**Chapter 5**

**Scenario Optimization**

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**5.1 Preview**

In this chapter we develop the GAMS models for scenario-based portfolio optimization. The development is based on the discussion of Chapter PFO-5. The following models are discussed in this chapter and the GAMS source code for each is given in the associated FINLIB files:

**Mean absolute deviation (MAD) models** are based on Section PFO-5.3. We give models which select a portfolio by minimizing the mean absolute deviation from a reference point or a target liability. We also provide a tracking model where the target is a market index.

• MAD.gms

• TrackingMAD.gms

**Regret models** are based on Section PFO-5.4. In this case the risk function is measured in terms of negative deviations from a benchmark; we also use the model to highlight the differences with MAD tracking models.

**Conditional Value-at-Risk (CVaR) models** are based on Section PFO-5.5 and optimize CVaR, which has the nice property of being a coherent risk measure.

**Expected utility maximization models** are based on Section PFO-5.6 and maximize the expected value of investors’ utility.

**Put/call efficient frontier models** are based on Section PFO-5.7. We build put/call efficient frontiers and show the effects of liquidity constraints.

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**5.2 Data sets**

The GAMS models of this chapter are set up using three common data sets. As far as possible identical data are used in setting up the models so that users can compare and contrast the results. ...