Two stocks, A and B. are available on a market. The mean returns and standard deviations...

 

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Two stocks, A and B. are available on a market. The mean returns and standard deviations of the returns are given as follows: Stock A B Mean return Standard deviation of return 15% 20% 8% 12% The correlation coefficient between the returns of the two stocks is PAB = 0.9. In this question, assume short-selling of stocks is allowed unless specified otherwise. (a) Show that Σ = where is the covariance matrix of the returns of the two stocks. [2 marks] (b) Calculate the mean return and the standard deviation of the return for the minimum-variance portfolio formed from these two stocks. [5 marks] (c) Is your answer to part (b) the same if short-selling is not allowed? If your answer is yes, provide your reasoning. If your answer is no, provide the asset weights for the new minimum-variance portfolio. [3 marks] Two more stocks, C and D. are now available in the same market, with mean returns. and standard deviations of the returns as follows: 0.0225 0.027 0.027 0.04 Stock Mean return Standard deviation of return C 25% 25% D 12% 14% The returns of these stocks are uncorrelated with each other, and are also uncorrelated with the returns of stocks A and B. (d) Pamela, a STAT3904 student, claims that it is never optimal to include stock Cin a portfolio because: if the inverse of A exists.] • stock C offers a lower mean return than stock D, but the two stocks carry the same amount of risk (standard deviation of return); • stock C offers the same mean return as stock B, but the former has a higher risk. Explain why Pamela's claim is incorrect. [3 marks] (e) Suppose the risk-free rate is 3% per annum effective. Using all four stocks and the risk-free asset, calculate the smallest risk (standard deviation of return) that one has to take in order to earn a mean return of 10%. [Hint: Suppose A is a block diagonal matrix, i.e., it can be written as A¹ = A = where B and C are square matrices of possibly different sizes, and 0 is a zero matrix appropriate dimensions. Then, we have B 0 OT C B-1 0 0T C-1 Two stocks, A and B. are available on a market. The mean returns and standard deviations of the returns are given as follows: Stock A B Mean return Standard deviation of return 15% 20% 8% 12% The correlation coefficient between the returns of the two stocks is PAB = 0.9. In this question, assume short-selling of stocks is allowed unless specified otherwise. (a) Show that Σ = where is the covariance matrix of the returns of the two stocks. [2 marks] (b) Calculate the mean return and the standard deviation of the return for the minimum-variance portfolio formed from these two stocks. [5 marks] (c) Is your answer to part (b) the same if short-selling is not allowed? If your answer is yes, provide your reasoning. If your answer is no, provide the asset weights for the new minimum-variance portfolio. [3 marks] Two more stocks, C and D. are now available in the same market, with mean returns. and standard deviations of the returns as follows: 0.0225 0.027 0.027 0.04 Stock Mean return Standard deviation of return C 25% 25% D 12% 14% The returns of these stocks are uncorrelated with each other, and are also uncorrelated with the returns of stocks A and B. (d) Pamela, a STAT3904 student, claims that it is never optimal to include stock Cin a portfolio because: if the inverse of A exists.] • stock C offers a lower mean return than stock D, but the two stocks carry the same amount of risk (standard deviation of return); • stock C offers the same mean return as stock B, but the former has a higher risk. Explain why Pamela's claim is incorrect. [3 marks] (e) Suppose the risk-free rate is 3% per annum effective. Using all four stocks and the risk-free asset, calculate the smallest risk (standard deviation of return) that one has to take in order to earn a mean return of 10%. [Hint: Suppose A is a block diagonal matrix, i.e., it can be written as A¹ = A = where B and C are square matrices of possibly different sizes, and 0 is a zero matrix appropriate dimensions. Then, we have B 0 OT C B-1 0 0T C-1

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a The covari ance matrix of the returns of the two stocks can be calculated as follows C ov A B PA BC ov A B 0 9 x 0 15 x 0 20 0 027 The covari ance m... View the full answer