Find one variable that is most uncorrelated to current set of variables I'm currently holding 100 stocks. From another pool of 400 stocks, I want to pick one that are most uncorrelated to my current set of 100.
My plans are

*

*Find the stock that has least total correlation in the sample correlation matrix with my current one

*Regress each of the 400 stocks in the pool against my current set, find the one that has lowest $R^2$
Which one, if any, of the two is preferred? If neither, what are the general statistical methods for such problem?
 A: Since the most uncorrelated new stock is what you want (1) and not which whose variance is best explained by another stock's variance (2) the first route should be followed since the second plan requires at least 400 regressions.
Calculate the correlation matrix for the existing 100 stocks and 400 candidates together, while remembering that the first 100 row and column indices are the existing pool (call it the first partition of the combined correlation matrix), and the remaining 400 row and column indices belong to the candidate pool (second partition). From there, locate the minimum correlation (off-diagonal) in the lower diagonal of the second partition, because this is the region where correlations between the first and second partitions will appear.
\begin{array} {|r|r|}\hline A & a,a & a,b & a,b & a,b \\ \hline a,a & A & a,b & a,b & a,b \\ \hline b,a & b,a & B & b,b & b,b \\ \hline b,a & b,a & b,b & B & b,b \\ \hline b,a & b,a & b,b & b,b & B \\ \hline  \end{array}
In the miniaturized example above, with partitions for groups $A$ (existing pool) and $B$ (candidate pool), the bottom left $3\times 2$ region consisting of $b,a$ off-diagonals would be your area of interest in the combined correlation matrix. In your case, just extend the framework to a $(100+400)\times (100+400)$ sized matrix
