One problem with 3 questions....expected return of stock, standard deviation, and would you buy or not.

Test Book: Behavioral Finance by Ackert & Deaves 2-2 A stock has a beta of 1.2 and the standard deviation of its return is 25%. The market risk premium is 5% and the risk-free rate is 4%. A)What is the expected return for the stock? B)What are the expected return and standard deviation for a portfolio that is equally invested in the stock and the risk-free asset? C)A financial analyst forecasts a return of 12% for the stock. Would you buy it? Why or why not? Consider a person with the following utility function over wealth: u(w) = e^w, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $50,000 and a 60% chance of wealth of $1,000,000 as summarized by P(0.40, $50,000, $1,000,000). a. What is the expected value of wealth? b. Construct a graph of this utility function. c. Is this person risk averse, risk neutral, or a risk seeker? d. What is this person's certainty equivalent for the prospect? Ans 3 a Wealth(in hundreds of Probability (P) thousands of dollars) 0.4 0.6 Utility=e^wealth 0.5 10 Expected Utility Expected Value 1.6487212707 13216.538965392 6.2 22026.4657948067 Ans 3b Ans 3c As graph is convex person should be a risk seeker Ans 3d Prospect Certainty Equivalent Expected Utility(EU) Wealth =LOG(EU) [Base exp] 13216.539 9.48922427621 $948,922.43 4. An individual has the following utility function: u(w) = w.5 where w = wealth. a. Using expected utility, order the following prospects in terms of preference, from the most to the least preferred: P1(.8, 1,000, 600) P2(.7, 1,200, 600) P3(.5, 2,000, 300) b. What is the certainty equivalent for prospect P2? c. Without doing any calculations, would the certainty equivalent for prospect P1 be larger or smaller? Why? please show all steps and how to do utility graph in excel for 3. Ans 4 a P1 Probability (P) Wealth 1000 600 P2 Probability (P) Probability (P) 2000 300 Utility=Wealth ^0.5 Expected Utility 44.72135955 31.0209338128 17.3205080757 Wealth 0.5 0.5 Most Preferred to least preffered P2 P3 P1 Utility=Wealth ^0.5 Expected Utility 34.6410161514 31.5971805343 24.4948974278 Wealth 0.7 0.3 P3 Utility=Wealth ^0.5 Expected Utility 31.6227766017 30.1972007669 24.4948974278 1200 600 0.8 0.2 Expected Utility Ranking 31.5971805343 31.0209338128 30.1972007669 1 2 3 Ans 4 b P2 Certainty Equivalent Expected Utility(EU) Wealth =(EU)^2 31.597 998.38181771802 Ans 4c The certainty equivalent for prospect P1 will be smaller as compared to P2 because P2 is ranked higher as compared to prospect P1 A stock has a beta of 1.2 and the standard deviation of its return is 25%. The market risk premium is 5% and the risk-free rate is 4%. A)What is the expected return for the stock? Exp return = risk free rate + Beta(market risk premium) = 4 + 1.2(5) = 10% B)What are the expected return and standard deviation for a portfolio that is equally invested in the stock and the risk-free asset? Expected Return is .5(.10) + .5(.04) = .07 Standard Deviation is (.5)(.25) = 0.125 C)A financial analyst forecasts a return of 12% for the stock. Would you buy it? Why or why not? if the forecsat is 12% and the required return is 10%, you should buy the stock as it is undervalued. (A) EXPECTED RETURN = = = (B) RISK FREE RATE OF RETURN + BETA*MARKET RISK PREMIUM 4% + 1.2*5% 10% PORTFOLIO WEIGHT STOCK 0.5 RISK FREE ASSET 0.5 EXPECTED RATE OF RETURN= = 0.50*10% + 0.50*4% 7% STANDARD DEVIATION OF PORTFOLIO = WEIGHT OF STOCK * STANDARD DEVIATION = 0.50 * 0.25 = 0.125 CLARIFICATION SINCE THERE IS NO RISK IN RISK FREE ASSETS THEREFORE STANDARD DEVIATION WILL BE NIL FOR SUCH ASSETS (C ) RETURN AS PER CAPM RETURN FORECASTED = = 10% 12% SINCE CAPM RETURN IS LESSER THAN FORCASTED RETURN IT MEANS STOCK IS UNDERVALUED ADVISE BUY STOCK