Problem: 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= 077. with the S&P 500 index and that Fidelity Real Estate Fund has correlation r= 0.37 with the index. Which of the following is correct?
Required:
(i) The Fidelity Technology Fund has a closer relationship to returns from the stock market as a whole and also has higher returns than the Fidelity Real Estate Fund.
(ii) The Fidelity Technology Fund has a closer relationship to returns from the stock market as a whole, but we cannot say that it has higher returns than the Fidelity Real Estate Fund.
(iii) The Fidelity Real Estate Fund has a closer relationship to returns from the stock market as a whole and also has higher returns than the Fidelity Technology Fund.
(iv) The Fidelity Real Estate Fund has a closer relationship to returns from the stock market as a whole, but we cannot say that it has higher returns than the Fidelity Technology Fund.