# Finding the covariance of a stock portfolio

So my question goes like this, I have the returns of 3 different stocks AAPL, NKE and BBRY I make 4 portfolios out of them as follows:

and the question asks me to compute the correlation coefficient and covariance for each portfolio...

Now this seems a bit odd to me, since it already asked me to compute the covariance and correlation of each stock pair in an earlier question. Also, how would I go about doing it for the portfolio with 3 stocks?

• Hint: The difference is the 1) portfolios are weighted unevenly between stocks, and 2) you can't just sum the variances to get the whole. You need to add covariances also.. – RegressForward Apr 5 '15 at 15:35
• So am I suppose to find the weighted variance of the portfolio and use that as the covariance? i.e. $$Cov[Portfolio] = \sum_{i=0}^n \sigma_i^2w_i^2 + \sum_{i=0}^n\sum_{k\ne i} w_iw_k\sigma_{i,k}\sigma_i\sigma_k$$ So like for the 3 stock portfolio I will be using $$Cov[Portfolio] = \sum_{i=0}^3 \sigma_n^2w_n^2 + 2w_1w_2\sigma_{1,2}\sigma_1\sigma_2+ 2w_1w_3\sigma_{1,3}\sigma_1\sigma_3+ 2w_2w_3\sigma_{3,2}\sigma_3\sigma_2$$ – asosnovsky Apr 5 '15 at 17:15
• Looks great to me! – RegressForward Apr 6 '15 at 13:43
• Now how would I get the correlation? – asosnovsky Apr 6 '15 at 13:59
• The correlation can be found if you know the covariance. math.stackexchange.com/questions/186959/… – RegressForward Apr 6 '15 at 14:41