Value at Risk (VaR)

Given a particular likelihood of occurrence, the value at risk (VaR) determines an estimated loss amount at a given confidence interval. Broadly, there are three different methods to calculate VaR.

Analytical VAR:

Analytical VaR assumes the returns to be following a normal distribution and is considered to be one of the simplistic approaches.

VAR[Rρ-(Z)(σ)]Vρ

Where,
Rρ = Return of the portfolio.
Z= Z value for a 5% level of confidence in a one-tailed test.
σ = Standard Deviation of the portfolio.
Vρ= Value of the portfolio

For example, if the portfolio value is $20,000 and if the 1-month average return and the standard deviation are 10% and 15% respectively. Daily VAR at a 5% level of significance can be calculated as

VAR= [Rp – (z) (σ)] Vp => VAR = [0.1 – (1.65) (0.15)] 20000 => -$3000 (rounded) => 15% of the Portfolio

Historical VAR:

VAR can be calculated in a variety of ways, but this method is perhaps the most straightforward. All you have to do is gather data on the asset’s historical returns, organise them in ascending order, and then determine the percentile of the observations based on the needed level of confidence. VAR’s time period is determined by the periodicity of the returns.
The 5th percentile of the monthly return distribution, for example, is used to compute the 5% monthly VAR.

Monte Carlo VAR:

Montecarlo is probably the most complicated method to calculate VaR. In MC, the distribution of returns is generated on a security/portfolio. This is done based on the analyst’s inputs, which include the security’s historical return and standard deviation. This approach runs a large number of simulations in order to capture all possible security movement scenarios.
This method’s drawback is that it relies heavily on assumptions.

Example of Value at Risk:

At the 95 per cent confidence level, a financial institution’s one-day VaR might be \$2.5 million. This translates to a 5% possibility that a loss of more than \$ 2.5 million will occur on any given day.

Why is it important to know VAR?

VaR is the most diversified model used for measurement of a variety of risks including market risk, operational risk and credit risk. It is a useful measure for liquid positions operating under normal market circumstances over a short period of time. It is less useful and potentially dangerous when attempting to measure risk in non-normal circumstances, in illiquid positions, and over a long period of time