Answer:
Part A:
Probability that average single manager beat the index=
Part B:
Fund Managers to beat index 7 years=78.125≅78 managers.
Step-by-step 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=
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.