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Portfolios and Optimization

Portfolios and Optimization. Andrew Mullhaupt. Maximize profit with risk bound:. In ‘unit risk’ coordinates:. Mean-variance portfolio. Portfolio Selection. THE END. Transaction Costs. Commissions and Fees. Taxes. Slippage -. Slippage. Induced Costs. Expected Costs.

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Portfolios and Optimization

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  1. Portfolios and Optimization Andrew Mullhaupt

  2. Maximize profit with risk bound: In ‘unit risk’ coordinates: Mean-variance portfolio Portfolio Selection THE END

  3. Transaction Costs Commissions and Fees Taxes Slippage -

  4. Slippage

  5. Induced Costs Expected Costs Proportional Costs Trade size

  6. Total Loss Risk relative to optimal mean-variance portfolio Cost relative to Initial Portfolio Loss Mean-variance portfolio Initial Portfolio Portfolio Optimal Portfolio

  7. Loss Portfolio

  8. Mean-variance Portfolio OriginalPortfolio

  9. Trading cannot reduce the loss Mean-variance Portfolio Original Portfolio

  10. No Trade Regions

  11. No Trade Region = Optimality for Proportional Costs Optimality for Superproportional Costs Contains The No Trade Region

  12. The no trade region is a Parallelopiped

  13. Proportional Costs are Incredible!

  14. Who Says Say’s Law? • Say’s Law: Supply Creates Demand • In the large? (Supply Side Economics). • In the small? Look for sublinear transaction costs (‘volume attracts volume’). • Not frequent enough to explain the expectation but it could be a variance component.

  15. Iterated Diagonal Box QP

  16. Iterated Diagonal Box QP

  17. Modified Steepest Descent Alternate between: Move as far as feasible 1) toward the vertex 2) Toward the minimum along the gradient direction

  18. Postprocessing

  19. Accuracy Comparison

  20. Time Comparison – 5 instances3000x150 The unstructured method is too slow to compare for enough instances

  21. Time and Accuracy 150 instances3000x15

  22. Time and Accuracy 150 instances3000x50

  23. Time and Accuracy 150 instances3000x150

  24. Covariance Distortion Hedge

  25. Question Time Yes, you have questions.

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