An investor allocates his wealth among N risky assets. The vector of expected returns of these assets is denoted mu and their return covariance matrix is sigma. The investor's goal is to design his portfolio such that it has the smallest return variance possible (i.e. he wishes to invest in the global minimum variance portfolio). Using a constrained optimization, derive the set of portfolio weights he should choose and interpret your result. Now assume that N = 2. Use your results from to provide simple expressions for the optimal portfolio weights and interpret the resulting expressions