YouTube T2-9b Bayes Theorem, adding a bit of complexity

Nicole Seaman

Director of FRM Operations
Staff member
Here is the question: "You are an analyst at Astra Fund of Funds. Based on an examination of historical data, you determine that all fund managers fall into one of two groups. Stars are the best managers. The probability that a star will beat the market in any given year is 75%. Ordinary, nonstar managers, by contrast, are just as likely to beat the market as they are to underperform it. For both types of managers, the probability of beating the market is independent from one year to the next. Stars are rare. Of a given pool of managers, only 16% turn out to be stars. A new manager was added to your portfolio three years ago.

Since then, the new manager has beaten the market every year. What was the probability that the manager was a star when the manager was first added to the portfolio? What is the probability that this manager is a star now? After observing the manager beat the market over the past three years, what is the probability that the manager will beat the market next year?" -- Miller, Mathematics and Statistics, (Chapter 6)

Here is David's XLS: