Problem 1 Imagine that a randomly selected mutual fund has a fifty percent chanc

Question

Problem 1 Imagine that a randomly selected mutual fund has a fifty percent chance of beating the perfor- mance of the stock market in any given year. Furthermore, assume that a fund's chances of outperforming the market are independent from year to year.
a. What is the probability that a randomly selected mutual fund will outperform the market for five consecutive years?
b. What is the probability that a randomly selected mutual fund will outperform the market for ten consecutive years?
c. Out of 10,000 mutual funds, how many would you estimate will outperform the market for ten consecutive years?
d. Does the existence of a handful of market funds that outperform the market year after year demonstrate "proof " that certain fund managers are amazingly skillful in selecting stocks, or is there an alternative way to explain their success? Problem 1 Imagine that a randomly selected mutual fund has a fifty percent chance of beating the perfor- mance of the stock market in any given year. Furthermore, assume that a fund's chances of outperforming the market are independent from year to year.
a. What is the probability that a randomly selected mutual fund will outperform the market for five consecutive years?
b. What is the probability that a randomly selected mutual fund will outperform the market for ten consecutive years?
c. Out of 10,000 mutual funds, how many would you estimate will outperform the market for ten consecutive years?
d. Does the existence of a handful of market funds that outperform the market year after year demonstrate "proof " that certain fund managers are amazingly skillful in selecting stocks, or is there an alternative way to explain their success?

Explanation / Answer

Rule: When determining successive probabilities, always multiply.

For each year, probability = 0.5. So...

1st Year = 0.5
2nd Year = 0.5
3rd Year = 0.5
4th Year = 0.5
5th Year = 0.5

a. Therefore, the answer is 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = (0.5)^5 = 0.03125 = 3.125%.

b. So, for ten years, the answer is (0.5)^10 = 0.000977 = 0.0977%.

c. out of 10,000 number of mutual funds will outperform the market for ten consecutive years = 0.000977*10,000 =9.77 or roughly 10

d. The obvious explanation is that since about ten funds will outperform the market for ten years in a row without anything but chance operating, the chance of finding at least *someone* who outperforms the market for so long just by chance is quite high

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