Suppose there are only two types of mutual fund managers: Skilled and Average. Skilled managers outperform the stock market index in 80% of years, while Average managers outperform the stock market index in 40% of years. 99% of mutual fund managers are Average, and only 1% are Skilled.

Suppose a fund has outperformed the stock market index for a year. Use Bayes Rule to compute the investor's updated belief that the manager is Skilled.

Now consider an investor who suffers from base-rate neglect. That is, the investor forms beliefs as though 50% of mutual fund managers are Skilled. Use Bayes Rule to compute the investor's updated belief that the manager is Skilled.

"Growth stocks" refer to the stocks that had unusually high earnings (and stock returns) over the past few years and garnered much attention in the media (which is why they are sometimes called "glamor stocks"). Briefly explain how base-rate neglect bias might explain why growth stocks are usually overpriced.