Question

A manager of unknown ability is managing an investment fund. Well-managed funds rise in value in 60% of time periods, while badly managed funds only rise in value 40% of the time. It is observed that a particular fund rises in value on four consecutive occasions. Assuming that there is a prior probability of 0.5 that the fund is well-managed:

3.1 (10 points) What would be the rational investor’s estimate of the probability of the fund being well managed, after observing four consecutive rises?
3.2 (5 points) If the investor suffers from one of the ”Law of Small Numbers” biases, how would her estimate be different from the rational investor? Which bias does she potentially suffer from?

Answer 1

3.1

3.2

so her estimate would be that if in the whole population 50% are well managed then this fund also has 50% probability of being well managed according to her.

it has judgemental bias

P.S. (please upvote if you find the answer satisfactory)