Given the following information, determine the beta coefficient for Stock J that is consistent with equilibrium: ^rJ = 12.5%; rRF = 4.5%; rM = 10.5%.
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Subject: Finacial strategy & policy
8.8: Given the following information, determine the beta coefficient for
Stock J that is consistent with equilibrium: ^rJ = 12.5%; rRF = 4.5%; rM = 10.5%.
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- The following data have been developed for the Donovan Company:Probability of Stateof NatureState of Nature Market Return, Rm Return for the Firm, Rj0.10 1 -0.15 -0.300.30 2 0.05 0.000.40 3 0.15 0.200.20 4 0.20 0.50The risk-free (Rf) rate is 6%.Calculate the following:(a) The covariance of the return for the Donovan Company with the marketreturn.(b) What is the required return for the Donovan Company? How does thiscompare with its expected return?free rate is 6%, find the beta for a portfolio that has expected rate of returnof 10%.(i). What percentage of this portfolio must an individual put into the marketportfolio in order to achieve an expected return of 10%?Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi. (b) Calculate the optimal weight of combining asset i and the index portfolio M . (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .Suppose the index model for stocks A and B is estimated with the following results: rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB, σM = 20%, and RM = rM − rf . The regression R2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. Total: (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
- The standard deviation of return on investment a is 0.10, while the standard deviation of return on investment b is 0.04. If the correlation coefficient between the returns on A and B is_____________. A. -0.0447 B. -0.0020 C. 0.0020 D. 0.0447Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
- (c)If you rank portfolio A, B and C according to theirbetas and return variances respectively, will the threeportfolios have same ranking? Can you provide economic reasons as to why the two rankings should be (in)consistent with each other? 1a) Individual computations Unilever PLC (ULVR.L) easyJet plc (EZJ.L) Vodafone Group Plc (VOD.L) BP p.l.c. (BP.L) Rio Tinto plc (RIO.L) Rolls-Royce Holdings plc (RR.L GlaxoSmithKline plc (GSK.L) The Royal Bank of Scotland Group plc (RBS.L) United Utilities Group PLC (UU.L) Legal & General Group Plc (LGEN.L) FTSE All Average 0.8195% -0.7525% -0.7816% -0.2164% 1.2769% -1.2955% 0.4389% -1.4360% 0.1905% -0.1855% -0.0710% Variance 0.2703% 1.3022% 0.5005% 0.4719% 0.6608% 0.9559% 0.2603% 0.8903% 0.2848% 0.5415% 0.1391% Standard deviation 5.1990% 11.4112% 7.0747% 6.8692% 8.1289% 9.7771% 5.1019% 9.4355% 5.3363% 7.3585% 3.7298% Beta 0.4755 1.6528 1.0369 1.1451 0.9749 1.3961 0.7123 1.5693 0.4809 1.2841 1.0000…Consider the following information regarding a new investment that a company intends toundertake:.State of the Economy Probability Market Return Investment ReturnExpansion 0.30 40% 60%Normal 0.50 10% 25%Recession 0.20 -15% -40%a). Compute the variance and standard deviation of each b). Compute the correlation between the market the investment return(s) c). Compute the beta of the investment d). Assuming the risk free rate is 5% p.a. Compute the required rate return and advice if the investment is worth undertaken.Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA= 4.0% + 0.50RM + eA RB= -1.2% + 0.7RM + eB sigmaM= 17% ; R-squareA = 0.26 ; R-squareB= 0.18 Break down the variance of each stock to the systematic and firm-specific components (write in decimal form, rounded to 4 decimal places). Risk for A Risk for B Systematic Firm-specific
- APT An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk-free rate is 6%, the expected return on the first factor (r1) is 12%, and the expected return on the second factor (r2) is 8%. If bi1 = 0.7 and bi2 = 0.9, what is Crisp’s required return?Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of −0.3, and a beta coefficient of −1.5. Security B has an expected return of 12%, a standard deviation of returns of 10%, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?Consider the following information about the various states of economy and the returns ofvarious investment alternatives for each scenario. Answer the questions that follow.% Return on T-Bills, Stocks and MarketIndexState of the Economy Probability TBills Phillips PayupRubbermadeMarketIndexRecession 0.2 7 -22 28 10 -13Below Average 0.1 7 -2 14.7 -10 1Average 0.3 7 20 0 7 15Above Average 0.3 7 35 -10 45 29Boom 0.1 7 50 -20 30 43MeanStandard DeviationCoefficient of VariationCovariance with MPCorrelation with Market IndexBetaCAPM Req. ReturnValuation(Overvalued/Undervalued/FairlyValued)Nature of stock(Aggressive/Defensive)Question 1 Fill the parts in the above table that are shaded in yellow. You will notice that there are nineline items. Each line item is worth 2 marksQuestion 2 Using the data generated in the previous question (Question 1);a) Plot the Security Market Line (SML) b) Superimpose the CAPM’s required return on the SML c) Indicate which investments will plot on, above and…