$3\mathrm{.}3$ You manage an equity fund with an expected risk premium of $10\%$ and a standard deviation of $14\%.$ The rate on Treasury bills is $6\%.$ Your client chooses to invest R$70000$ of her portfolio in your equity fund and R$30000$ in a T$-$bill money market fund.

a$)$ What are the expected return and standard deviation of your client$$s portfolio. $(3$ marks$)$

b$)$ What is the reward$-$to$-$volatility $($Sharpe$)$ ratio for the equity fund? $(2$ marks$)$

c$)$ What do you think would happen to the expected return on shares if investors perceived an increase in the volatility of stocks? $(2$ marks$)$