1. In our study of mean-variance portfolio theory we considered fully invested portfolios which satisfy the budget constraint 1=11x=1. A self financed portfolio is one which uses proceeds from short positions to pay for long positions and hence has the budget constraint 1=01x=0. Derive the formula for the allocation vector for a self financed portfolio, composed of n risky assets only, that maximises the utility function =[]122U=E[r]12A2. You should express your answer in terms of the parameters a, b, c and d used in lectures. You may write the solution by hand and insert a photograph into your solution template. [8]