Practical Financial Optimization: A Library of GAMS Models

Chapter 3

Mean-Variance Portfolio Optimization

3.1 Preview

In this chapter we develop the GAMS models for mean-variance portfolio optimization. The development is based on the discussion of Chapter PFO-3. The following models are discussed in this chapter and the GAMS source code for each is given in the associated FINLIB files:

Basics of mean-variance models are based on Section PFO-3.2. We set up the framework to trace mean-variance efficient frontiers. The relevant statistics - expected returns and variance-covariance matrixes - are estimated from historically observed data.

• MeanVar.gms

• Estimate.gms

Sharpe ratio model is based on Section PFO-3.2.2 with the optimal Sharpe ratio.

• Sharpe.gms

Portfolio limits are based on Section PFO-3.2.2. We determine portfolios with a limited number of assets, or minimum proportions, using binary variables.

• MeanVarShort.gms

• MeanVarMip.gms

• Borrow.gms

International mean-variance portfolio management formulates a large model for managing a portfolio of international stock and bond indices.

• InternationalMeanVar.gms

3.2 Basics of Mean-Variance Models

The classic mean-variance model addresses the question of trading off the portfolio expected return against its risk as measured by the variance of return. The model assumes normally distributed returns and multivariate normal correlation structures, but it is also applied in practice when the distributions are almost normal. For more details on the theoretical background of the model, ...