![]() The daily profits-and-losses (PL) against value-at-risk (VaR) for an actual trading portfolio is usually plotted in the following way. We can see the VaR result is closed to the one obtained in historical method. The corresponding inverse normal distribution at 1% is calculated to be -0.009644698, which is interpreted as the worst return at 99% confidence level. Using the same example above, we compute mean = 0.39307%, and standard derivation = 0.004314818 for the return series. These 2 factors define the shape of a normal distribution curve. In other words, it only requires to estimate 2 parameters: The parametric method is also called Variance-Covariance method, which assumes that stock returns are normally distributed. The VaR at level α ∈ (0,1) is the smallest number y such that the probability of loss Y := -X does not exceed y is at least 1-α. Let X be a profit-and-loss distribution where loss is negative and profit is positive. It can also be interpreted as: on average for every 10/(1-99%) = 1000 days, there would occur a loss more than 15%. It means a 99% chance of the asset declining in value no more than 15% during a 10-day time frame. ![]()
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