Value at Risk
Value at Risk (VaR) is a risk measure that measures the loss in a portfolio over a pre-specified time horizon, assuming some level of probability.
What do VaR results mean
For example, you choose to calculate Value at Risk for a portfolio with a 5% confidence level and get $24,592 as a result. This means that there is a 5% chance that the selected portfolio loses more than $24,592 over the next day.
The problem with VaR is that it does not consider the thickness of the tail of the distribution. That means it does not allow us to answer the question: "when losses exceed VaR, how severe should we expect that loss to be?". The answer to this is called expected shortfall.
Value at Risk Formula
— Significance level of VaR
— Portfolio average return
— Standard deviation of portfolio returns
— Z-score based on the VaR significance level
— Current portfolio value
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