Conditional volatility estimate for a portfolio

Hello,

On MATLAB, I did a PCA analysis on 4 stocks and used an univariate GARCH(1,1) for each PC to create the conditional variance covariance matrix. So now I have multiple 4x4 matrices with the variance/covariance of the stocks for each trading day. And I am now trying to use these matrices to estimate the conditional volatility of an equally weighted portoflio containing those 4 stocks. Do you have an idea on how I can proceed?

Thanks in advance,

Answer 1

[Akanksha]

Hey Rol ,

To calculate the daily conditional volatility of an equally weighted portfolio using your 4×4 conditional variance-covariance matrices, here’s how you can achieve it:

1.Set the Portfolio Weights - Since the portfolio has 4 stocks and is equally weighted, each stock will get 25%:

 w = [0.25; 0.25; 0.25; 0.25];

2. Construct Daily Covariance Matrices - Construct a 3D matrix called Sigma, where each Sigma(:,:,t) is the 4×4 covariance matrix for day t.

3. Calculate Portfolio Volatility for Each Day - Now you can loop through each day and compute the portfolio’s conditional volatility like this:

 T = size(Sigma, 3);  % Number of trading days
 w = ones(4,1) / 4;   % Equal weights
 portfolio_volatility = zeros(T,1);  % Preallocate result
for t = 1:T
    Sigma_t = Sigma(:,:,t);  % Covariance matrix for day t
    portfolio_volatility(t) = sqrt(w' * Sigma_t * w);  % Volatility 
end

This will give a vector of daily volatilities for your portfolio.

PFA the documentation links along with the subsection to refer for any further queries :

https://www.mathworks.com/help/finance/portfolioriskcontribution.html : Compute Individual Asset Risk Contribution

https://www.mathworks.com/help/finance/portfolio-analysis.html : portvar and portstats

https://www.mathworks.com/help/risk/estimate-var-using-parametric-methods.html : Normal VaR Calculation

Hope this helps!