For each statement below, explain whether this may be evidence against the efficient market hypothesis, and why:

a$.$ The price of Microsoft stock is unlikely to fall below $$100$ a share.

b$.$ A professional fund manager that has outperformed the market in the past year will continue to outperform the market in the future.

c$.$ Energy$-$stock investment managers with personal connections to oil companies tend to outperform investment managers without such connections.

Briefly answer the following questions regarding the efficient market hypothesis $($EMH$)$:

a$.$ Suppose you observed that returns to the S&P $500$ index in the past $5$ January have been less than the simple CAPM would suggest. Does this appear to contradict the weak form EMH? Why?

b$.$ Your friend does not believe this is evidence against weak form EMH, and actually thinks you are data mining. What does data mining mean? What could you do to test whether you indeed find a predictable pricing pattern?

c$.$ Suppose you found another phenomenon: companies that are traded less frequently tend to show positive alphas $($implied by the simple CAPM$).$ Which version of the EMH may be violated with this evidence? Why?

d$.$ Your friend stops you from jumping to the conclusion again. Instead, he$/$she argues that this actually means the simple CAPM gives us poor estimates of expected returns, as indicated by Fama and French. Briefly explain your friend's argument.