Question $9(20$ points$)$

Suppose the market portfolio is equally likely to increase by $30\%$ or decrease by $10\%.$ So there

are two states of the world: goes up with probability $0\mathrm{.}5$ and goes down with probability $0\mathrm{.}5.$

Calculate the beta of a firm that goes up on average by $43\%$ when the market goes up

and goes down by $17\%$ when the market goes down.

Calculate the beta of a firm that goes up on average by $18\%$ when the market goes down

and goes down by $22\%$ when the market goes up$.$

Calculate the beta of a firm that is expected to go up by $4\%$ independently of the market.

Use the beta you calculated in $(1).$ What is the expected return of the stock in $(1)$ using

CAPM?

Use the beta you calculated in $(2).$ What is the expected return of the stock in $(2)$ using

CAPM?