Assignment #3
Suppose that you are a fund manager managing a portfolio worth $50 million. You have adopted a fixed investment policy of 60% stocks (spread 30/20/10 amongst large, medium, and small cap stock portfolios, labeled LRGSTK, MEDSTK, and SMLSTK), 20% Corporate Bonds (CBOND), and 20% Government Bonds (GBOND) over the years. In spreadsheet Data for Assignment #3, you can find monthly returns for these assets. The spreadsheet also provides returns on three additional asset classes: Real Estate (Equity REITs), International Stocks (EAFE), and Precious Metals (PM). In addition, it provides the monthly returns on the value- weighted market portfolio (VWRET), the S&P 500 Index (SPRET), and one-month U.S. Treasury bills (TBILL).
Please use data to do the following analysis using Excel and upload your Excel file (with your detailed work) to Canvas. You may highlight your answer when necessary.
1. Provide performance statistics, including the annualized mean returns, annualized standard deviation, and Sharpe ratio for the following three funds: 1) fund under your management, 2) the value-weighted market portfolio (VWRETD), and 3) the S&P500 index over the whole period.
2. Plot the portfolio frontier given only the five risky assets (i.e., LRGSTK, MEDSTK, SMLSTK, CBOND, and GBOND) in which you are investing.
3. Is the portfolio of risky assets currently chosen an efficient portfolio (i.e., on the efficient frontier)? If not, calculate the investment proportions in the five risky assets required to construct an efficient risky portfolio that would deliver the same expected return as the current choice of risky portfolio.
4. Assume that risk-free rate is available. Calculate the investment proportions required to achieve the optimal risky (tangency) portfolio with the five risky assets. Calculate the expected return and standard deviation of this tangency portfolio.
5. Assume that you can invest in the risk-free asset. Suggest an efficient portfolio allocation to achieve your client’s objective of a floor rate of return equal to 1% per month. Also calculate the expected standard deviation of such a portfolio. Note: remember to annualize the floor rate of return.
6. You want to further diversify your portfolio holdings by including real estate (represented by Equity REITs), international stocks (represented by the MSCI EAFE index which includes stocks from Europe, Asia, and the Far East), and precious metals (denoted as PM) in your portfolio. Plot the minimum variance frontier in the presence of the eight risky assets vs. the earlier five risky assets.
7. You decide to include these three additional assets. Calculate the efficient portfolio allocations (risk-free asset & optimal risky portfolio) required to achieve the ‘floor’ rate of return of 1% per month with this expanded universe of assets. Also calculate the expected standard deviation of such a portfolio.