Stock fund managers are investment professionals who decide which stocks should be part of a portfolio. In a recent article in the Wall Street Journal (Not a Stock-Picker's Market, WSJ January 25, 2014), the performance of stock fund managers was considered based on dispersion in the market. In the stock market, risk is measured by the standard deviation rate of return of stock (dispersion). When dispersion is low, then the rate of return of the stocks that make up the market are not as spread out. That is, the return on Company X is close to that of Y is close to that of Z, and so on. When dispersion is high, then the rate of return of stocks is more spread out; meaning some stocks outperform others by a substantial amount. Since 1991, the dispersion of stocks has been about 7.1%. In some years, the dispersion is higher (such as 2001 when dispersion was 10%), and in some years it is lower (such as 2013 when dispersion was 5%). So, in 2001, stock fund managers would argue, one needed to have more investment advice in order to identify the stock market winners, whereas in 2013, since dispersion was low, virtually all stocks ended up with returns near the mean, so investment advice was not as valuable.
(a) Suppose you want to design a study to determine whether the proportion of fund managers who outperform the market in low-dispersion years is less than the proportion of fund managers who outperform the market in high-dispersion years. What would be the response variable in this study? What is the explanatory variable in this study?
(b) What or who are the individuals in this study?
(c) To what population does this study apply?
(d) What would be the null and alternative hypothesis?
(e) Suppose this study was conducted and the data yielded a P-value of 0.083. Explain what this result suggests.