Group Project
Instructions
This group assignment is due no later than Friday 10/18 at 11:59pm CST. You can do the assignment either in Microsoft Excel or Python.
- If you do your assignment in Excel, please submit your spreadsheet showing your work and a pdf document with your analysis. I expect your spreadsheet and document to be formatted professionally.
- If you do your assignment in Python, please convert your Jupyter notebook to HTML and submit the HTML file. The resulting HTML file should look like this document, meaning you must use titles, proper capitalization, markdown paragraphs explaining your work, properly formatted tables and figures, equations if necessary, and full sentences.
Using ChatGPT to get the Python code to run is okay, but copy-and-pasting full paragraphs in your report is not. I strongly advise that you do this in Python since you will be able to get the code almost instantly. Also, explain each part of your code as you write your report.
Presentation will count for 40% of the grade of this assignment. I will check all assignments for plagiarism using Turnitin.
Assignment
As a group of portfolio managers at an asset management firm, you have been tasked with implementing the Treynor-Black model to construct a portfolio designed to outperform the market.
Security Selection
Begin by selecting six stocks that you believe are either underpriced or overpriced. For each stock, provide a justification for your selection, such as financial ratios suggesting mispricing, recent news events, a broker’s recommendation, or other relevant factors.
For each selected security, perform a standard OLS regression as follows: \[
R_{i} = \alpha_{i} + \beta_{i} R_{m} + e_{i},
\] where \(R_{i} = r_{i} - r_{f}\) represents the monthly excess returns for security \(i\) over the risk-free rate, and \(R_{m} = r_{m} - r_{f}\) represents the monthly excess returns of the market. Use the 13-week Treasury Bill CBOE Index (^IRX) as a proxy for the risk-free rate, and be sure to convert its annualized rate into a monthly rate compounded monthly for your calculations. For the market proxy, use the SPDR S&P 500 ETF Trust (SPY), and ensure that you use Adjusted Prices to account for dividends when computing returns. Run the regressions using five years of historical data.
I do not need to see the output of each regression. Instead, generate one table that displays the relevant information for all securities at once:
- Alpha
- Beta
- R-square
- Volatility of returns
- Firm-specific volatility
Please explain whether you are reporting monthly or annualized estimates. To compute the firm-specific volatility, you can use \[ \sigma^{2}(e_{i}) = \sigma_{i}^{2} - \beta_{i}^{2} \sigma_{M}^{2}. \] Therefore, you will also need to compute the volatility of excess market returns.
For each security, generate a scatter plot that includes the regression line. Display all your plots tighlty in a three-row two-column configuration.
Computing the Portfolio Weights
As mentioned in the slides, to solve for the Treynor-Black model you need to compute \[ \lambda = \frac{1}{\frac{\ev{R_{M}}}{\sigma^{2}_{M}} + \sum_{i = 1}^{n} \frac{\alpha_{i}}{\sigma^{2}(e_{i})} (1 - \beta_{i})}. \] You have almost all the information but still need some. First, you need an estimate of the market risk-premium \(\ev(R_{M}).\) There is no right answer to estimate this number. It is one of the big mysteries in Finance. Do a Google search or ask ChatGPT to determine an estimate for it. For the alphas, you can either use the results of your regression if you believe that past alphas are a good forecast for future alphas, or just use numbers that adjust with the views you expressed at the begining when you selected the stocks.
You can now compute the portfolio weights as \[ \begin{aligned} w_{i} & = \lambda \frac{\alpha_{i}}{\sigma^{2}(e_{i})}, \\ w_{M} & = 1 - \sum_{i = 1}^{n} w_{i}. \end{aligned} \] If your weights are too extreme, like you are shorting 200% of one stock and buying 400% of another stock, revise your alpha estimates until you are satisfied with your estimates. Finally, compute the expected return, standard deviation of returns and Sharpe ratio of your portfolio.
Conclusion
Write a convincing paragraph explaining the potential of your portfolio selection. Comment on the proportion of the portfolio that stays passive vs active, and whether the weights of the active portfolio make sense.