QUESTION $1[10$ MARKS$]$

Following extensive analysis and forecasting, you have established that an investment in Mills Ltd offers the following probability distribution of returns, given different states of

the economy:

State of Economy Probability of State of Economy Return

Super Boom

Boom

Normal

Recession

Severe Recession $10\%$

$20\%$

$45\%$

$15\%$

$10\%50\%$

$30\%$

$10\%$

$-10\%$

$-29\%$

REQUIRED

a$)$ Determine the expected return for this portfolio. $(4$ marks$)$

b$)$ Calculate the variance for the portfolio $(4$ marks$)$

c$)$ Find the Standard deviation for the portfolio $(2$ marks