Value at Risk – Methods with Example

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

1. Analytical VaR:

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

VARRp-(Z)(σ)Vp

Where,

Rp = Return of the portfolio.
Z = Z value for a 5% confidence level in a one-tailed test.
σ = Standard Deviation of the portfolio.
Vp= Value of the portfolio.

For example, if the portfolio value is \$20,000 and the 1-month average return and 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

2. Historical VaR:

VaR can be calculated in various 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. The periodicity of the returns determines VaR’s time.

The 5th percentile of the monthly return distribution, for example, is used to compute the 5% monthly VaR.

3. 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, including the security’s historical Return and standard deviation. This approach runs many simulations 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 to measure various risks, including market risk, operational risk, and credit risk. It is a valuable measure for liquid positions operating under normal market circumstances over a short time. It is less useful and potentially dangerous when measuring risk in non-normal cases, in illiquid positions, and over a long time.