# Can you sum correlation coefficients to find overall correlation?

I have a pool of 10 stocks to choose from. All stocks correlate differently with one another. I can create a portfolio of 5 stocks from this pool. Let's say I really like FaceBook out of my pool of stocks. I find as many positively correlated stocks to FaceBook out of my pool. Can I take each correlation coefficient and sum it to find the overall correlation of my portfolio? Is this a statistically sound method?

Example Portfolio:

Stock        Correlation

Stock A     .89

Stock B     .76

Stock C     .69

Stock D     .56

Sum         2.9

• What do you mean by correlation of your portfolio? Correlation is a bivariate measure, you'll need to define it between two variables and not many. Perhaps what you're thinking is the correlation of a weighted sum of the stocks in your portfolio, weighted by the % allocated in the stock. Is that what you're looking for? Oct 29, 2020 at 19:45
• No, all the correlation values are the correlation coefficient to FaceBook. Oct 29, 2020 at 22:56
• Yeah I got that, but what I meant is what do you mean by "overall correlation"? As I said, correlation is established between two variables, so you'd have to define that variable, right? Oct 29, 2020 at 23:15

No, summing correlation between different variables does not make much sense. In fact, given that correlation has to be on an interval $$[-1,1]$$ (as correlation of $$1$$ or $$-1$$ implies perfect positive or negative relationships respectively) the value of $$2.9$$ is meaningless.
Furthermore, also as pointed in the comments correlation is calculated for two variables, as it measures strength of relationship between them. The Pearson correlation coefficient (which I assume was used here) is given by $$r_{xy} = \frac{Cov(X,Y)}{s_X s_Y}$$ so in essence it is a standardized covariance between two variables. Adding different standardized covariances together is again meaningless.