$\mathrm{.}3$ After your client reviews your proposal from the exercise involving two stocks, she really likes the idea of risk diversification. As a portfolio manager, you are given the right to invest in all $10$ of the securities listed in the pool $($note$,$ this does not include DJI$).$

Can you work out your $$optimal risky portfolio$($a$.$k$.$a$.$ tangent portfolio$)$ on the efficient frontier using all $10$ securities$?$

Hint: You can use the same logic and Solver built from Step $3\mathrm{.}2.$

Calculate your final portfolio weights in each stock and the portfolio characteristics $($mean$,$ std dev, and sharpe ratio$).$

You should find that some of your weights come out negative. This means that the optimal risky portfolio contemplates $$short selling.$$ See Module $3$ for more information on short selling $($if your minimum weight $=0$ instead of being negative, please make sure to uncheck the $$Make Unconstrained Variables Non$-$Negative$$ option in the Solver Parameters window$).$

What if your mandate does not allow you to participate in short selling activity? In other words, the lowest weight you can impose on the stocks in your portfolio is zero. What is your portfolio composition under this $$constrained$$ or $$long$-$only$$ regime?

Hint: You can repeat the same exercise as in the short selling case. You only need to check $$Make Unconstrained Variables Non$-$Negative$$ this time.