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Filtered Historical Simulation Example Determination of Variance

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Michael Muhle
Michael Muhle on 11 Jul 2021
I have a question on determining the variance in the Econometrics Toolbox example "Using Bootstrapping and Filtered Historical Simulation to Evaluate Market Risk". Everything is pretty straitforward till the end of the example where they use the filter function to determine the portfolio returns. Here is the command.
portfolioReturns = filter(fit, bootstrappedResiduals, ...
'Y0', Y0, 'Z0', Z0, 'V0', V0);
I would like to obtain the conditional variance paths. Hence I used the command
[V, Y] = filter(fit, bootstrappedResiduals, ...
'Y0', Y0, 'Z0', Z0, 'V0', V0);
Here is a plot of the first 10 horizon results for V
Here is the plot of the firt 10 horizon results for Y
The results for Y look like one would expect - plus and minus values around zero. However, the results for V should all be positive since according to the filter function for conditional variances V is the filtered variance result. When comparing the value of V to that of the variable portfolioReturns I fould them to be identical.
I can always square the value of the portfolioReturns to get the squarded returns. Is this the value of the conditional variance for the FHS simulation?

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