# Right metric to manage a portfolio based on correlation?

I want to algorithmically add a new investment to an existing portfolio. The decision should be based on a low correlation to the existing assets.

E. g. the following situation

• The portfolio already contains 5 stocks: A1 ... A5
• My trading system generates 3 buy signals for new investments that aren’t in the portfolio yet: B1 ... B3
• I want to pick one out of three investments to add to the portfolio

So I will calculate for each investment the correlation coefficient: correlation(Bx, Ay) which gives me a matrix with 3 rows (B1 ... B3) and 5 columns (A1 ... A5). What will then be the right decision criteria to pick the row with the least correlation?

• The row with the lowest correlation average?
• Or the lowest correlation average weighted by invest volume?
• Or the row with the lowest maximum correlation?
• Other variants?

Other topic: Am I right that I just have to take take the negative value of the correlation coefficient in case my system also creates short-signals?

Alen

If you want the lowest correlation then just short your portfolio. Correlation -1, now you have zero exposure. But I don't think that's really your objective function.

For a two asset portfolio ... $$\sigma =\sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2+2w_1w_2Cov_1,_2}$$