR formula is similar to conditional value-at-risk but commonly is not as accurate. This is because the VaR only reports the percentage of loss a business can encounter before major loss occurs. With CVaR, the formula reports an exact number before loss becomes too high to sustain.

CVaR also gives the investor or business a range of loss. The lowest point of loss, known as minimum loss, is when the investor or business is trending toward losing the entire value. At this point, it may be good to let go of the investment or deal before it gets worse. Maximum loss is at the highest point of loss, and by that point the investor or business has already lost the money and is usually losing more as time goes by.