1. You are provided with a file labelled “Multibetadata12,” with monthly data running from January of 2007 through June of 2012. Use the data to estimate a four-variable model (by using regression analysis) to address the issue of whether more than one factor might help to improve the CAPM. Does more than one factor appear to matter? As always, you will need to test for the significance of the R-squared and the individual coefficients. Note that “Rp-Rf” is a portfolio’s excess returns over the Treasury bill returns and represents the dependent variable on an index of equity returns; “Market” is the market’s excess return over the Treasury bill rate of return (i.e., a market effect); “Size” measures the difference in performance between small stocks and large stocks (i.e., a size effect); and “Value” stands for the difference between high “book-to-market” stocks and low “book to market” stocks (i.e., a value effect). Each of these three independent variables should be positively related to Rp-Rf, the portfolio excess return. What do you conclude? Why?
2. describe what it means to “beat the market.” Why do many individuals - both academic and non-academic believe that such is not systematically possible? Please be thorough. What may move you to temper this view? As part of your response, please provide a brief summary of the last two articles discussed in class.
3. Answer the following problems either separately or as an integrated essay, whichever you prefer.
a. In a file labelled “Complete Data File 3” on Blackboard, you will find monthly rates of return on 370 securities, the rates of return on the S&P 500, and the returns on the three-month U.S. Treasury bill. An accompanying file lists the securities. The rates of return run from January of 2007 through July of 2012. Please do the following: (1) for each of 75 securities that you choose, estimate the single-index model in excess form using the returns from January of 2006 through December of 2010, 60 observations, and (2) build a mean-variance efficient portfolio (using the arithmetic mean excess return of each security as the measure of the expected excess return).
b. Following the instructions below, please test the monthly performance of your portfolio against that of the S&P 500 from January of 2012 through July of 2012. In your testing, remember to use the geometric mean and to show your work. Did your portfolio outperform the market? Why or why not? As part of your discussion, does your portfolio contain any uncomfortably high correlation coefficients? Overall, what do you conclude?
DIRECTIONS FOR TRACKING THE MEAN-VARIANCE PORTFOLIOS
1. For January of 2012, find the rate of return for security i.
2. Multiply step 1 by the weight assigned to security i.
3. Repeat steps one and two for all securities in the mean-variance efficient portfolio.
4. Add the results in step 3. This is your portfolio’s return for January.
5. Multiply security i’s beta by the weight assigned to security i.
6. Repeat step 5 for all betas in the mean-variance efficient portfolio.
7. Add the results in step 5. This is your portfolio’s beta.
8. Subtract January’s risk-free rate of return from step 4. This is your portfolio’s excess return for January.
9. Divide the result of step 8 by the result of step 7. This is the Treynor measure for January.
10. Repeat steps 1-9 for February through July for all securities in the mean-variance efficient portfolio.
11. Subtract January’s risk-free rate of return from January’s S&P 500 rate of return.
12. Divide step 11 by the S&P 500’s beta (=1).
13. Repeat steps 11 and 12 for February through July.
14. Find the geometric mean of the mean-variance efficient portfolio’s returns from January through July and subtract the geometric mean of the risk-free rates of return from it. Divide the result by step 7, the portfolio’s beta, to get the portfolio’s Treynor measure for January through July. (Note: You will end up with one number.)
15. Find the geometric mean of the S&P 500’s rates of return from January through July and subtract the geometric mean of the risk-free rates of return from it. Divide the result by the S&P 500’s beta to get the S&P 500’s Treynor measure for January through July.
16. Compare the mean-variance efficient portfolio’s Treynor measure, month by month, with the S&P 500’s Treynor measure, month by month, and draw conclusions.
17. Compare the mean-variance efficient portfolio’s Treynor measure computed for January through July (i.e., step 14) with the S&P 500’s Trey nor measure computed for January through July (i.e., step 15) and draw conclusions.