Problem $1.$

Suppose you currently have a portfolio of three stocks, A$,$ B$,$ and C$.$ You own $500$ shares of A$,$

$300$ of $B,$ and $1000$ of $C.$ The current share prices are $$42\mathrm{.}76,$$$81\mathrm{.}33,$ and $$58\mathrm{.}22,$ respectively.

You plan to hold this portfolio for at least a year. During the coming year, economists have

predicted that the national economy will be awful, stable, or great with probabilities $0\mathrm{.}2,0\mathrm{.}5,$ and

$0\mathrm{.}3.$ Given the state of the economy, the returns $($one$-$year percentage changes$)$ of the three stocks

are independent and normally distributed. However, the means and standard deviations of these

returns depend on the state of the economy, as indicated in the table below.

Simulate the value of the portfolio and the portfolio return in the next year by randomly

generating $10000$ samples.

What is the probability that your will have a return at least $25\%?$ Can you provide a $95\%$

$($two$-$sided$)$ confidence interval of this probabilityProblem $1.$

Suppose you currently have a portfolio of three stocks, A$,$ B$,$ and C$.$ You own $500$ shares of A$,$

$300$ of $B,$ and $1000$ of $C.$ The current share prices are $$42\mathrm{.}76,$$$81\mathrm{.}33,$ and $$58\mathrm{.}22,$ respectively.

You plan to hold this portfolio for at least a year. During the coming year, economists have

predicted that the national economy will be awful, stable, or great with probabilities $0\mathrm{.}2,0\mathrm{.}5,$ and

$0\mathrm{.}3.$ Given the state of the economy, the returns $($one$-$year percentage changes$)$ of the three stocks

are independent and normally distributed. However, the means and standard deviations of these

returns depend on the state of the economy, as indicated in the table below.

Simulate the value of the portfolio and the portfolio return in the next year by randomly

generating $10000$ samples.

What is the probability that your will have a return at least $25\%?$ Can you provide a $95\%$

$($two$-$sided$)$ confidence interval of this probability Crystal Ball must be used, so please type out the Crystal Ball formulas you would use in the template and write a step$-$by$-$step process on your work. Please ALSO attach an Excel File; if that's not possible, then please submit SCREENSHOTS of the Excel Spreadsheet with the formulas visible.