You may use graph paper to answer this question. Assume investors are allowed to

Question

You may use graph paper to answer this question. Assume investors are allowed to choose only one of the following risky portfolio. Assuming there is no a risk-free asset, which portfolios make up the efficient set? Now assume there is a risk-free asset with a return of 10%. Further assume you can invest in a combination of the risk-free asset and one of the risky portfolios A through G. Which one of the risky portfolios should be combined with the risk-free asset to obtain in the best risk-return tradeoff? Using the combination of the risk-free asset and the one risky portfolio in your answer to part (B), what is the highest expected return you can obtain for a standard deviation of 10%? To obtain the expected return in part (c), what proportion of your money must be invested in the risk-free asset? What is the beta of the portfolio in (c)?

Explanation / Answer

Answer: Part A: If we have more than one portfolio are available but we have to decide invest in only one portfolio, we decide on the basis of Coefficeint of variation. Coefficeint of variation means risk per unit of mean data Coefficeint of variation = standard deviation / mean return Portfolio Return Standard Deviation Coefficeint of variation A 15% 20%                                         1.33 B 20% 20%                                         1.00 C 30% 20%                                         0.67 D 25% 25%                                         1.00 E 30% 25%                                         0.83 F 30% 30%                                         1.00 G 35% 35%                                         1.00 As per the above analysis coefficient of variation of portfolio C is lower than other portfolio. It means portfolio C is less risky as compare to other. Hence we select portfolio C for Investment. Part B: We asuume that weight of risk free return & other risky portfolio are equal Portfolio Return = Sum of (Weight of securities *return of Securities) Portfolio Standard Deviation = Sum of (Weight of securities *Standard Deviation of Securities) Standard Deviation of risk free return = 0 Portfolio with Risk free return Return Standard Deviation Coefficeint of variation A 12.50% 10.00%                                         0.80 B 15.00% 10.00%                                         0.67 C 20.00% 10.00%                                         0.50 D 17.50% 12.50%                                         0.71 E 20.00% 12.50%                                         0.63 F 20.00% 15.00%                                         0.75 G 22.50% 17.50%                                         0.78 As per the above analysis coefficient of variation of portfolio C with risk free return is lower than other portfolio. It means portfolio C with risk free return is less risky as compare to other. Hence we select portfolio C for Investment. Part C: As per calculated in part B standard deviation of combination of risk free return & Portfolio C is 10% , return is 20%. Here given standard deviation is also 10% so highest expected return will be also 20% Part D: We must be invest 50% of Money in the risk free asset to get expected return calculated in part C. Part E: Assume there is only A, B, C, D, E, F, G securities in the Market Market Return = average return of securities =(15+20+30+25+30+30+35)/7 26.43% Require Return of Portfolio C =risk free return +Beta*(market return - risk free return) 30% =10%+Beta*(26.43%-10%) 20%/16.43% =Beta Beta =1.217 Portfolio Beta =weight of C*Beta+Weight of risk free return*Beta =0.5*1.217+0.5*0 =0.6085

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