Question Details

Part One 

Part One 

Select five mutual funds, each with a different objective. Do not use money market or tax-exempt funds. A mutual fund can specify whatever objective its management wishes, and the fund can use its own terminology. You will encounter many objectives other than those listed in the textbook. Common examples are “balanced”, “growth and income”, “small company growth”, “BBB-rated bonds”, “precious metals”. Just make sure to select five different objectives. Then select one more fund whose objective is “international” investment. 

Also make sure that all funds have at least 10 years of annual performance data available. You must download (or create from higher frequencies) QUARTERLY DATA. The easiest way to obtain the data is at Yahoo Finance. When you have selected your funds, request a prospectus on each of them: this can be done at Yahoo Finance, by downloading the PDF file directly. 

• Prepare a single table showing the following for each of your six funds [TABLE 1]:  

• Fund name 

• Quarterly total return statistic for the past ten years. Make sure to use NAV that have been adjusted for dividends. 

• Arithmetic average quarterly return. 

• Geometric average quarterly return. 

• Standard deviation of quarterly returns. 

• The current value of $10,000 invested 10 years ago, assuming all distributions were reinvested. 

• Prepare a covariance matrix of the six funds [TABLE 2] 

• Prepare a correlation matrix of the six funds [TABLE 3] 

Part Two 

• Using Treasury bill rates and the S&P 500 index, estimate the beta of each fund. Constant maturity 3-month T-bill rates may be obtained on the web site of The Federal Reserve Bank of Saint Louis, Missouri (“FRED”), Yahoo Finance, or Bloomberg. 

• Repeat part A using this time the Dow Jones Industrial Average instead of the S&P 500 index. 

• Show the T-bill rates and the two index levels in tabular form [TABLE 4]. 

• Write a short essay on why your answers from part A and B might be different. 

• Conduct a “Run Test” on the quarterly changes in the level of the S&P 500 index. Write a short essay on the interpretation of the results. 

Part Three 

• Construct an equally-weighted portfolio of your five funds. Prepare a table showing the arithmetic mean return, geometric mean return, and standard deviation of return for the five-fund portfolio over the ten years [TABLE 5A]. 

• Now add the international fund to your portfolio and construct an equally-weighted portfolio of your six funds. Prepare a table showing the arithmetic mean return, geometric mean return, and standard deviation of return for the six-fund portfolio over the ten years [TABLE 5B]. 

• Using Excel, prepare a graph showing the ten-year performance of each of your six funds, the five fund portfolio and the six-fund portfolio. This chart should show the dollar value of an initial $10,000 investment over the ten-year period [GRAPH 1]. 

Part Four 

Using the ten-year performance statistics of your six funds and the five-fund and six-fund portfolios determine and show graphically the efficient set using the following: 

• Mean-variance plot: this is merely a standard deviation / expected return plot showing six points, one for each fund and one for the five-fund portfolio and one for the six fund portfolio. Identify the point that shows the best return per unit of risk [GRAPH 2]. 

• Using the matrix Excel-based techniques learned in class, use the five funds and their statistics to derive the mean-variance frontier with no short sale allowed. Draw a plot showing the frontier along with the 5 mean-variance points of the five individual funds [GRAPH 3]. 

• Using the matrix Excel-based techniques learned in class, use the five funds and their statistics to derive the mean-variance frontier when short sale is allowed. Draw a plot showing the frontier along with the 5 mean-variance points of the five individual funds [GRAPH 4]. 

• Using the matrix Excel-based techniques learned in class, use the six funds and their statistics to derive the mean-variance frontier when short sale is allowed. Draw a plot showing the frontier along with the 6 mean-variance points of the six individual funds [GRAPH 5]. 

• Using the average T-Bill rate from part two calculate the expected return and the standard deviation of the optimal portfolio on efficient frontier (from part D) and show it on a graph. [Graph 5] 

• Assume A (risk aversion) of 3 and calculate the proportion of investment in the risky optimal portfolio and the risk free asset. 

Part Five  

Rank the performance of the six funds, the six-fund portfolio and the optimal risky portfolio according to the following criteria: 

• The Sharpe Measure 

• The Treynor Measure 

• The geometric mean return   

Part Six 

Write a short essay on how you would use results of your analysis in forming an optimal investment strategy.