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As a financial analyst for CKC Corporation, you have provided a forecast (as demonstrated below) of the economy and the performance of your company in the economy. Use this information to illustrate the expected rate of return and the risk as measured by the standard deviation of those returns. Economic State Probability Return (r - E( r ))2 Recession 15% -2% 0.01932 Normal Growth 65% 12% 0.00000 Prosperity 20% 22% 0.01020 Expected Return 11.90% Variance 0.00494 Standard Deviation 7.03% Summary Measures Formula E(r) = S pi*ri mean s = S pi*(ri-E(r)) 2 2 variance 2 1/2 s = (s ) standard deviation Summary Measures You have decided to create a portfolio that includes only two assets, Mars, Inc. common stock and JVC Common stock. Before making your investment, you would like to determine the risk and return tradeoffs between these two stocks as you create your portfolio. Given the following return information, determine the correlation between these stocks and create the efficient frontier (using 10% weight increments) their combinations would reveal. Period rMars rJVC wMars rportfolio sportfolio rportfolio 1 18% 19% 0% 16.30% 7.47% 16.30% 2 14% 12% 10% 16.29% 6.75% 16.29% 3 13% 26% 20% 16.28% 6.04% 16.28% 4 14% 14% 30% 16.27% 5.33% 16.27% 5 15% 6% 40% 16.26% 4.65% 16.26% 6 17% 8% 50% 16.25% 3.99% 16.25% 7 19% 28% 60% 16.24% 3.37% 16.24% 8 18% 12% 70% 16.23% 2.81% 16.23% 9 18% 15% 80% 16.22% 2.37% 16.22% 10 16% 23% 90% 16.21% 2.10% 16.21% mean 16.20% 16.30% 100% 16.20% 2.10% 16.20% Std. Dev. 2.10% 7.47% Variance 0.00044 0.00558 Correlation 0.109214 Covariance 0.000171 rportfolio 68b374c6-2be8-4ff7-b26f-71abcdea699f.xls rportfolio 16.32% 16.30% 16.28% 16.26% 16.24% 16.22% 16.20% 16.18% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 68b374c6-2be8-4ff7-b26f-71abcdea699f.xls Suppose you are the money manager of a $4 million investment fund. The fund consists of 4 stocks with the following investments and betas. If the market's required rate of return is 14%, and the risk-free rate is 6%, what is the fund's required rate of return? Stock Investment Beta w rM 14% rRF 6% A $400,000 1.50 10.00% B $600,000 -0.50 15.00% C $1,000,000 1.25 25.00% D $2,000,000 0.75 50.00% Port $4,000,000 0.7625 rp 12.10% Portfolio Return HR Industries (HRI) has a beta of 1.8, while LR Industries (LRI) beta is 0.6. The risk-free rate is 6%, and the required rate of return on an average stock is 13%. Now the expected rate of inflation built into rRF falls by 1.5 percentage points, the real risk-free rate remains constant, the required return on the market falls to 10.5%, and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI? b HRI 1.80 old rM 13% rRF 6% Dp -1.5% b LRI 0.60 Dr* 0% new rM 10.5% new rRF 4.5% rHRI 15.3% rLRI 8.1% rHRI - rLRI 7.20% CAPM Stock X has a 10% expected return, a beta of 0.9, and a 35% standard deviation of expected return. Stock Y has a 12.5% expected return, a beta of 1.2, and a 25% standard deviation of expected return. The risk- free rate is 6% and the market risk premium is 5%. expected r b s rRF 6% rM - rRF 5% X 10% 0.9 35% Y 12.5% 1.2 25% a Calculate each stock's coefficient of variation. CVX 3.5 CVY 2.0 b Which stock is riskier for a diversified investor? Y, since the beta is higher than X c Calculate each stock's required rate of return. rX 10.500% rY 12.000% On the basis of the two stocks' expected and required returns, which d stock would be more attractive to a diversified investor? Y since its expected return exceeds its required return. Calculate the required return of a portfolio that has $7,500 invested in e Stock X and $2,500 invested in Stock Y. X $7,500 Y $2,500 rp 10.875% If the market risk premium increased to 6%, which of the two stocks would f have the larger increase in its required return? Y, since its beta is higher CV You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks. Kish's beta coefficient can be found as a weighted average of its stocks' beta. The risk-free rate is 6%, and you believe the following probability distribution for future market returns is realistic. Stock Investment Beta w Prob rM rRF 6% A $160 0.50 0.32 0.1 7% B $120 2.00 0.24 0.2 9% C $80 4.00 0.16 0.4 11% D $80 1.00 0.16 0.2 13% E $60 3.00 0.12 0.1 15% $500 1.8 0.11 a What is the equation for the SML? ri = 6.00% + b* ( 11.00% -6.00% ) b Calculate Kish's required rate of return. 15.00% c Suppose Rick Kish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is $50 million, it has an expected return of 15%, and its estimated beta is 2.0. Should Kish invest in the new company? At what expected rate of return should Kish be indifferent to purchasing the stock? exp. ret. 15% b 2 required return on new stock 16.00% No, the return is below the required return. indifferent at 16%. SML required return. SML

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posted: | 11/27/2011 |

language: | English |

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