$4.$ You have graduated from your school and decided you want to be an independent investor. You are considering an investment in either a single stock or a portfolio of stocks. The two stocks you are doing due diligence on$,$ Maxwell, Corp. and Tru$-$Deal, Inc. The table below shows their historical returns. $(25$ points$)$

Year Maxwell $-$ Returns Tru$-$Deal $-$ Returns

$2017-20\mathrm{.}00\%-5.00\%$

$202042\mathrm{.}0015\mathrm{.}00$

$202120\mathrm{.}00-13\mathrm{.}00$

$2022-8\mathrm{.}0050\mathrm{.}00$

$202325\mathrm{.}0012\mathrm{.}00$

a$)$ Calculate the average rate of return for each stock during the $5-$year period.

b$)$ Suppose you had invested in a portfolio consisting of $50\%$ in each of the two stocks.

I. What would have been the realized rate of return on the in each year?

II$.$ What would have been the average return on the portfolio each year.

III. Calculate the standard deviation of returns for each stock and the portfolio.

IV$.$ If you are a risk averse investor. Assuming Maxwell, Corp AND Tru$-$Deal Inc. are your only choices. Would you prefer to hold each as a stand$-$alone investment or the portfolio? Explain your answer.