Question 4: The purpose of this question is to put the theoretical knowledge learned from chapter 13 to empirical use. Make sure to include all the relevant information in your answers and provide the references for your work.We will focus on two public companies, JPMorgan Chase & Co. (JPM) and Apple Inc. (AAPL). The historical information for the price is available online from January 1st, 2019, to January 1st,2021 (the Market Insider website or other sources such as Yahoo Finance). Download the historical daily share prices for this horizon. Select the S&P500 index as a measure of the market for this horizon and download historical daily prices for this index as well. To be able to calculate the risk-free rate, we need the yield of US treasury bonds with the same duration of 2 years. Note that the yield reported for treasury bonds is an annual rate of return, so you must calculate the daily risk-free rate.a) (8 marks) Calculate the arithmetic average daily return on the stocks of the companies for the horizon. Calculate the variance and standard deviation of the return on the stocks of the companies as well. Based on your answers and selecting the standard deviation as the measure of risk, does higher risk, higher return hold? Discuss. Also, calculate the correlation coefficient between the returns of two stocks using Excel.b) (7 marks) Assume that CAPM holds. Based on the given information, calculate the beta for each of the two stocks. Based on the returns calculated in the previous part, and selecting the beta as the measure of risk, does higher risk, higher return hold? Discuss.c) (5 marks) Assume that you want to create three portfolios from the two stocks you selected (but not the risk-free rate or the market index). The weights of each stock for each of the three portfolios are given below. For each portfolio, calculate the return and beta. Which portfolio has the higher return? Also, calculate the portfolio standard deviation for each pair of the weights. Keeping the beta as a measure of risk, does higher risk, higher return hold? Discuss.

Question 4: The purpose of this question is to put the theoretical knowledge learned from chapter 13 to empirical use. Make sure to include all the relevant information in your answers and provide the references for your work. We will focus on two public companies, JPMorgan Chase & Co. (JPM) and Apple Inc. (AAPL). The historical information for the price is available online from January 1st, 2019, to January 1st, 2021 (the Market Insider website or other sources such as Yahoo Finance). Download the historical daily share prices for this horizon. Select the S&P500 index as a measure of the market for this horizon and download historical daily prices for this index as well. To be able to calculate the risk- free rate, we need the yield of US treasury bonds with the same duration of 2 years. Note that the yield reported for treasury bonds is an annual rate of return, so you must calculate the daily risk- free rate. a) (8 marks) Calculate the arithmetic average daily return on the stocks of the companies for the horizon. Calculate the variance and standard deviation of the return on the stocks of the companies as well. Based on your answers and selecting the standard deviation as the measure of risk, does "higher risk, higher return hold? Discuss. Also, calculate the correlation coefficient between the returns of two stocks using Excel. b) (7 marks) Assume that CAPM holds. Based on the given information, calculate the beta for each of the two stocks. Based on the returns calculated in the previous part, and selecting the beta as the measure of risk, does higher risk, higher return hold? Discuss. c) (5 marks) Assume that you want create three portfolios from the two stocks you selected (but not the risk-free rate or the market index). The weights of each stock for each of the three portfolios are given below. For each portfolio, calculate the return and beta. Which portfolio has the higher return? Also, calculate the portfolio standard deviation for each pair of the weights. Keeping the beta as a measure of risk, does higher risk, higher return" hold? Discuss. Portfolio Y 0.25 0.75 X 0.5 0.5 AAPL JPM Z 0.6 0.4 Weights Question 4: The purpose of this question is to put the theoretical knowledge learned from chapter 13 to empirical use. Make sure to include all the relevant information in your answers and provide the references for your work. We will focus on two public companies, JPMorgan Chase & Co. (JPM) and Apple Inc. (AAPL). The historical information for the price is available online from January 1st, 2019, to January 1st, 2021 (the Market Insider website or other sources such as Yahoo Finance). Download the historical daily share prices for this horizon. Select the S&P500 index as a measure of the market for this horizon and download historical daily prices for this index as well. To be able to calculate the risk- free rate, we need the yield of US treasury bonds with the same duration of 2 years. Note that the yield reported for treasury bonds is an annual rate of return, so you must calculate the daily risk- free rate. a) (8 marks) Calculate the arithmetic average daily return on the stocks of the companies for the horizon. Calculate the variance and standard deviation of the return on the stocks of the companies as well. Based on your answers and selecting the standard deviation as the measure of risk, does "higher risk, higher return hold? Discuss. Also, calculate the correlation coefficient between the returns of two stocks using Excel. b) (7 marks) Assume that CAPM holds. Based on the given information, calculate the beta for each of the two stocks. Based on the returns calculated in the previous part, and selecting the beta as the measure of risk, does higher risk, higher return hold? Discuss. c) (5 marks) Assume that you want create three portfolios from the two stocks you selected (but not the risk-free rate or the market index). The weights of each stock for each of the three portfolios are given below. For each portfolio, calculate the return and beta. Which portfolio has the higher return? Also, calculate the portfolio standard deviation for each pair of the weights. Keeping the beta as a measure of risk, does higher risk, higher return" hold? Discuss. Portfolio Y 0.25 0.75 X 0.5 0.5 AAPL JPM Z 0.6 0.4 Weights