Case Studies

Grantham, Mayo, Van Otterloo and Company

Bertsimas, D., Darnell, C. and Soucy, R. (1999). Portfolio construction through mixed-integer programming at Grantham, Mayo, Van Otterloo and Company. Interfaces, 29:1, 49-66.

Grantham, Mayo, Van Otterloo and Company. Grantham, Mayo, Van Otterloo and Company LLC (GMO) is an investment-management firm that offers a wide range of mutual funds to clients world-wide. Most of its clients are pension funds, educational endowments, foundations, and similar organizations. GMO makes extensive use of statistical methods, simulation, and optimization techniques to manage billions of dollars of assets.

In 1996, GMO's quantitative group had accumulated $15 billion in assets, but the large number of different stocks in the portfolio, as well as the huge number of transactions required to rebalance these assets, had many clients uneasy about GMO's ability to manage the portfolio. Moreover, the large numbers of different stocks and transactions were straining GMO's operations and increasing the costs of maintaining these assets.

In response, GMO developed and put into practice a mixed-integer-programming model that includes the use of 0-1 decision variables to construct portfolios that are close to target portfolios in terms of liquidity, risk, turnover, and expected return, yet include fewer distinct stocks and require far fewer stock transactions. Typically, these portfolios consist of several subportfolios that represent different investment philosophies. An important advantage of such a structure is that in optimizing the portfolio, the subportfolios can trade with one another, thus avoiding transaction costs for the fund. Currently, GMO uses this approach to construct and manage eleven different portfolios representing over $8 billion in assets. The benefits to GMO of the implementation of this mixed-integer-programming process include:

  1. retaining the existing client base,
  2. opening new growth opportunities,
  3. reducing the number of distinct stocks held in the portfolios by an average of 48.7%,
  4. reducing the number of stock transactions by an average of 79.3%, and
  5. as a result of points 3 and 4, reducing the annual cost of trading the portfolios by $4 million.

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