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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


Where


µ is the mean return

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

          is .3%

 

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

 

Where

 

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