Find the optimal weights you should invest in each company if your objective is to minimize the risk of the portfolio. What is your portfolio$$s expected return and risk?

Remember that you have N $=5$ stocks, therefore the number of covariance terms is determined by $($N$^2-$N$)/2,$ and

E$($R$\_$p $)=$w$\_1$ E$($r$\_1)+$w$\_2$ E$($r$\_2)+$w$\_5$ E$($r$\_5)$

$\backslash$sigma $^\_$p$=(\_($i$=1)$w$\_$i$^2\backslash$sigma $\_$i$^2+\_$i$\_($j$!=$i$)$w$\_$j w$\_$j $\backslash$rho $\_($i$,$j$)\backslash$sigma $\_$i $\backslash$sigma $\_$j $)$

Matrix calculation is a more efficient way to calculate the variance of a portfolio with multiple assets, especially when dealing with a large number of assets. Using matrix notation, we can represent the weights, standard deviations, and correlations of assets in matrices and vectors, which simplifies the calculation process. Let's denote:

W as the vector of weights of assets in the portfolio.

$\backslash$Sigma as the covariance matrix of asset returns.

W$^$T as the transpose of the weight vector.

Then, the portfolio variance can be calculated using matrix notation as:

$\backslash$sigma $\_$p$^2=$ W$^$T$.\backslash$Sigma $.$W

Hints:

Follow the following steps:

Data $$ Solver

Set target cell $($refer to the cell with the Standard Deviation of portfolio formula calculated in c$)$ to Min

By Changing Cells $($refer to cells with weights $($w$1,$ w$2,...,$w$5)$

You will find that the weights will change $$ the resulting weights are those that will give you the minimum risk

for the stocks

jnj

apple

coca$-$cola

pfizer

mcdonalds

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