UE and your team have decided to invest in the following five stocks: Caterpillar Inc. $($CAT$)$

Johnson and Johnson $($JNJ$),$ Walmart $($WMT$),$ Nvidia $($NVDA$),$ and Proctor and Gamble $($PG$).$

The analysis will be conducted assuming a risk$-$free rate of $0\%$ and no exchange rate fluctuations.

Trading fees and transaction costs are negligible given the size of UE$$s portfolio. Assume UE

uses historical averages as proxies for expected returns unless otherwise instructed. For portfolio

construct purpose, use historical monthly returns from January $2016$ to December $2020($note that

you need prices on $1/1/2021$ to calculate returns for December $2020).$ For portfolio performance

evaluation purpose, use monthly returns from January $2021$ to December $2022.$

$1.$ UE$$s current risky portfolio invests in CAT, JNJ$,$ and WMT$.$ UE$$s CFO is considering

expanding its investment universe to include NVDA and PG$.$ Assuming no trading

restrictions, plot the efficient frontier using the three stocks that UE currently invests in$.$

Compare it with the efficient frontier generated using all five proposed stocks. Do you

recommend UE to expand its investment universe? Why or why not?

$2.$ Assuming no trading restrictions, how should UE construct its risky portfolio using the

aforementioned five stocks? Refer to this portfolio as P$1.$

$3.$ How should UE construct its risky portfolio if it is not allowed to short sell? Refer to this

portfolio as P$2$ and report its weights.

$4.$ Explain whether the weights for P$1$ and P$2$ make economic sense.