Choose any $10$ risky assets from the market. These could be stocks investable assets with readily available price data.

$2.$ Gather the closing prices for your chosen assets over the past $3$ months.

$3.$ Calculate the simple$/$log returns for each asset over the chosen period.

$4.$ Apply Markowitz's mean$-$variance optimization to construct the efficient frontier.

$5.$ Choose two points on the efficient frontier representing two different risk tolerance

levels. For each point, calculate the corresponding weights for each asset to construct

a portfolio that maximizes expected return for that given level of risk.

$6.$ Use the CAPM formula to calculate the expected return for each of your $10$ risky

assets.

$7.$ Calculate the Capital market line $($CML$)$ equation using CAPM model. Plot the

efficient frontier and CML$.$

$8.$ Identify the tangency point on efficient frontier where CML touches it$.$ Discuss what this point represents and its significance.

$9.$ Choose $3$ of your risky assets and calculate individual security market lines.

$10.$ Calculate relevant performance measures $($e$.$g$.,$ Sharpe Ratio, Treynor Ratio$)$ for each of your optimized portfolios and compare them to individual assets. Discuss the implications of these measures in evaluating portfolio performance.

Submission guidelines:

You can complete the task using Python.

The report should include:

$1.$ A brief description of your chosen assets

$2.$ The calculated returns and risk measures for each asset.

$3.$ A graph showing the Markowitz efficient frontier and the two chosen points.

$4.$ The optimal portfolio weights for each chosen point on the efficient frontier.

$5.$ A brief discussion of the trade$-$off between risk and return in your portfolio choices.

$6.$ Discussion of the limitations of Markowitz optimization and its real$-$world

applications.