Portfolio Construction Through Mixed-Integer Programming at Grantham, Mayo, Van Otterloo and Company

and Company LLC (GMO) uses mixed-integer-programming (MIP) methods to construct portfolios that are close (in terms of sector and security exposure) to target portfolios, have the same liquidity, turnover, and expected return as the target portfolios, control frictional costs, and do so with fewer distinct stocks and with fewer transactions. It also applies MIP methods to portfolios consisting of several subportfolios. It uses the MIP approach to construct 11 quantitatively managed portfolios representing over $8 billion in assets. The benefits from this implementation include (1) keeping the existing client business; (2) making possible important new growth opportunities; (3) reducing the number of stock names by an average 40 to 60 percent; (4) reducing the annual cost of trading the portfolios by at least $4 million by reducing the number of trading tickets written by 75 to 85 percent; (5) improving the trading process; and (6) improving performance in simulation in a US fund consisting of growth stocks with small market capitalization.