FINC3017 Investments and Portfolio Management

Assignment 1

Due: 11:59PM, 20 September 2024

Objective

The objective of Assignment 1 is to gain a deeper understanding of modern portfolio theory and the CAPM. The assignment consists of two parts. In the first part, you need to apply the portfolio theory to ten US stocks. In the second part, you need to evaluate if the returns of the ten stocks can be explained by the CAPM.

Part 1

You are hired as an investment consultant by a hedge fund that focuses on the following ten US stocks: Exxon Mobile (ticker XOM), PepsiCo (ticker PEP), 3M (ticker MMM), Walter Disney (ticker DIS), McDonald’s (ticker MCD), Nike (ticker NKE), Adobe (ticker ADBE), Starbucks (ticker SBUX), Ralph Lauren (ticker RL), and Costco (ticker COST).

Your task is to submit a professional report for your manager to address the following investment issues. Your analysis is based on implementing the Markowitz approach and monthly returns of the ten stocks over the sample period from January 2000 to December 2023, as contained in the Excel file ‘Assignment1_data’.

  1. Discuss the risk return characteristics of the ten stocks. Generate a table that reports summary statistics of stock returns including mean, standard deviation, skewness, minimum, and maximum. You also need to prepare a cumulative return plot.
  2. Plot and describe the investment opportunity set and efficient frontier of the ten stocks without and with the risk-free asset. Moreover, highlight the ten stocks on the same mean variance diagram. Generate a table that reports the weight of each stock in the tangency portfolio as well as the expected return and standard deviation of the tangency portfolio.

Assume the risk-free rate is 2% per annum.

  1. There are two individual investors, John and Alice who are interested in investing in your fund. Both investors’ utility is represented by:

= () − 1 2 σ2. John has a risk aversion coefficient () of 4 and $1 million USD to invest, and Amy has a risk aversion coefficient of 12 and $2 million USD to invest. Prepare a table that shows the portfolio allocation (in dollar amount) to the ten stocks and risk-free asset you would recommend to the two investors to maximise their utilities, as well as the expected returns, standard deviations, and Sharpe ratios of these recommended portfolios. Also, highlight the recommended portfolios for both investors on the same mean variance diagram used in question 2.

Additional Information

  • Express returns, standard deviations, and Sharpe ratios in annual term.
  • Set the initial weights to equal weights when conducting each optimization with Solver.
  • The data provided is adapted from real stock market data. You should only use the data provided to you in completing this report (you are not required to gather any additional data). Further, ignore any potential transaction costs, fees, and taxes in determining your responses.

Part 2

Using the above ten stocks as test assets, evaluate the ability of the CAPM to explain the variations in returns among these stocks.

  1. Plot average excess returns of the 10 stocks against their CAPM betas and discuss your findings.
  2. Use the Fama-MacBeth regression approach to evaluate the performance of the CAPM and discuss your findings.
  3. Discuss the current literature on the empirical performance of the CAPM (word limit: 300)

Additional Information

  • Estimate the betas using full sample information.
  • For Fama-MacBeth regressions, report both coefficient estimates and t-stats in a table
  • Use monthly returns of t-bills, provided in Assignment1_data’, as a proxy for risk-free rate.
  • Attach the references at the end of your report.

Submission

You need to prepare two files for submission in Canvas.

  1. a written report that contains your results and discussions. Submit your report as a pdf document via the ‘Assignment 1’ link in Canvas.
  2. Your workings. Submit your workings as an Excel spreadsheet (or code if using an alternative computing program) via ‘Assignment 1 – Supporting workings’ link in Canvas.

 

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