VaR for portfolios

In Chapter 9, Portfolio Theory, it was shown that when putting many stocks in our portfolio, we could reduce or eliminate firm-specific risk. The formula to estimate an n-stock portfolio return is given here:

Here Rp,t is the portfolio return at time t, wi is the weight for stock i, and Ri, t is the return at time t for stock i. When talking about the expected return or mean, we have a quite similar formula:

Here, is the mean or expected portfolio return, is the mean or expected return for stock i. The variance of such an n-stock portfolio is given here:

Here, is the portfolio variance, σi,j is covariance between stocks i and j; see the following formula:

The correlation between stocks i and j, ρi,j, is defined here:

When stocks are not positively perfectively correlated, combining stocks would reduce our portfolio risk. The following program shows that the VaR of the portfolio is not simply the summation or weighted VaR of individual stocks within the portfolio...