There are many things one can do with correlations of stocks in a portfolio. Ideally, every security one adds would not be related. Unfortunately, if you read how exposed are you in the next stock market crash? You will see just about everything moves together during panics because investors move into cash. Also, if you read limitations of financial models, you will also understand that most stocks are actually not normally distributed.
Whenever correlations are measured, typically a 3 month rolling moving average is computed. For the purpose of this exercise, we just took a basket of securities, and calculated three separate correlations over one year.
Ideally, everything in your portfolio shouldn't correlate together. Similarly, the correlations computed were Pearson (which unfortunately assumes a normal distribution), kendall, and spearman correlation. Investment Science prefers to take an average of the three measures of correlations. Similarly, each and every position should had a different time horizon (i.e. an investment one year from now or three months from now), a different strategy (some long positions, and some short positions).
So many people we talk to are overly-concentrated in one sector or all long or all short. All of these things could lead to a disaster. Feel free to play around with the spreadsheet we created for Microsoft, and a hypothetical basket of securities. Our product, Investment Lab, did these computations.