1. Use WRDS to download monthly prices for 10 years for three stocks: Kroger, Walmart, and Century Casinos. For each stock calculate (a) the arithmetic average return, (b) the standard deviation, and...

1. Use WRDS to download monthly prices for 10 years for three stocks: Kroger, Walmart, and Century Casinos. For each stock calculate (a) the arithmetic average return, (b) the standard deviation, and (c) skewness. What does this tell you about the distribution of returns for each firm?

2. Calculate the correlation coefficient between Kroger and Walmart and between Walmart and Century Casinos.

3. Using the stock returns you downloaded in class and your answers to questions 1 and 2 above, calculate the returns and standard deviations for portfolios of (1) Kroger and Walmart and (2) Walmart and Century. For each pair of stocks, calculate portfolios with weights that go from 0% to 100% in increments of 20%. In other words, for Kroger and Walmart, calculate the return and sigma for portfolios containing 0% Walmart and 100% Kroger, 20% Walmart and 80% Kroger, and so on until you get to 100% Walmart and 0% Kroger. Here’s a hint. To calculate the return and standard deviation for any portfolio, you can either (1) use the formulas in the Portfolio Theory slide deck or you can (2) create a historical series showing what the portfolio return would have been in each month from 2010-2019 (by multiplying the historical return each month of each stock by the appropriate portfolio weight), and then taking the mean and standard deviation of that historical series. For both sets of portfolios (i.e., Kroger and Walmart and Walmart and Century) use Excel to plot an XY graph of the standard deviation (X) return (Y) relation.

4. There are N risky assets in the economy and 1 risk-free asset. The N assets all have the same expected return (10%) and the same standard deviation (30%). The assets are positively correlated with each other, but not perfectly positively correlated. You created an equal-weighted portfolio of all the risky assets, with the weight in each asset equal to 1/N. Will the expected return on this portfolio be greater than, equal to, or less than 10%? Will the standard deviation of this portfolio be greater than, equal to, or less than 30%? Write a sentence or two to explain each of your answers.

5. Open the file “Regression Results” from Canvas. Based on the single-index model regression output and other data in that file, calculate the total variance of Facebook’s excess return and show how to decompose that into its systematic and unsystematic components.

6. In the file “Regression Results” on Canvas you have single-index model regressions for 6 stocks. I want you to form an equal-weighted portfolio of those stocks and show what return that portfolio would have earned each month over the historical period covered by the file. Next, run a single-index model in which the Y variable is the monthly excess return on this equally weighted portfolio. Compare the alpha, beta, and R-squared values from this regression to the same numbers (alpha, beta, and R-squared) for the six individual regressions already reported in that file. Comment on (a) how does the beta in the single-index model regression for the portfolio compare to the average of the 6 betas reported in the single-index regressions for each of the 6 stocks (b) how does the alpha of the portfolio compare to the average of the alphas of the individual stocks (c) how does the R-square of the portfolio compare to the average of the R-square values in each of the 6 individual stock regressions.

7. You have obtained the following data on the CAPM Beta, the annual expected returns (E[R]) calculated as the arithmetic average return over the previous 10 years, and the annual standard deviations of returns for the following investment companies. SPY is an S&P 500 Index ETF, VTI is the Vanguard Total Stock Market ETF (U.S. only), VICEX is the actively managed USA Mutuals Barrier Investor (formerly known as the Vice Fund), CSIEX is the actively managed Calvert Equity A fund, FMAGX is the Fidelity Magellan Fund (formerly managed by Peter Lynch, whose record we discussed in class), and MKT is the CRSP value-weighted stock market index (i.e. the market portfolio). VICEX invests in “Vice Stocks,” which include stocks of gambling, alcohol, tobacco, firearms , and defense companies. CSIEX invests in “socially responsible” companies with positive environmental, social, and corporate governance policies (ESG) and excludes stocks of gambling, alcohol, tobacco, firearms, and defense companies. FMAGX invests primarily in large cap “growth” and “value” stocks of both domestic and foreign companies. FMAGX uses fundamental analysis of factors such as issuer’s financial condition and industry position, as well as market and economic conditions, to select investments. The annual risk-free rate is 0.5%.

For each fund and the MKT, complete the table below by calculating the performance evaluation measures.

You believe that the funds’ past performance is at least somewhat indicative of future fund performance.

a.) If you were to pick one fund only and invest all your money in that one fund, which fund would you choose based on the analysis above? [1-2 sentences]

b.) If you were to pick one fund only, but already owned shares in twenty other mutual funds (i.e., you are well diversified), which fund would you choose based on the analysis above? [1-2 sentences]