Problem 1 (5 points). Portfolio Optimization Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 200 of C. The current share prices are $42.76, $81.33, and $58.22, respectively. The expected returns and the covariances are provided in the table below. Stock A Stock B Stock C Expected Return 12.00% 9.40% 14.00% Covariance StockA 0.0916431?! -0.0188809 -0.0022385 Stock B -0.01888085 0.03885393 -0.0005562 Stock C -0.00223864 -0.0005562 0.0080718 1. Compute the expected return of your current portfolio. 2. You want to trade stocks so that your new portfollo's return can be no less than 13% while minimizing new portfolio's risk (standard deviation). There is a 1% fee on selling or trading each stock. For example, if you sell 10 shares of Stock A and buy 5 shares of Stock B, the total dollar amount traded is 10*542.76+5*$81.33=$834.25 and you have to pay a transaction fee of $58.34. These two transactions generate a net amount of 10*$42.76 - 5*'338133 - $8.34 =$12.61 in cash. You would like this net amount to be always non-negative but no more than 85. Also, you cannot have short position in any stock, i.e., you cannot sell more than what you have