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Homework_3_solutions

Homework_3_solutions - UNIVERSITY OF NORTH CAROLINA AT...

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U NIVERSITY OF N ORTH C AROLINA A T C HAPEL H ILL K ENAN -F LAGLER B USINESS S CHOOL B USI 408: C ORPORATE F INANCE S OLUTIONS TO A SSIGNMENT #3 P ROF . A RZU O ZOGUZ F ALL 2009 1. Go to http://finance.yahoo.com and download monthly stock prices for the following three stocks: Proctor and Gamble (PG) Apple Computer (AAPL) Caterpillar (CAT) a. Enter each ticker symbol at the top of the page. Then, click on “Historical Prices” on the left-hand side. Download monthly stock price data for each stock, starting in December 2001 and ending in December 2007. (Note that you can download data at many frequencies; make sure you download the monthly data). Then do the same for the S&P 500 index (ticker symbol ^GSPC) over the same period. b. Use the price data to calculate monthly returns from January 2002 through December 2007 for each stock. See attached spreadsheet. c. Compute the mean monthly return and standard deviation for the monthly returns of each stock. Convert the monthly statistics to annual statistics for easier interpretation (multiply the mean monthly return by 12, and multiply the monthly standard deviation by the square root of 12.) See attached spreadsheet. d. Consider four portfolios with the following weights: i. Equally-weighted ii. 30% in PG, 20% APPL, and 50% CAT iii. 50% in PG, 30% APPL, and 20% CAT iv. 20% in PG, 50% APPL and 30% CAT Compute the expected return and volatility for each portfolio. See attached spreadsheet. e. Plot the three stocks, the S&P index and the four portfolios in part (d) on the return-volatility space, with volatility on the x-axis and the average return on the y-axis. Compare the eight investment opportunities. Can you recommend buying (or not buying) any of these investments?
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f. Using Excel regression analysis, run a regression of each stock’s monthly returns on the ‘market’ (S&P 500) returns to estimate each stock’s beta. ߚ ஼஺் ൌ 1.30 ߚ ஺஺௉௅ ൌ 1.47 ߚ ௉ீ ൌ 0.18 CAT Beta Estimation AAPL Beta Estimation
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PG Beta Estimation g. Using your best estimates for the current risk-free rate and the historical market risk premium, calculate each stock’s required rate of return on equity based on its beta. Let ݎ ൌ 3.5%. This is the current yield on the 10-year Treasury note. Coming up with the market risk premium is trickier. Let ܧሺܴ ሻ െ ݎ 5%. This is a conservative estimate. ܧሺܴ ஼஺் ሻ ൌ ݎ ൅ ߚ ஼஺் ൣܧ൫ܴ െ ݎ ൯൧ ൌ 3.5% ൅ 1.30 ൈ 5% ൌ 10% ܧሺܴ ஺௉௉௅ ሻ ൌ ݎ ൅ ߚ ஺஺௉௅ ൣܧ൫ܴ െ ݎ ൯൧ ൌ 3.5% ൅ 1.47 ൈ 5% ൌ 10.85%
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