Consider a portfolio P with two financial assets (e.g., stocks) over the period t = 1, . .., T. In the absence of rebalancing, the portfolio is composed of w1 X 100% of asset 1 and w2 = (1 - w1) X 100% of asset 2, withD w2 (what is the financial intuition?). Max Sharpe ratio (MSR) portfolio The Sharpe ratio of a given portfolio is a risk-adjusted performance measure defined by SR = TP - TS SP where sp is the standard deviation of the excess return of the portfolio (with respect to the risk-free asset). The Sharpe ratio captures the reward in term of mean excess return per unit of risk: risk adverse investors will prefer large Sharpe ratios! The objective of this part is to find the optimal weights of the Max Sharpe Ratio portfolio, denoted WMsR, using the following optimization problem: TP - Tf WMSR =argmax VwT Ew s.t. e, w = 1T where : = wTF and F = [ F1 F2 ] . The optimal weights wuss are given by: 1 E'1 FF e e2TE*1(FFfeg) ( f 2) wuss = 5. Using matrix notation, nd the analytical expression of the objective function when w = 101453- 6. Suppose that 1" f = 0 and the variance-covariance matrix of the annualized returns is given by: 0.6 0.3 0.3 0.4 E: T After choosing some annualized average returns for the two assets/stocks, F = [ F1 F2 ] , (a) Find the optimal MSR allocation 131.45\". (b) What happens when the covariance term of E has now the opposite sign? 0.6 0.3 0.3 0.4 2: Explain carefully. Compare the results of question (5a) and (5b). 7. Suppose that F; = 0.015 (i.e., 1.5%). Using one of the two variance-covariance matrices of question (5), nd the optimal MSR weights. Compare the result with the corresponding one (question (5a) or (5b)). Explain