Value-at-Risk: The Most Famous Risk Management Metric

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Risk Management remains one of the crucial functions of financial institutions. One of the most used metrics to measure risk is the Value-at-Risk, or VaR. 

VaR measures the extent of potential loss, a portfolio of risky investments might face over a given time horizon. 

Technical Explanation of VaR
Value-at-Risk expressed in dollars ($VaR) can be explained by the equation below:

Prob$Loss>$VaR= α

Let’s understand this equation first. If we choose a confidence level α, say 5%, and a certain time horizon, suppose 1 year, the equation above says that the probability of the loss on your risky portfolio exceeding $VaR will be 5%.
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Having explained $VaR, VaR is a similar except that it is represented in terms of log-returns:
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Probrw<-VaR= α

VaR can be understood by the distribution of log-returns of your portfolio over a given time-period as in the following graph.: 





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Measuring VaR:
There are 3 approaches to measuring VaR:

1. Historical method
2. Parametric method (also known as variance – covariance method)
3. Monte-Carlo method

Historical Method
Historical VaR, the simplest method to calculate VaR, assumes that past returns can act as a good proxy to understand future returns. To calculate Historical VaR, collect market data for a given time period. For example, if you own a portfolio of stocks, collect daily closing prices for the past 251 days. From prices, calculate daily returns and then log-returns of your portfolio. You’ll have 250 values of log-returns. Now sort the returns in ascending order. The daily VaR at a confidence level α is simply the return at αth percentile. For example, if you want to calculate VaR at 10% level, find the 25th log-return in your sorted data.

Parametric Method
Without going into much detail of this method, Parametric method assumes a normal distribution in log-returns. Expected return and standard deviation are estimated to compute VaR.

Monte-Carlo Method
As in a typical Monte-Carlo simulation, VaR is calculated by randomly creating a large number of scenarios for future rates using non-linear pricing models. Then, returns are calculated for each scenario, and worst losses are then used to calculate VaR.

Benefits of VaR:

• Applicable on all risky asset classes
• Universally understood and used
• Arguably the easiest risk management measure

Drawbacks of VaR:

• Different calculation methods give slightly different VaR values
• For large portfolios, calculating individual and then portfolio returns is a lengthy task

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