Chapter 6.2, Problem 53AYU

Putting It Together: Beating the Stock Market One measure of successful investing is being able to “beat the market.” To beat the market in any given year, an investor must earn a rate of return greater than the rate of return of some market basket of stocks, such as the Dow Jones Industrial Average (DJIA) or Standard and Poor’s 500 (S&P 500). Suppose in any given year, there is a probability of 0.5 that a particular investment advisor beats the market for his/her clients.

1. a. Suppose there are 5000 investment advisors across the country. How many would be expected to beat the market in any given year?
2. b. Assume beating the market in one year is independent of beating the market in any other year. What is the probability that a randomly selected investment advisor beats the market in two consecutive years? Based on this result, how many of 5000 investment advisors would be expected to beat the market for two consecutive years?
3. c. Assume beating the market in one year is independent of beating the market in any other year. What is the probability that a randomly selected investment advisor beats the market in five consecutive years? Based on this result, how many of 5000 investment advisors would be expected to beat the market for five consecutive years?
4. d. Assume beating the market in one year is independent of beating the market in any other year, What is the probability that a randomly selected investment advisor beats the market in ten consecutive years? Based on this result, how many of 5000 investment advisors would be expected to beat the market for ten consecutive years?
5. e. Assume a randomly selected investment advisor can beat the market with probability 0.5 and investment results from year to year are independent, Suppose we randomly select 5000 investment advisors and determine the number X who have beaten the market the past ten years, Explain why this is a binomial experiment (assuming there are tens of thousands of investment advisors in the population) and clearly state what a success represents.
6. f. Use the results of part (e) to determine the probability of identifying at least six investment advisors who will beat the market for ten consecutive years, Interpret this result, Is it unusual to identify at least six investment advisor who consistently beats the market even though his/her underlying ability to beat the market is 0.5? Explain.