What is Value at Risk (VaR) and How to Calculate it?

What is Value at Risk (VAR)?

Value At Risk is a risk management approach and metric that calculates the highest possible loss of an investment or portfolio over a given time frame. It indicates that, in a specified high proportion of situations (often 95% or 99%), your portfolio is unlikely to lose more than that sum of money. It is an important consideration when making investment decisions.
Value at risk formula considers period, confidence level, loss amount, correlation, and risk factors. It can be expressed in price units or as a percentage of portfolio value. In other words, your loss is likely to exceed that figure in a specific small percentage of occurrences (e.g., 5% or 1%).

What is the Value at Risk formula?

The VaR formula determines the possible decline in a portfolio's value over a specified time horizon at a given confidence level.
VaR=μ+Z×σ
Where:
μ: the expected return or mean
Z: the Z-score, representing the number of standard deviations
σ: the standard deviation of the portfolio's returns

Value at Risk (VaR) Methodologies

There are three main ways of computing VaR: the historical method, the variance-covariance method, and the Monte Carlo method.

1. Historical Method

The historical method analyzes the prior returns history of a particular trader and arranges them in order of worst loss to the best gain. It is phased by the system claiming that previous returns experience will determine the later experience.
Historical Method Value at Risk formula:
Value at Risk = vm (vi / v(i - 1))
Where,
M = the number of days from which historical data is taken
vi = the number of variables on the day i

2. Variance-Covariance Method

The variance-covariance method, also known as the parametric method, takes the view that future gains and losses will occur according to a normal distribution. In this manner, the potential loss can be described based on standard deviation only from the means.
The variance-covariance method is most applicable where the distribution is known, and there is a reliable measure of risk. The sampling technique is, however, less reliable when the size of the sample is very small.

3. Monte Carlo Method

The third approach to VaR is to perform a Monte Carlo simulation. This technique employs computational models the expected returns are modeled over several hundred or thousands of potential scenarios. It then looks at the risks that a loss is likely to happen—perhaps 5 % probability—and shows the effect.
The Monte Carlo method applies to most of the risk measurement problems and is independent of the distribution of the risk factors.

Conclusion

Value at risk (VaR) is one of the most effective and widely applied risk measures. The value at risk measures generated are utilized by investors to make specific investment choices.
VaR is believed to fail to present the maximum possible loss, yet VaR provides an impression that risks are well controlled. One of its shortcomings is that most likely forecasts are not always achieved in the real sense of the word.