1. (10 points) What are the inputs you need in order to maximize the expected return subject to a maximun level of risk? 2. (10 points) The best strategy when you choose two assets for your portfolio in order to reduce its risk is to invest in assets with the highest positive correlation, given this way you will maximize the expected return in economic booms. True or False and explain. 3. (10 points) Explain how is it possible in the CAPM to have assets with a lower expected return than the risk-free rate. 1. (10 points) If you know that the risk free rate is 5%, the return on the market portfolio is 10% and the B = 1 What is the expected return on asset i? 2. (10 points) If the weights on your portfolio composed of three assets are 50%, 20% and 30% and the expected return on the same assets are 2%, 5%, and 9%, respectively. What is the expected return on the portfolio? 3. (10 points) If you know that the covariance between assets ABC and the market port- folio is 3 and the variance on the market portfolio is 2, What is the risk free rate if asset ABC has an expected return of 10% and the return on the market portfolio is 8%? You want to optimize a portfolio composed of 3 assets. These are assets A, B and C. Asset C is risk free (means its return is given by rf). Assets A and B have a of 1.2 and 0.8, respectively. Assume the risk free rate is 2% (rf) and the market portfolio return is 20%. 1. (8 points) What are the expected returns on assets A and B, given by the CAPM? 2. (8 points) Using the information from the previous points, what is the expected return of a portfolio if you invest 20%, 30%, and 50% in assets A, B, and C, respectively? 3. (14 points) Suppose, in the previous exercise, you want to choose the weights optimally to get a 15% expected return. What are all the steps you have to carry out in order to perform this? Describe these steps and set the inputs, outputs and constraints you will need/obtain. 1. (10 points) What are the inputs you need in order to maximize the expected return subject to a maximun level of risk? 2. (10 points) The best strategy when you choose two assets for your portfolio in order to reduce its risk is to invest in assets with the highest positive correlation, given this way you will maximize the expected return in economic booms. True or False and explain. 3. (10 points) Explain how is it possible in the CAPM to have assets with a lower expected return than the risk-free rate. 1. (10 points) If you know that the risk free rate is 5%, the return on the market portfolio is 10% and the B = 1 What is the expected return on asset i? 2. (10 points) If the weights on your portfolio composed of three assets are 50%, 20% and 30% and the expected return on the same assets are 2%, 5%, and 9%, respectively. What is the expected return on the portfolio? 3. (10 points) If you know that the covariance between assets ABC and the market port- folio is 3 and the variance on the market portfolio is 2, What is the risk free rate if asset ABC has an expected return of 10% and the return on the market portfolio is 8%? You want to optimize a portfolio composed of 3 assets. These are assets A, B and C. Asset C is risk free (means its return is given by rf). Assets A and B have a of 1.2 and 0.8, respectively. Assume the risk free rate is 2% (rf) and the market portfolio return is 20%. 1. (8 points) What are the expected returns on assets A and B, given by the CAPM? 2. (8 points) Using the information from the previous points, what is the expected return of a portfolio if you invest 20%, 30%, and 50% in assets A, B, and C, respectively? 3. (14 points) Suppose, in the previous exercise, you want to choose the weights optimally to get a 15% expected return. What are all the steps you have to carry out in order to perform this? Describe these steps and set the inputs, outputs and constraints you will need/obtain