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Calculating VaR via parametric method
Using the parametric method to calculate VaR is the simplest methodology of the 3 main ways of calculating VaR. We need only calculate two values – the standard deviation of our asset returns and the mean value of the asset return.
The formula we need is
Var 1-α= - (µ + zα x σ ) x P
µ is the mean return
zα is the left-tail α percentile of a normal distribution
σ is the standard deviation of the return
Let’s plug these values into some example scenarios
1) Calculate the VaR at 95% confidence level over a 1 day period on a single asset worth $1M. Assuming the mean return is 3% and the standard deviation
VaR 1-day,95% = -(.002 - 1.6449 * .03) * $1M = $46,347
This means there is a 5% chance that this asset will lose $47K under normal market conditions by the end of tomorrows trading day
2) Lets assume we wanted the 99% VaR
VaR 1-day, 99% = -(.002 – 2.3263 * .03) * $1M = $66,789
If we want to convert the period from 1 day we have to multiply by the square root of the holding period.
e.g VaR 1 mnth, 99% = VaR 1 day, 99% * √21
3) For N assets the only difficult bit is calculating the standard deviation which you may recall is best dome using matrix notation
σ2 = W’ΣW
W is the 1 x N matrix of the asset weights
W’ is the transpose of W i.e a N x 1 matrix
Σ is the variance -covariance matrix