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Unformatted text preview: ARE 171a Fall 2011 Homework 3 (due in class Monday, Nov. 21) 1. (12) Jennifer's portfolio consists of three stock holdings, with their portfolio weights shown: Nucor Defense Systems (35%) Vista Travel (40%) Tom's Toothpaste (25%) These stocks' returns are affected by the state of international relations, as follows: State of the world Major int'l. hostilities Minor int'l tensions Peaceful relations Prob: 30% 50% 20% Stock: Nucor 40% 14% -6% Vista -20% 12% 18% Tom's 9% 11% 12% a.(1) Do these stocks' returns appear to be correlated, and if so, in which direction? (consider each pair of 2, verbal answers only) b. (6)) Find the expected rate of return, standard deviation of return, and coefficient of variation of each stock, if held alone. Which has the highest expected rate of return? Which has the lowest CV? c. (5) Now find the expected rate of return, standard deviation of return, and CV for Jennifer's portfolio. Is the portfolio's expected value equal to the weighted average of the 3 stocks' individual returns? Is the portfolio's standard deviation equal to the weighted average of the 3 stocks' individual std. deviations? Show your last 2 answers numerically. (hint, it's quick and easy to work this problem on a spreadsheet) 2. (22) Simon is considering investing in 2 stocks: Luxe Jewelry (LUX) and Ben's Wholesale Foods (BEN). Based on past returns, the stocks returns are expected to perform as follows: LUX expected return RL = 10%, L=9% BEN expected return RB = 8%, B=5% The correlation coefficient between LUX and BEN is +.2 a. (2) Calculate each firm's CV. Based on this result, which would be the safer investment, if held alone? b. (7) Suppose Simon is very risk averse, and he wants to choose portfolio weights such that his portfolio std. deviation is minimized. What weights should he choose? What is the expected return, std. deviation of return, and CV for this portfolio? c. (13) Calculate the portfolio's expected return and std. deviation of return for the following weights: wL = 0, .2, .4, .6, .8 and 1.0. Using these results, plus your answer from part b, plot the risk-return choices that can be obtained by blending these 2 stocks, and shade in the efficient frontier. (expected return on y axis, sigma on x axis) 3. (8) Suppose a broadly diversified bundle of stocks is expected to yield a return of Rmbar = 8%, with a standard deviation of m = 7%. The risk-free rate of return is Rf = 1%. a. George is cautious, so he invests 30% of his $10,000 in stocks, and the other 70% in short-term Treasury bills. Find his portfolio's expected return, std. deviation of return, and CV. b. Justine is more adventurous. She invests her $10,000 in personal funds, plus another
$10,000 borrowed from her broker, and puts all the money into stocks. Find her portfolio's expected return, std. deviation of return, and CV. c. Alexis has big plans for the future, and she decides she must earn an expected return of 10%. What portfolio weights must she use to achieve this goal? Find her portfolio's deviation of return and CV. d. Max has decided that he is willing to bear risk so long as his portfolio std. dev. does not exceed p = 3.5%. Find his portfolio weights, expected return and CV. e. Sketch a graph that shows how these friends' portfolios are positioned along the capital market line. 4. (8) A firm's balance sheet as of Dec. 31st, 2010 is shown below: (all values in millions) Assets 12-31-2010 Cash 50 Other current assets 155 Net fixed assets 340 Total assets 545 Liabilities and shareholders equity Current liabilities 85 Long term debt 135 Shareholders' equity 325 Total liab and s. equity 545 (Note: this firm is also shown on the income and balance sheet handout, posted under resources) a. (5) During 2011, the firm's sales were $700 m., cost of goods sold was $400 m, depreciation was $88 m., interest paid was $12 m., and taxes paid were 25% of EAT. A dividend of $50m was issued to shareholders. Using this information, prepare the 2011 income statement. Also find 2011 EPS and dividend per share, assuming there are 20 million shares outstanding. If the firm previously (in 2010) had EAT of $105 m., and paid dividends of $45m, also with 20 million shares outstanding, what was the rate of growth in EPS between 2010 and 2011? What was the rate of growth in div. per share? b. (3) Now that 2011 has come to an end, we need to prepare the balance sheet for 12-31-2011. Using the 2010 balance sheet above, the 2011 income statement from part a, and the information below, write the 12-31-2011 balance sheet. During the 2011 calendar year, the firm paid off $10 million in long-term bond principal. It increased its holdings of cash by $5m, and increased other current assets by $15 m. Its current liabilities increased by $5 m. (Hint: to finish the balance sheet, you will need to calculate the change in net fixed assets such that the balance sheet balances.) How much did the firm invest in new fixed assets? ...
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