Value at Risk (VaR)
factor.formula
At a given confidence level α, the probability that the portfolio loss exceeds the VaR is (1 - α):
In the formula:
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Represents the change (gain or loss) in the value of a financial asset or portfolio over a specific holding period (\Delta t). A negative value of (\Delta P) indicates a loss, while a positive value indicates a gain.
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It represents the maximum amount of loss that the portfolio may suffer during the holding period (\Delta t) under a given confidence level (\alpha). This is an absolute value that represents the upper limit of the loss.
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Represents the confidence level, indicating our confidence in the accuracy of the VaR forecast. Typically, the value of ( \alpha ) ranges from 90% to 99%, with common values of 95% or 99%. For example, if ( \alpha = 95% ), it means that in 100 holding periods, we expect only 5 holding periods with losses exceeding the VaR value.
factor.explanation
Value at Risk (VaR) is a tool to measure market risk. It quantifies the maximum possible loss of a financial asset or portfolio over a specific holding period (( \Delta t) ) at a given confidence level (( \alpha ) ). More specifically, VaR answers the question: What is the probability (1 - α) that we will lose more than a certain amount in the future? For example, a VaR of 1 million yuan at a 95% confidence level means that in the future, we are 95% sure that we will not lose more than 1 million yuan, but it also means that there is a 5% probability that we will lose more than 1 million yuan. The calculation of the VaR model usually requires consideration of the distribution of asset returns, for example, it can be estimated through historical data simulation, Monte Carlo simulation or parametric methods (such as the normal distribution assumption). It is worth noting that VaR is a tail risk measure that focuses on the tail of the loss distribution without describing the size of the loss exceeding VaR.