A 2-stock portfolio

Clearly, a 2-stock portfolio is the simplest one. Let's assume that the weights of those two stocks are w1 and w2. The portfolio returns are given here:

Here, Rp,t, is the portfolio return at time t, w1 (w2) is the weight for stock 1 (2), and R1,t (R2,t) is return at time t for stock 1 (2). When talking about expected return or mean, we have a quite similar formula:

Here, is the mean or expected portfolio returns and is the mean or expected returns for stock 1 (2). The variance of such a 2-stock portfolio is given here:

Here, is the portfolio variance and is the standard deviation for stock 1 (2). The definitions of variance and standard for stock 1 are shown here:

is the covariance (correlation) between stocks 1 and 2. They are defined here:

For covariance, if it is positive, then those two stocks usually would move together. On the other hand, if it is negative, they would move in the opposite way most of times. If the covariance is zero, then they are not...