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Please explain and show all working An investment portfolio is composed of three shares (X, Y, and Z), which have an expected annual (discrete) return

Please explain and show all working

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An investment portfolio is composed of three shares (X, Y, and Z), which have an expected annual (discrete) return of 1%, 3%, and 5% respectively. The corresponding standard deviations are 3%, 6%, and 20%. The correlation in the returns between A and B is 0.1, the correlation between A and C is 0.3, and the correlation between B and C is -0.45. The weights of the three shares are 80%, 10%, and 10% in the portfolio. (i) (ii) (iii) [2 marks] What is the expectation of the portfolio return? [4 marks] What is the standard deviation of the portfolio return? [2 marks] The Board asks you to provide VaR 1% of the portfolio. Is there enough information provided to calculate this value? If yes, provide your estimated VaR 1%. If not, state what information is needed to calculate VaR 1%. [2 marks] An external consultant suggests a Gaussian copula can be used to study the worst returns. Calculate the appropriate tail dependence of this copula and comment if it should be used for the proposed purpose. (iv) An investment portfolio is composed of three shares (X, Y, and Z), which have an expected annual (discrete) return of 1%, 3%, and 5% respectively. The corresponding standard deviations are 3%, 6%, and 20%. The correlation in the returns between A and B is 0.1, the correlation between A and C is 0.3, and the correlation between B and C is -0.45. The weights of the three shares are 80%, 10%, and 10% in the portfolio. (i) (ii) (iii) [2 marks] What is the expectation of the portfolio return? [4 marks] What is the standard deviation of the portfolio return? [2 marks] The Board asks you to provide VaR 1% of the portfolio. Is there enough information provided to calculate this value? If yes, provide your estimated VaR 1%. If not, state what information is needed to calculate VaR 1%. [2 marks] An external consultant suggests a Gaussian copula can be used to study the worst returns. Calculate the appropriate tail dependence of this copula and comment if it should be used for the proposed purpose. (iv)

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