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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

FaceBook

Stock A     .89

Stock B     .76

Stock C     .69

Stock D     .56

Sum         2.9
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    $\begingroup$ 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? $\endgroup$
    – Caio C.
    Oct 29, 2020 at 19:45
  • $\begingroup$ No, all the correlation values are the correlation coefficient to FaceBook. $\endgroup$ Oct 29, 2020 at 22:56
  • $\begingroup$ 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? $\endgroup$
    – Caio C.
    Oct 29, 2020 at 23:15

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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.

However, if you would like to aggregate the result then instead of summing the correlations you could, for example, calculate an average of all correlations and report that. This will tell you how on average are those different stocks correlated with Facebook.

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