Many organizations use value-at-risk (VaR) metrics when assessing risk exposure. This is a statistical risk management technique that measures the maximum loss that an investment portfolio may face to some extent within a particular time frame. Confidence.

VaR modeling determines the potential loss of the entity being evaluated and the defined probability of loss. One measures VaR by assessing the amount of potential loss, the probability of occurrence of the amount of loss, and the time frame.

For example, a financial company may determine that an asset has a monthly VaR of 2%. This means that there is a 3% chance that the value of the asset will decline by 2% over the course of a month. Converting a 3% probability of occurrence to a daily rate can result in a 2% loss per day per month.

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Important point

- Value at risk (VaR) is a statistical method for determining the potential loss that an asset, portfolio, or company may incur over a period of time.
- The parametric approach to VaR uses mean variance analysis to predict future outcomes based on past experience.
- The calculation of parametric VaR is simple, but we assume that the possible results are usually distributed around the mean.

## Parametric vs. Nonparametric VaR

Nonparametric methods do not require the population being analyzed to meet specific assumptions or parameters. This gives analysts a great deal of flexibility and allows them to include qualitative or ordinal variables. Nonparametric statistics have the advantage of having to meet some assumptions, but they are not as powerful as parametric statistics. This means that even if one actually exists, it may not show the relationship between the two variables. As a result, most risk managers prefer a more quantitative approach.

The parametric method, also known as the covariance method, is a risk management method for calculating the VaR of an asset portfolio that first identifies the mean or expected value and standard deviation of the investment portfolio. The parametric method examines the price fluctuations of an investment over the lookup period and uses probability theory to calculate the maximum loss of the portfolio. The value-at-risk diversified covariance method calculates the standard deviation of investment or security price fluctuations. The maximum loss within the specified confidence level is calculated assuming that the stock price returns and volatility follow a normal distribution.

## One security example

Consider a portfolio that contains only one security ABC. Suppose $ 500,000 is invested in stock ABC. The standard deviation of 252 days of stock ABC, or one trading year, is 7%. According to the normal distribution, the z-score for the one-sided 95% confidence level is 1.645.

The value at risk of this portfolio

$ 57,575 = ($ 500,000 * 1.645 * .07).

Therefore, with 95% confidence, the maximum loss will not exceed $ 57,575 in a particular trading year.

## Two securities examples

The value at risk of a portfolio containing two securities can be determined by first calculating the volatility of the portfolio. Multiply the square of the weight of the first asset by the square of the standard deviation of the first asset and add it to the square of the weight of the second asset multiplied by the square of the standard deviation of the second asset. increase. Add that value to 2 and multiply by the weights of the first and second assets, the correlation coefficient between the two assets, the standard deviation of asset 1, and the standard deviation of asset 2. Then multiply the square root of that value by the z-score and portfolio value.

For example, suppose a risk manager wants to calculate value at risk using a one-day period parametric method. The weight of the first asset is 40% and the weight of the second asset is 60%. The standard deviation is 4% for the first asset and 7% for the second asset. The correlation coefficient between the two is 25%. The Z score is -1.645. The value of the portfolio is $ 50 million.

With a 95% confidence level, the parametric values at risk over a one-day period are:

$ 3.99 million = ($ 50,000,000 * -1.645) * √ (0.4 ^ 2 * 0.04 ^ 2) + (0.6 ^ 2 * 0.07 ^ 2) +[2(0.4*0.6*0.25*0.04*0.07*)]

## Conclusion

If the portfolio has multiple assets, their volatility is calculated using the matrix. The covariance matrix is calculated for all assets. The asset weight vector in the portfolio is multiplied by the transpose of the asset weight vector multiplied by the covariance matrix of all assets.

In practice, VaR calculations are usually done through a financial model. Modeling capabilities depend on whether VaR is calculated for a portfolio with one security, two security, or three or more securities.