4. Consider the following scenario analysis for asset A and asset B. State of economy Recession Normal Expansion 0.3 Probability Return on asset A Return on asset B 0.2 -20% -15% 0.5 18% 20% 50% 10% Assume that of your $40,000 portfolio, you invest $15,000 in asset A and $25,000 in asset B. (a) Write down the probability distribution of your future portfolio value. (b) Find the correlation between the return on the two assets. (c) Find (i) the expected rate of return of your portfolio, and (ii) the volatility of your portfolio. (d) (i) Determine the minimum variance portfolio consisting of asset A and asset B. Explain how you can construct a $40,000 portfolio with the two assets. (ii) Compare the minimum variance portfolio with your portfolio in terms of expected rate of return and volatility. (e) Suppose now you want to construct a $10,000 portfolio with different targets. Determine all the possibilities of constructing such a portfolio (with exact amounts stated for the two assets) that you can achieve the following targets: (i) The expected return (in dollar term) is $4,800. (ii) The portfolio variance is 0.0175. 4. Consider the following scenario analysis for asset A and asset B. State of economy Recession Normal Expansion 0.3 Probability Return on asset A Return on asset B 0.2 -20% -15% 0.5 18% 20% 50% 10% Assume that of your $40,000 portfolio, you invest $15,000 in asset A and $25,000 in asset B. (a) Write down the probability distribution of your future portfolio value. (b) Find the correlation between the return on the two assets. (c) Find (i) the expected rate of return of your portfolio, and (ii) the volatility of your portfolio. (d) (i) Determine the minimum variance portfolio consisting of asset A and asset B. Explain how you can construct a $40,000 portfolio with the two assets. (ii) Compare the minimum variance portfolio with your portfolio in terms of expected rate of return and volatility. (e) Suppose now you want to construct a $10,000 portfolio with different targets. Determine all the possibilities of constructing such a portfolio (with exact amounts stated for the two assets) that you can achieve the following targets: (i) The expected return (in dollar term) is $4,800. (ii) The portfolio variance is 0.0175