Large-Scale Portfolio Optimization

MS&E348Winter 2011/2012

Professor Gerd Infanger

The classical mean-variance model (Markowitz, 1952, 1959)

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Large-scale portfolio optimization

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Historical returns for measuring risk

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Markowitz modelTraditional formulation:

Practical formulation:

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Factor model

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Factor model formulation in practice

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Factor model formulation in practice, alternative

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Tracking error as a measure of risk

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Mean absolute deviation (MAD) model (Konno et al., 1990)

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MAD model with historical returns

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Expected utility optimization using factor models(Infanger, 2010)

• The problem can be solved efficiently.• Allows for derivatives (e.g., options) in the portfolio.

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Components of asset return

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Calibrating the expected utility model to a benchmark

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• Implied means (Black and Litterman, 1992, Grinold, 1999)

Active portfolio management using expected utility maximization

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• By adding the conditional mean forecast (based on the value of the factors), we take on active bets in a graduated fashion.

Active portfolio management using mean-variance optimization

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Commercial implementations

• Mean-variance (and MAD)– E.g., Barra, Northfield, Axioma

• Scenario-based– Allows also for options and other derivatives– E.g., Algorithmics (Ron Dembo, especially for risk evaluation)

• Issues of accuracy of parameter estimation– Richard Grinold: Mean-Variance and Scenario based Approaches to

Portfolio Optimization, J. of Portfolio Management, Winter 1999– (Richard Micheaud, “resampled efficient frontier” , Efficient Asset

Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation, Harvard Business School Press, Boston, June 1998.)

– Robust portfolio optimization

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Commercial implementations (cont.)

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Commercial implementations (cont.)

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Commercial implementations (cont.)

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Commercial implementations (cont.)