You are to build a portfolio of four stocks.

Each stock should have at least $10$ years of data. Do not pick all stocks from the same sector.

Part $1$: $(15\%)$ Choosing the portfolio and getting some basic statistics for each stock

$1.$ Download monthly data for the last ten years for the four stocks from Yahoo! Finance. $(5\%)$

$2.$ Calculate monthly average returns, monthly excess returns, standard deviations and Sharpe

Ratios for the four stocks for the entire period. Use the adjusted close field to calculate returns.

$(10\%)$

T$-$bill rates can be accessed through Yahoo! Finance using the symbol $^$IRX.

Part II: $(10\%)--$ Build the variance covariance matrix for the four stocks.

Part III: $(30\%)$ Graph the efficient frontier.

Using the entire period:

Plot $1000$ random portfolios of the four stocks $($do not allow for short sales$).(10\%)$

Find the minimum variance portfolio and plot it on the graph. $(5\%)$

Find the optimal portfolio and plot it on the graph. $(5\%)$

Using the risk free rate, plot the investor$$s opportunity set. $(5\%)$

Plot the $4$ stocks individually on the graph. $(5\%)$

Part IV: $(10\%)$ Find the complete portfolio.

For an investor with A$=5,$ find their complete portfolio and calculate the utility. $(5\%).$

Plot the indifference curve which contains this portfolio. $(5\%)$

Part V: $(35\%)$ Create structured products

Create a product which provides investors with double the monthly exposure to the portfolio

you created. Calculate the average monthly return, standard deviation of returns, and Sharpe

ratio of the product. $(10\%)$

Create a product which $$volatility controls$$ the portfolio you created by targeting a $10\%$

volatility. Use the first year of your data to calculate the standard deviation of your portfolio.

Then use that calculation to allocate to the portfolio and risk$-$free rate. For example, if you

calculate a $20\%$ volatility, then you should invest $50\%$ in the portfolio and $50\%$ in the risk$-$free

rate. Continue this process each month. $(20\%)$

Calculate the average monthly return, standard deviation of returns, and Sharpe ratio of the

product.

Which of the three performs best $($in terms of Sharpe ratio$)?$ Explain the relative performance

of these two structured products as compared to the portfolio$$s performance. $(5\%)$