Question $4$

Consider a market with $d=3$ risky assets with the following parameters:

$r=[6\%,2\%,4\%]$

$V={10}^{-3}$

Note that the mean returns on the assets are in $\%$ but the variance is not. $($Note that the asset returns and variances are not representative of realistic market conditions$).$

a$)$ Compute the mean return on the portfolio $w=\frac{1}{3}(1,1,1)$ consisting of the risky assets.

b$)$ Compute the volatility of the return on the portfolio $w=\frac{1}{31},1,1)$ consisting of the risky assets $($i$.$e$.$ same portfolio as Question a$).$

c$)$ Compute the mean return on the minimum variance portfolio of the risky assets.

The minimum variance portfolio is defined as the portfolio of risky assets that has the least volatility among all possible portfolios of just the risky assets. This portfolio is the solution to the optimization problem

$\backslash$table$[[Min{w}^{TT}Vw$