Question

2. Consider the following expected return on two stocks for two particular market returns:
With probability 1/2 the market return is equal to 4%, return of stock A is 1% and B is 6%.
With probability 1/2 the market return is equal to 20%, return of stock A is 33% and B is 10%.
(Hint: these are realizations and not expected values, you should calculate the expected returns using the given probabilities and returns)
(a) What is the expected rate of return on each stock? Suppose the risk-free rate is 6% , draw the SML.
(b) Plot the two securities on the SML graph, i.e., calculate beta of each security.

What are the alphas for each security?

Answer 1

a so. expected resurn = {pxr where, p- probability re referrn expected return of STOCK A = 1/2+1% + I + 33% = 0.5% + 16.5% - 1741 STOCK 8 +6) + 10) = 3% +5%. = 8.4 expected return on market = 1 = 2+10 - 121. SML Equation = R + B (Rm - Rs) Rf = risk free rate Rm - market return = market risk Premium

SML Centar crisk free rate) Risk SI = 6+ B (12-6) = 6+ B (6) (6) B. change in security return change in market return - 32 for STOCK A = - 33-1 33 20-4 B = 10-6 16 for Stock - 4 = 0.25 20-4 STOCK-A CAPM return = 6+2 (6) = 18% expected return = H/ so alpha = expected return - SML return - 17 - 18 = -1/- STOCK-B CAPM return= 6+0.25 (6) = 7.5% expected return = 8% so alpha = 8-7.5% = 0.5%

MU Return STOCK A C46 B 0.25 risk (B)