Correlation Between Independent Stocks

In a recent analysis of two stocks, Stock A and Stock B, an analyst computed the correlation coefficient between their returns. The correlation coefficient was found to be 0.85. The analyst then stated that this high correlation indicates a strong relationship between the returns of Stock A and Stock B.

If the analyst were to introduce a third stock, Stock C, whose returns have no correlation with either Stock A or Stock B, what would be the correlation coefficients between the pairs of returns for Stock A & Stock C and Stock B & Stock C?

Assuming the returns of Stocks A and C and stocks B and C are independent, the correlation coefficients for Stock A & Stock C, and Stock B & Stock C can be calculated as:

$$ ext{Correlation}(A, C) = 0 $$ and $$ ext{Correlation}(B, C) = 0 $$