12. When we calculated the efficient portfolios in Table 9.1, we assumed that the investor could not hold short positions (that is, have negative holdings). The book website contains an Excel program for calculating the efficient frontier with short sales.

1. Look at the efficient portfolios constructed from the 10 stocks in Table 9.1. How does the possibility of short sales improve the choices open to the investor?
2. Now download "Monthly Adjusted Prices" for 10 different stocks from the Standard and Poor's Market Insight website (www.mhhe.com/edumarketinsight) and enter the past returns into the Excel program. (The program will take up to 10 years of returns.) Enter some plausible figures for the expected return on each stock and find the set of efficient portfolios.

13. Download "Monthly Adjusted Prices" for General Motors (GM) and Harley Davidson (HOG) from the Standard & Poor's Market Insight website (www.mhhe.com/edumarketinsight). Use the Excel function SLOPE to calculate beta for each company. (See Practice Problem 11 for details.)

1. Suppose the S&P 500 index falls unexpectedly by 5%. By how much would you expect GM or HOG to fall?
2. Which is the riskier company for the well-diversified investor? How much riskier?
3. Suppose the Treasury bill rate is 4% and the expected return on the S&P 500 is 11%. Use the CAPM to forecast the expected rate of return on each stock.

14. Download the "Monthly Adjusted Prices" spreadsheets for Boeing and Pfizer from the Standard & Poor's Market Insight website (www.mhhe.com/edumarketinsight).

1. Calculate the annual standard deviation for each company, using the most recent three years of monthly returns. Use the Excel function STDEV. Multiply by the square root of 12 to convert to annual units.
2. Use the Excel function CORREL to calculate the correlation coefficient between the stocks' monthly returns.
3. Use the CAPM to estimate expected rates of return. Calculate betas, or use the most recent beta reported under "Monthly Valuation Data" on the Market Insight website. Use the current Treasury bill rate and a reasonable estimate of the market risk premium.
4. Construct a graph like Figure 9.3. What combination of Boeing and Pfizer has the lowest portfolio risk? What is the expected return for this minimum-risk portfolio?

16. Most of the companies in Table 9.2 are covered in the Standard & Poor's Market Insight website (www.mhhe.com/edumarketinsight). For those that are covered, use the Excel SLOPE function to recalculate betas from the monthly returns on the "Monthly Adjusted Prices" spreadsheets. Use as many monthly returns as available, up to a maximum of 60 months. Recalculate expected rates of return from the CAPM formula, using a current risk-free rate and a market risk premium of 7%. How have the expected returns changed from the figures reported in Table 9.2?

17. Go to the Standard & Poor's Market Insight website (www.mhhe.com/edumarketinsight), and find a low-risk income stock—Exxon Mobil or Kellogg might be good candidates. Estimate the company's beta to confirm that it is well below 1.0. Use monthly rates of return for the most recent three years. For the same period, estimate the annual standard deviation for the stock, the standard deviation for the S&P 500, and the correlation coefficient between returns on the stock and the S&P 500. (The Excel functions are given in Practice Questions above.) Forecast the expected rate of return for the stock, assuming the CAPM holds, with a market return of 12% and a risk-free rate of 5%.

1. Plot a graph like Figure 9.5 showing the combinations of risk and return from a portfolio invested in your low-risk stock and in the market. Vary the fraction invested in the stock from zero to 100%.
2. Suppose you can borrow or lend at 5%. Would you invest in some combination of your low-risk stock and the market? Or would you simply invest in the market? Explain.
3. Suppose you forecast a return on the stock that is 5 percentage points higher than the CAPM return used in part (a). Redo parts (a) and (b) with this higher forecasted return.
4. Find a high-beta stock and redo parts (a), (b), and (c).