The lab project for this week is to put a version of the portfolio re-balance problem into the MATLAB standard form for linear programming. Find vectors $f$ and $b$ and a matrix $A$ such that the optimal trade list satisfies -
$argmin_x f'x$ s.t. $Ax\le b, x\ge 0$ where $x=(buy_1,sell_1,buy_2,sell_2,...)'$ for assets 1, 2, 3, etc.
Initial allocations and prices and current prices for the assets are available in the file case9.dat. The object is to minimize transactions costs (0.05 per share) and capital gains taxes (20%) on gains or losses from sales. The constraints are that the new allocations must be positive, the new weights must be within 1% of initial weights, and cash must be raised through sales to cover purchases and costs.