You are analyzing the performance of a group of 500 mutual fund managers. If markets are efficient, approximately how many would you expect to have ranked in the top half (or beat the market) in terms of performance for three consecutive years?
A) 250
B) 375
C) 63
D) 31
E) 125
The correct answer and explanation is:
The correct answer is D) 31.
Explanation:
In an efficient market, mutual fund managers are expected to perform in a way that is consistent with random chance, meaning their success or failure should be similar to the overall market’s performance over time. If the market is efficient, the probability of a manager being ranked in the top half of performers in any given year is 50%, as there is no systematic way to consistently outperform the market over the long term.
Step-by-step breakdown:
- Initial Year: In the first year, we would expect half of the 500 managers (i.e., 250 managers) to outperform the market, as the market is assumed to be efficient. This is because the probability of being in the top half is 50%.
- Second Year: In the second year, the same principle applies. From the 250 managers who outperformed the market in the first year, half of them (i.e., 125 managers) would still be able to outperform the market. This is again assuming the market remains efficient and the performance is like a random chance.
- Third Year: In the third year, only half of those 125 managers (i.e., 62.5, rounded to 63) would be expected to maintain their top-half ranking.
Therefore, the expected number of mutual fund managers who would outperform the market (or rank in the top half) for three consecutive years is approximately 31. This is based on the repeated halving of the number of managers who maintain consistent superior performance across multiple years in an efficient market.
In summary, the efficiency of the market essentially randomizes performance over time, leading to a sharp drop in the number of managers able to continue beating the market year after year. The probability of a manager consistently beating the market decreases exponentially with each additional year.