QUESTION 2 (i) Consider an equally weighted portfolio of three stocks, each of which is independently...

 

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QUESTION 2 (i) Consider an equally weighted portfolio of three stocks, each of which is independently distributed of the others [that is, Cov(ri, rj) = 0 for different securities i and j]. Assume also that each stock has the same total risk (o). What fraction of each stock's risk is diversified away by including it in this portfolio? [5 marks] (ii) The returns on three risky securities satisfy the following: = = 0.015, R₂ = 0.012, R3 = 0.04 dij R₁ 0012 013 021 02 023 = 631632 63 0.02 0.01 0.02 0.01 0.04 0.03 0.02 0.03 0.05 where R, is the expected return on security i, o, is the standard deviation of return on security i and oi, is the covariance between returns on securities i and j. Short selling of assets is allowed. (a) Calculate the proportions of securities 1, 2 and 3 in the global minimum variance portfolio. [6 marks] (b) Calculate the proportions of securities 1, 2 and 3 in the minimum variance port- folio such that the expected return on that portfolio is 2%. [6 marks] [Total: 17 marks] QUESTION 2 (i) Consider an equally weighted portfolio of three stocks, each of which is independently distributed of the others [that is, Cov(ri, rj) = 0 for different securities i and j]. Assume also that each stock has the same total risk (o). What fraction of each stock's risk is diversified away by including it in this portfolio? [5 marks] (ii) The returns on three risky securities satisfy the following: = = 0.015, R₂ = 0.012, R3 = 0.04 dij R₁ 0012 013 021 02 023 = 631632 63 0.02 0.01 0.02 0.01 0.04 0.03 0.02 0.03 0.05 where R, is the expected return on security i, o, is the standard deviation of return on security i and oi, is the covariance between returns on securities i and j. Short selling of assets is allowed. (a) Calculate the proportions of securities 1, 2 and 3 in the global minimum variance portfolio. [6 marks] (b) Calculate the proportions of securities 1, 2 and 3 in the minimum variance port- folio such that the expected return on that portfolio is 2%. [6 marks] [Total: 17 marks]

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