Question

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

Pg No-0 Solution:- given datas • will probability / the market Return is equal to u% Return Stock A is 1% and B is 6% • with Poo bability 1/2 the market Return is Equal to 20% Retum af stock A is 33%, and B is 10% → Expected Return = {pxy. • Expected Return of stock A = 4 x 19%+ x 33% : 01591, +16.5%. . = 1714 Stock B = {x6% + x 100% • Expected Return of = 31, +56 • Expected return on market 4x4+x20 - 2+10 = 120%

Pg No- → SML Equation = Rf + BC Rm-Rf) Rf = risk free rate - Rm= market return Rm-R= market Risk Remium Return a I SME Risk Free Bate) SML = 6+ B (12-6) SML = 6 + B (6) B) Be Change in Security Return / Change in market return i fos Stock A - 33-1 . 20-4- - 346 = 2 for Stock B - 10-6 20-4 .4 -0.25 for stock A:- CAPM . return = 6+2 (6) '=180%

So, alpha - Expected return - SML Return Pg No- = 17-18 - - For Stock B3 - · CAPM return = 6 +0.25 (6) = 7.56 • Expected Returo = 80% So, alpha = 8= 7,5% -0.59% 1. Return of Stock A € RA 0.25 Risk (B)