Question $4[85$ points$]$: The objective of this question is to extend the optimal portfolio problem by incorporatingreal$-$world data and employing Monte Carlo simulation for more general Utility functions.NOTE: To answer this question, you must complete the accompanying Excel file with your solution and submitit as a separate file. Please make sure to properly label all the plots and axes before submission.Part I: The initial segment of this assignment involves replicating the exercises conducted in class using real$-$worlddata$\mathrm{.}1.$ Select a stock of your preference and obtain its historical monthly prices for the past $10$ years $($you can usethe STOCKHISTORY$()$ function in excel to download the data. See here for the details$).$ Ensure that thedates align with those in the provided file. $[$Use sheet Monthly Return Histogram Plot$]2.$ Populate the Realized Monthly Return column using the obtained price information. $[$Use sheet MonthlyReturn Histogram Plot$]3.$ Following procedures similar to those covered in class, generate a histogram of the monthly returns andcompare it with the histogram of a normal distribution that matches the mean and standard deviation of thehistorical returns. Use sheet Monthly Return Histogram Plot$\mathrm{.}4.$ Apply similar methodologies as discussed in class to compute and visualize the Capital Allocation Line, Utilityas a function of y$,$ and the Tangent Indifference Curve. $[$Use sheet Portfolio Optimization $1]$Part II: This section entails modifying the structure of the utility function to observe its impact on the portfoliochoice problem. A more conventional approach in modeling the utility for portfolio choice is to assume investorsderive utility from their final wealth after investment rather than the expected return minus the costs of risk.Suppose the investor begins each month with an initial wealth of w$0=$ $$1$ and invests y percent of that in a riskyasset, allocating the remaining $1$ y percent to the risk$-$free asset. At the end of the month, the investors finalwealth is represented by w$1($y$)=$ $$1\backslash$times $(1$ rf y$($rp rf $)).$ In this alternative mode of modeling, the investor gainsutility of U$($w$1($y$))$ from this final wealth, where U$()$ is the chosen utility function. In this approach, the parametery is selected to maximize E$[$U$($w$1($y$))]\mathrm{.}1.$ For instance, the Constant Absolute Risk Aversion $($CARA$)$ utility function is represented as U$($w$)=$exp$($A $\backslash$times w$),$ where A is the Absolute Risk Aversion parameter of the investor. Proceed to fill in thetable with the final realized wealth after investment for each value of y$.$ Then, calculate the realized utilityfor each observation using the CARA utility function. $[$Use sheet Portfolio Optimization $2]2.$ For each level of y$,$ compute the Expected Utility by taking the average of realized utility over the entiresample$\mathrm{.}3.$ Plot the expected utility as a function of y$,$ and identify the value of y at which the utility reaches its peakas the solution to the portfolio choice problem. $[$Use sheet Portfolio Optimization $2]4.$ Another standard utility function is the Constant Relative Risk Aversion $($CRRA$)$ function, given by U$($w$)=$w$1$A$1$A $,$ where A denotes the Relative Risk Aversion parameter of the investor. In the specified sheet, modify theutility function to the CRRA utility function and replicate the aforementioned exercise. $[$Use sheet PortfolioOptimization $3]5$