You have recently passed out as a finance graduate and have been hired as a financial analyst by Fincorp Securities, a financial services company. Your boss has assigned you the task of investing Rs$.8,00,000$ for a client who has an I$-$year investment horizon. You have been asked to consider only the following alternatives: T$-$Bills, Stock P$,$ Stock Q$,$ and Market index.

The economics cell of Fincorp Securities has developed the probability distribution for the state of the economy and the equity researchers of Fincorp Securities have estimated the rates of return under each state of the economy. You have gathered the following information from them

Returns on alternative Investments

State Economy

of

Probability

T$-$Bills

Stock P

Stock Q

Market Portfolio

Depression

Normal

Boom

$0\mathrm{.}1$

$7\%$

$(10\%)$

$15\%$

$(10\%)$

$0\mathrm{.}5$

$7\%$

$18\%$

$14\%$

$17\%$

$0\mathrm{.}4$

$7\%$

$30\%$

$25\%$

$28\%$

Your client is a very knowledgeable investor who knows a lot relating to portfolio and asset pricing theory. He requests you to answer the following questions

a$)$ What are the expected return and the standard deviation of return for Stock P & Q and the market portfolio $(3$ marks$)$

b$)$ What is the covariance between the returns of P & Q $(2$marks$)$

c$)$ What are the expected return and standard deviation on a portfolio in which Stock

P & Q are equally weighted $(3$ marks$)$ d$)$ If the Betas of T$-$bills is $0$ Stock P & Q is $1\mathrm{.}3$ and $0\mathrm{.}8$ respectively, calculate the alpha for stock P & Q $(2$ marks$)$