Fun with Bayes’ Theorem: You are an analyst at Chaudo Fund of Funds. Based on an
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Question
Fun with Bayes’ Theorem: You are an analyst at Chaudo Fund of Funds. Based on an examination of historical data, you determine that all fund managers fall into one of two groups. Group 1 are “stars,” the best managers. The probability that a member of Group 1 will beat the market in a given year is 75%. Group 2 members are “others,” who’s performance is random—they are just as likely to beat the market as they are to underperform the market—so they have a 50% probability of beating the market. For both types of managers, the probability of beating the market is independent from one near to the next.
“Stars” are uncommon. Of a given pool of managers, only 10% are Group 1 members.
A new fund manager was added to your portfolio of funds five years ago. Since then, that manager has outperformed the market each and every year—5 straight years.
a. Five years ago you had no track record for the manager. Without any performance track record to learn from, what is the (prior) probability that you hired a “star” manager?
b. What is the probability that this manager is a “star” now, after observing 5 straight winning years?
Explanation / Answer
a) Probability that we hired a star manager = 0.10 since there are only 10% star managers
b) P( Star after 5 winning years) = 0.10*0.75^5/[0.10*0.75^5 +0.90*0.5^5]=0.4576
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