Question

a) Today’s price of one share of General Motors is $50. The price of the stock next year will be $65 if the economy is in a boom, $52 if the economy is normal and $35 if the economy is in a recession. The probability of a boom is three times as high as the probability of a recession and the probability of a normal state is four as high as the probability of a recession state. Assume that General Motors does not pay any dividends. The market risk premium is 8% and the T-Bill rate is 4.5%. Assuming that the CAPM holds, calculate the beta of General Motors.

b) If an analyst expects the return on General Motors to be 12%, does she believe the stock is over- or undervalued relative to the CAPM? Explain.

c) Consider the Robeco automobile industry fund, that has $500 million invested in the following six stocks, one of which is General Motors (GM):

Stock	Investment	Beta
GM	$110 million	? (use your answer to question a)
BMW	90 million	2.0
Mercedes	80 million	4.0
Toyota	80 million	1.0
KIA	40 million	3.0
Ferrari	100 million	?

Again, the risk free rate is 4.5% and the market risk premium is 8%. Assume that the CAPM holds. The standard deviation of the market return is 12%. The required rate of return of the fund is 20%. Calculate the covariance between the return on Ferrari shares and the market return.

Answer 1