If a firm employs 50 analysts, how many of them are likely to issue forecasts that beat the market five years in a row, assuming none of them has any superior ability and that there are
No transaction costs?

Question

Quizplus · Accepted Answer

The probability of an analyst beating the market in any given year is about 50% (assuming a normal distribution of returns). The probability of beating the market five years in a row is (0.5)^5 = 0.03125 or 3.125%. Therefore, with 50 analysts, we would expect fewer than 2 to beat the market five years in a row purely by chance. This calculation assumes no transaction costs, which would make it even less likely for any analyst to beat the market consistently. The probability of consistently beating the market through random chance is extremely low. Assuming a 50/50 chance of beating the market in any given year, the probability of beating the market five years in a row is 1/32. Therefore, the probability of none of the 50 analysts beating the market five years in a row is (31/32)^50, which is approximately 0.028. This means that there is a very low probability of any of the analysts consistently beating the market, and it is unlikely that any of them will do so for five years in a row. Therefore, the answer is likely to be fewer than 2 analysts.

If a Firm Employs 50 Analysts, How Many of Them