Question

There are 10,000 mutual fund managers. 22 claim that they are the best, since their fund beat the relevant index every year for 7 years. However, you think that markets are efficient and that the average fund manager is as likely to deliver a better performance than the index as to underperform the index, before fees.

Part 1 | Attempt 1/10 for 10 pts. What is the probability that the average single fund managers beats the index 7 years in a row (before fees)? 4+ decimals
Part 2 | Attempt 1/10 for 10 pts. How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved? No decimals

Answer 1

Part A:

Probability that average single manager beat the index=
`(0.5)^7=0.0078125=0.0078 (4\ decimals)`

Part B:

Fund Managers to beat index 7 years=78.125≅78 managers.

Explanation:

Part A:

Given data:

Since there are equal chances for delivering equal better performance and of under performance so

Probability of better performance =0.5

Required:

Probability that the average single fund managers beats the index 7 years in a row (before fees)=?

Solution:

Since there is 7 year index:

Probability that average single manager beat the index=
`(0.5)^7=0.0078125=0.0078 (4\ decimals)`

Part B:

Given Data:

Number of mutual fund managers=10,000

Probability that average single manager beat the index= 0.0078125 (Calculated in part A)

Required:

How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved?

Solution:

Fund Managers to beat index 7 years=Total number of managers*probability average single member beat the index

Fund Managers to beat index 7 years=10,000*0.0078125

Fund Managers to beat index 7 years=78.125≅78 managers.