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

7/22/2022

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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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    He traded for a hedge fund and then went on his own. He specializes in scalping and fast day trading. His scalping book "Scalping Is Fun!" is an international bestseller and has been sold more than 30.000 times. His books have been translated into 11 languages.

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