Problem 5: You have $50,000 in cash and you would like to allocate it between the common stock of American International Group, Inc. (AIG) and Citigroup, Inc. (C) or (CITI). Before making your investment, you have decided to examine the past performance of these stocks under the assumption that their performance from Jan. 1, 2012- Dec. 31, 2012 is representative of their expected future performance. Assume that the annual risk-free rate is 0. 15%. a) Using Yahoo Finance or Google Finance, download the weekly stock prices in 2012 for both firms. Using the adjusted closing price (which accounts for dividends), calculate the weekly excess return. What was the mean, standard deviation, variance, and covariance of the two series? Note: you want to download the adjusted price, so that it accounts for dividend distributions. Then, for each day you calculate the weekly return as (price thisweek - price lastweek) / price lastweek. If you want to be really consistent, you may want to compute the log-returns!. Then use Excel to calculate the mean, standard deviation, variance, and covariance of the two series. See the example Excel file for details. The mean and standard deviation of AIG are 0.867% and 4.241% and for CITI they are 0.734% and 4.654%. The covariance (correlation) is 0. 100% (.0.517). b) Your friend suggests that you split your money 50% in AIG and 50% in CITI. If you followed his advice in 2012, what would the weekly excess return of this portfolio have been? What would the variance of this portfolio have been?See the example Excel le. The weekly portfolio variance in this case is 0. 149%, the standard deviation is 3.363%, and the expected return is 0.301% c) What was the Sharpe Ratio for the portfolio you calculated in part {b}? The Sharpe Ratio for this portfolio = {0.301%} 8.363% = .20'3'33 d} histead of following your friend's advice, you have decided to calculate the optimal risky portfolio. How much money {in dollars) should you invest in MG? How much money should you invest in CITI? [Hint You need to compute the weights of the tangent portfolio, just plug the numbers you calculated in the equation for the tangent portfolio]. See the example Excel file. The optimal weights are T1.I532% in AIG and 23.363% in CITI. e) Using your weights from part {d}, calculate the mean return and variance of this portfolio in 2012. See the example Excel file. The expected weekly excess return of the portfolio is 0.330% and the portfolio variance and standard deviation are 0.150% and 3.313%, respectively. I) What was the Sharpe Ratio for this portfolio? The Sharpe Ratio for the optimal portfolio = {0.330%} l 3.379% = 0.21314 g) True or False: The Sharpe ratio from the optimal portfolio will always be '-'_=- the Sharpe ratio from any other combination of the two assets. Briey explain your answer. True: by denition, the optimal portfolio is the portfolio that maximizes the risk-return tradeoff(1he Sharpe Ratio}. Thus, the expected Sharpe Ratio from the optimal portfolio should always be at least as large as the Sharpe ratio of any other combination of the assets, and it will typically be larger