What is the formula for calculating Value at Risk (VaR)?

The formula for calculating Value at Risk (VaR) involves using the mean, standard deviation, and a z-value corresponding to the desired confidence level. In the context of normally distributed returns, the correct relationship incorporates the standard deviation and a multiplier that reflects the z-value, which indicates how many standard deviations away from the mean you need to go to capture the desired level of risk.

The typical formula used is:

VaR = mean - (z-value * standard deviation)

This formula captures the downside risk — it provides a threshold loss level that should not be exceeded with a given probability over a defined time period. Although the provided answer suggests a multiplication of the mean by the standard deviation and the z-value, this does not align with the conventional understanding of how VaR is derived, as VaR is concerned primarily with potential losses rather than scaling the mean.

The correct formulation shows that VaR is not simply a multiplication of these variables but instead a calculation based on the dispersion of returns measured by standard deviation and the confidence level selected. Thus, understanding the foundational elements of risk management and the construction of the VaR metric is essential in financial risk analysis.