Statistics for investing. 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 500 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.

370 Part II Review TABLE II.4 Percentage of votes for President Bush, 2004 State Percent State Percent State Percent Alabama 62.5 Louisiana 56.8 Ohio 51.0 Alaska 61.8 Maine 44.7 Oklahoma 65.6 Arizona 54.9 Maryland 43.3 Oregon 47.6 Arkansas 54.3 Massachusetts 37.0 Pennsylvania 48.6 California 44.3 Michigan 47.8 Rhode Island 38.9 Colorado 52.0 Minnesota 47.7 South Carolina 58.0 Connecticut 44.0 Mississippi 59.6 South Dakota 59.9 Delaware 45.8 Missouri 53.4 Tennessee 56.8 Florida 52.1 Montana 59.1 Texas 61.2 Georgia 58.1 Nebraska 66.6 Utah 71.1 Hawaii 45.3 Nevada 50.5 Vermont 38.9 Idaho 68.5 New Hampshire 49.0 Virginia 54.0 Illinois 44.6 New Jersey 46.5 Washington 45.6 Indiana 60.1 New Mexico 50.0 West Virginia 56.1 Iowa 50.1 New York 40.5 Wisconsin 49.4 Kansas 62.2 North Carolina 56.1 Wyoming 69.0 Kentucky 59.5 North Dakota 62.9 Source: Federal Election Commission, www.fec.gov.

(a) Which of these funds has the closer relationship to returns from the stock market as a whole? How do you know? (Hint: See pages 297–298.)

(b) Does the information given tell Joe anything about which fund has had higher returns? (Hint: See pages 297–298.)