Question: Statistics for investing (3.1) Joe's retirement plan invests in stocks through an "index fund" that follows the behavior of the stock market as a whole, as measured by the Standard & Poor's (S&P) 500 stock index. Joe wants to buy a mutual fund that does not track the index closely. He reads that monthly returns from Fidelity Technology Fund have correlation r = 0.77 with the S&P 500 index and that Fidelity Real Estate Fund has correlation r = 0.37 with the index.
(a) Which of these funds has the closer relationship to returns from the stock market as a whole? How do you know?
(b) Does the information given tell Joe anything about which fund has had higher returns?