Consider a 2-factor model for stock market. You are given the following data on risk free...

  

Transcribed Image Text:

Consider a 2-factor model for stock market. You are given the following data on risk free asset and two well-diversified porfolios: Asset Risk free Average Return Factor-1 beta Factor-2 beta 4% 0 0 Portfolio X 8.5% 0.5 0.5 Portfolio Y 16% 2 1 Consider a portfolio with unit beta on all two factors. Using the table above, what is a fair estimate of the expected return of the portfolio? (28 marks) Q1(b) A stock with variance of 13% has beta of 0.8. If the market variance is 15%, what is the idiosyncratic variance of the stock? If you invest 5% in each of 9 stocks and remaining percentage in the 10th stock with same variance of 13% and beta of 0.8, what would be the variance of your portfolio? Assume idiosyncratic returns are independent across stocks and market return (36 marks) Q1(c) According to the Treynor-Black model, the optimal weight in the active portfolio is given by w: W = a(1-BA)+(Erp - Tp) Q1(c) According to the Treynor-Black model, the optimal weight in the active portfolio is given by w: w A a(1-BA)+(Erp-TF)- Where A, BA and 2 are Jensen's alpha, beta and idiosyncratic variance of active portfolio respectively. The expected return, variance of passive market portfolio as well as risk-free rate are Erp, op and r respectively. You notice a portfolio with beta of 0.9 has Sharpe ratio equal 1.2 times of the market index. The expected return and standard deviation of market index are 12% and 30% respectively. If the risk- free rate is 5% and the standard deviation of portfolio is 28%, work out the optimal mix of this portfolio and the market portfolio using the Treynor-Black Model (36 marks) Consider a 2-factor model for stock market. You are given the following data on risk free asset and two well-diversified porfolios: Asset Risk free Average Return Factor-1 beta Factor-2 beta 4% 0 0 Portfolio X 8.5% 0.5 0.5 Portfolio Y 16% 2 1 Consider a portfolio with unit beta on all two factors. Using the table above, what is a fair estimate of the expected return of the portfolio? (28 marks) Q1(b) A stock with variance of 13% has beta of 0.8. If the market variance is 15%, what is the idiosyncratic variance of the stock? If you invest 5% in each of 9 stocks and remaining percentage in the 10th stock with same variance of 13% and beta of 0.8, what would be the variance of your portfolio? Assume idiosyncratic returns are independent across stocks and market return (36 marks) Q1(c) According to the Treynor-Black model, the optimal weight in the active portfolio is given by w: W = a(1-BA)+(Erp - Tp) Q1(c) According to the Treynor-Black model, the optimal weight in the active portfolio is given by w: w A a(1-BA)+(Erp-TF)- Where A, BA and 2 are Jensen's alpha, beta and idiosyncratic variance of active portfolio respectively. The expected return, variance of passive market portfolio as well as risk-free rate are Erp, op and r respectively. You notice a portfolio with beta of 0.9 has Sharpe ratio equal 1.2 times of the market index. The expected return and standard deviation of market index are 12% and 30% respectively. If the risk- free rate is 5% and the standard deviation of portfolio is 28%, work out the optimal mix of this portfolio and the market portfolio using the Treynor-Black Model (36 marks)