MOSEK Portfolio Optimization Cookbook

• 1 Preface
  • 1.1 Purpose
  • 1.2 Content
  • 1.3 Code examples
• 2 Markowitz portfolio optimization
  • 2.1 The mean–variance model
  • 2.2 Constraints, modifications
  • 2.3 Conic formulation
  • 2.4 Example
• 3 Input data preparation
  • 3.1 Scenarios
  • 3.2 Modeling the distribution of returns
  • 3.3 Extensions
  • 3.4 Example
• 4 Dealing with estimation error
  • 4.1 Estimation of mean
  • 4.2 Estimation of the covariance matrix
  • 4.3 Using constraints
  • 4.4 Improve the optimization
  • 4.5 Example
• 5 Factor models
  • 5.1 Definition
  • 5.2 Classes of factor models
  • 5.3 Portfolio optimization with factor model
  • 5.4 Shrinkage as factor model
  • 5.5 Example
• 6 Transaction costs
  • 6.1 Variable transaction costs
  • 6.2 Fixed transaction costs
  • 6.3 Market impact costs
  • 6.4 Cardinality constraints
  • 6.5 Buy-in threshold
  • 6.6 Example
• 7 Benchmark relative portfolio optimization
  • 7.1 Active return
  • 7.2 Factor model on active returns
  • 7.3 Optimization
  • 7.4 Extensions
  • 7.5 Example
• 8 Other risk measures
  • 8.1 Deviation measures
  • 8.2 Tail risk measures
  • 8.3 Expected utility maximization
  • 8.4 Example
• 9 Risk budgeting
  • 9.1 Risk contribution
  • 9.2 Risk budgeting portfolio
  • 9.3 Risk budgeting with variance
  • 9.4 Example
• 10 Robust optimization
  • 10.1 Types of uncertainty
  • 10.2 Uncertainty in security returns
  • 10.3 Uncertainty in the factor model
  • 10.4 Parameters
  • 10.5 Example
• 11 Multi-period portfolio optimization
  • 11.1 Single-period model
  • 11.2 Multi-period model
  • 11.3 Example
• 12 Regression and regularization
  • 12.1 Linear regression
  • 12.2 Regularization
  • 12.3 Example
• 13 Appendix
  • 13.1 Conic optimization refresher
  • 13.2 Mixed-integer models
  • 13.3 Quadratic cones and riskless solution
  • 13.4 Monte Carlo Optimization Selection (MCOS)
• 14 Notation and definitions
  • 14.1 Financial notations
  • 14.2 Mathematical notations
  • 14.3 Abbreviations
• 15 References