Two long-time friends, Konanbonvieu and Gazoukpleufie were given a lumpsum of $ 400,000 by a good will samaritan because of their 40 years commitment for community service and helping other in dire needs. They used their own homes to provide a shelter to homeless people and treated them like their own kids although they were having hard time to make ends meet. The two friends decided to split the money in half. They wish to invest their $200,000 in three assets. For that, they need to determine how well your portfolio performs in a year. You have been assigned to advise them. You know that the returns characteristics of the three assets are normally distributed. In addition, you know that The first asset gives a mean yearly return of 4.59% with a standard deviation of 0.10. - The second asset gives a mean yearly return of 2.85% with a standard devi- ation of 0.05. The third asset gives a mean yearly return of 6.26% with a standard deviation of 0.16. The three assets are correlated as follows: - The correlation between asset 1 and 2 is 0.30. - The correlation between asset 1 and 3 is 0.15. - The correlation between asset 2 and 3 is -0.10. Answer the following questions by providing 4 decimal accuracy: 1 (a) The two long-time friends, Konanbonvieu and Gazoukpleufie, agreed on in- vesting in the following proportion 35%, 25%, and 40%. However, they cannot agree on what asset gets what proportion. Konanbonvieu who does not worry too much about volatility wants to go in for the highest return. His friend, Gazoukpleu worries a lot about volatility and would like to go in for the low- est volatility. Advice these two friends as to what investment they need to undertake. (14pts) You could consider the following six portfolios, find their returns and volatilities. Show the details of your work. (i) Portfolio 1: Invest 35% of your money in asset 1, 25% in asset 2, and the rest in asset 3. (ii) Portfolio 2: Invest 35% of your money in asset 1, 25% in asset 3, and the rest in asset 2. (iii) Portfolio 3: Invest 35% of your money in asset 2, 25% in asset 1, and the rest in asset 3. (iv) Portfolio 4: Invest 35% of your money in asset 2, 25% in asset 3, and the rest in asset 2. (v) Portfolio 5: Invest 35% of your money in asset 3, 25% in asset 1, and the rest in asset 2. (vi) Portfolio 6: Invest 35% of your money in asset 3, 25% in asset 2, and the rest in asset 1. (b) After giving some thoughts, Konanbonvieu, decided to invest 50% of his $ 200,000 in asset 3 but he is sure which of asset 1 or asset 2 to invest the rest of his money in to make the highest buck. In which asset will you recommend that he puts the rest of his money. He would also like to know the volatility of his portfolio. (5pts) (c) After giving some thoughts, Gazoukpleufie, decided to invest 50% of his $ 200,000 in asset 3 but he is sure about how to invest he should invest in asset 1 and asset 2 with the rest of his money to make the highest buck but he does not want the volatility of his portfolio to exceed 12%. In what proportions shall he be invested in asset 1 and asset 2, respectively? (9pts) (d) Discuss how would you consider changing the portfolio allocation in (c) to improve the performance of your investment for a similar return or a similar risk level? To what values would you change your portfolio allocation to optimize the performance of your investment? State the portfolio model to solve but do not solve it. (5pts) Two long-time friends, Konanbonvieu and Gazoukpleufie were given a lumpsum of $ 400,000 by a good will samaritan because of their 40 years commitment for community service and helping other in dire needs. They used their own homes to provide a shelter to homeless people and treated them like their own kids although they were having hard time to make ends meet. The two friends decided to split the money in half. They wish to invest their $200,000 in three assets. For that, they need to determine how well your portfolio performs in a year. You have been assigned to advise them. You know that the returns characteristics of the three assets are normally distributed. In addition, you know that The first asset gives a mean yearly return of 4.59% with a standard deviation of 0.10. - The second asset gives a mean yearly return of 2.85% with a standard devi- ation of 0.05. The third asset gives a mean yearly return of 6.26% with a standard deviation of 0.16. The three assets are correlated as follows: - The correlation between asset 1 and 2 is 0.30. - The correlation between asset 1 and 3 is 0.15. - The correlation between asset 2 and 3 is -0.10. Answer the following questions by providing 4 decimal accuracy: 1 (a) The two long-time friends, Konanbonvieu and Gazoukpleufie, agreed on in- vesting in the following proportion 35%, 25%, and 40%. However, they cannot agree on what asset gets what proportion. Konanbonvieu who does not worry too much about volatility wants to go in for the highest return. His friend, Gazoukpleu worries a lot about volatility and would like to go in for the low- est volatility. Advice these two friends as to what investment they need to undertake. (14pts) You could consider the following six portfolios, find their returns and volatilities. Show the details of your work. (i) Portfolio 1: Invest 35% of your money in asset 1, 25% in asset 2, and the rest in asset 3. (ii) Portfolio 2: Invest 35% of your money in asset 1, 25% in asset 3, and the rest in asset 2. (iii) Portfolio 3: Invest 35% of your money in asset 2, 25% in asset 1, and the rest in asset 3. (iv) Portfolio 4: Invest 35% of your money in asset 2, 25% in asset 3, and the rest in asset 2. (v) Portfolio 5: Invest 35% of your money in asset 3, 25% in asset 1, and the rest in asset 2. (vi) Portfolio 6: Invest 35% of your money in asset 3, 25% in asset 2, and the rest in asset 1. (b) After giving some thoughts, Konanbonvieu, decided to invest 50% of his $ 200,000 in asset 3 but he is sure which of asset 1 or asset 2 to invest the rest of his money in to make the highest buck. In which asset will you recommend that he puts the rest of his money. He would also like to know the volatility of his portfolio. (5pts) (c) After giving some thoughts, Gazoukpleufie, decided to invest 50% of his $ 200,000 in asset 3 but he is sure about how to invest he should invest in asset 1 and asset 2 with the rest of his money to make the highest buck but he does not want the volatility of his portfolio to exceed 12%. In what proportions shall he be invested in asset 1 and asset 2, respectively? (9pts) (d) Discuss how would you consider changing the portfolio allocation in (c) to improve the performance of your investment for a similar return or a similar risk level? To what values would you change your portfolio allocation to optimize the performance of your investment? State the portfolio model to solve but do not solve it. (5pts)