You are an prudent investor who is always on the look$-$out for good investment options. as per your research you came across the two assets A and B for which returns $(\%)$ under different conditions of economy are given as below.

$10$

Condition of Economy

Probability

Stock A Returns $(\%)$

Recession

$0\mathrm{.}10$

$-18$

$-10$

Slowdown

$0\mathrm{.}20$

$-4$

$2$

Normal

$0\mathrm{.}40$

$12$

$8$

Slow growth

$0\mathrm{.}20$

$24$

$12$

Boom

$0\mathrm{.}10$

$30$

Steck B Returns $(\%)$

$18$

a$)$ Calculate the expected return, standard deviation, and coefficient of varistion for stocks A and B$.(5$ marks$)$

b$)$ Which stock is more desirable

Based on the expected annual rate of retum $(1$ Marks$)$

ii$)$ Based on the risk. $(1$ Marks$)$

Based on relative risk $(1$ mark$)$

c$)$ If you have an investment in Government bonds that are selling in the market at a yield of $4$ percent, what would be your required rate of return on common stocks if you wanted a $5$ percent risk premium? $(2$ marks$)$