$)$ You have recently graduated as a major in finance and have been hired as a financial planner by Radisson Securities, a financial services company. Your boss has assigned you the task of investing Rs$10,00,000$ for a client who has a I year investment horizon. You have been asked to consider only the following alternatives: T$-$Bills, Stock A$,$ Stock B and Market index. The economics cell of Radisson Securities has developed the probability distribution for the state of economy and the equity researchers of Radisson Securities have estimated the rates of return under each state of economy. You have gathered the following information from them

Returns on Alternative Investment

State of Economy

Probability

T$-$Bills

Recession

$0\mathrm{.}2$

$6\%$

Normal

$0\mathrm{.}5$

$6\%$

Boom

$0\mathrm{.}3$

$6\%$

Stock A

$-15\%$

$20\%$

$5\%$

Market Portfolio

$-10\%$

$16\%$

$40\%$

Stock B

$30\%$

$-15\%$

$30$

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

a$)$ What is the expected return and the standard deviation of return for Stock A & B $(5$ marks$)$

$)$ Calculate the excess returns for both the stocks $(2$ marks$)$ b c$)$

If the Risk Aversion index of an Investor is $2,$ based on utility concept, which stock would provide more utility $(3$ marks$)$