Problem 4: Portfolio Optimization (25 pts) A technology company AFX is considering inve sting some of its savings in the stock market and has contacted a portfolio manager to optimize its asset allocation. The portfolio manager is highly familiar with four financial funds: Fund 1 PharmaPlus: a fund specialized in the pharmaceutical industry with an expected return of 2.4% over 5 years Fund 2 - AeroDyna: a fund specialized in the aircraft industry and related equipment with an expected return of 1.1% over 5 years. Fund 3 - FitWear: a fund specialized in the sports and sportswear industry with an expected return of 1.9% over 5 years Fund 4 Nano Comp: a fund specialized in nanotechnology components with an expected return of 2.1% over 5 years. The capital of AFX is 15,000$ and AFX has a particular interest in NanoComp since it overlaps with some of its own business activities. Hence, AFX requests that the amount invested in NanoComp is at least 30% of the total amount invested in the other funds. AFX also has a particular interest in the aircraft industry and requests that at least 10% of its capital be invested in the AeroDyna fund. Part A: Write a mathematical formulation for this problem. Clearly identify the objective function, the constraints, and the decision variables. (5 points) Part B: Solve the corresponding portfolio investment problem using AMPL. Provide a screen shot of your model and data file. Show the optimal asset allocation and the total expected return over 5 years How many funds are selected for the investment? (10 points) Part C: After some internal discussions, AFX is reconsidering its strategy in the light of risk management. Based on the portfolio manager estimation, the volatility of each fund with respect to a benchmark is: Fund Volatility (B-value) 1-PharmaPlus 1.65 2-AeroDyna 0.42 3-FitWear 0.81 4-NanoComp 1.24 AFX then requests that the total B-value of the portfolio should not be larger than 80% of the capital. Write the corresponding risk constraint and solve the updated portfolio investment problem using AMPL. Show the optimal asset allocation and the total expe cted return over 5 years. Which funds are selected for the investment? (10 points) Problem 4: Portfolio Optimization (25 pts) A technology company AFX is considering inve sting some of its savings in the stock market and has contacted a portfolio manager to optimize its asset allocation. The portfolio manager is highly familiar with four financial funds: Fund 1 PharmaPlus: a fund specialized in the pharmaceutical industry with an expected return of 2.4% over 5 years Fund 2 - AeroDyna: a fund specialized in the aircraft industry and related equipment with an expected return of 1.1% over 5 years. Fund 3 - FitWear: a fund specialized in the sports and sportswear industry with an expected return of 1.9% over 5 years Fund 4 Nano Comp: a fund specialized in nanotechnology components with an expected return of 2.1% over 5 years. The capital of AFX is 15,000$ and AFX has a particular interest in NanoComp since it overlaps with some of its own business activities. Hence, AFX requests that the amount invested in NanoComp is at least 30% of the total amount invested in the other funds. AFX also has a particular interest in the aircraft industry and requests that at least 10% of its capital be invested in the AeroDyna fund. Part A: Write a mathematical formulation for this problem. Clearly identify the objective function, the constraints, and the decision variables. (5 points) Part B: Solve the corresponding portfolio investment problem using AMPL. Provide a screen shot of your model and data file. Show the optimal asset allocation and the total expected return over 5 years How many funds are selected for the investment? (10 points) Part C: After some internal discussions, AFX is reconsidering its strategy in the light of risk management. Based on the portfolio manager estimation, the volatility of each fund with respect to a benchmark is: Fund Volatility (B-value) 1-PharmaPlus 1.65 2-AeroDyna 0.42 3-FitWear 0.81 4-NanoComp 1.24 AFX then requests that the total B-value of the portfolio should not be larger than 80% of the capital. Write the corresponding risk constraint and solve the updated portfolio investment problem using AMPL. Show the optimal asset allocation and the total expe cted return over 5 years. Which funds are selected for the investment? (10 points)