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Portfolio Optimization: Some Practical Considerations

Portfolio Optimization: Some Practical Considerations. Jim Hwang CPPIB 4-Oct-2014. Disclaimer All the opinions and views expressed in this presentation and talk are strictly those of the presenter and they do not necessarily reflect those of the institution to which he is affiliated.

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Portfolio Optimization: Some Practical Considerations

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  1. Portfolio Optimization: Some Practical Considerations Jim Hwang CPPIB 4-Oct-2014

  2. Disclaimer All the opinions and views expressed in this presentation and talk are strictly those of the presenter and they do not necessarily reflect those of the institution to which he is affiliated.

  3. Contents • Overview of the Portfolio Management Process • Optimal Portfolios • Characteristic Portfolio • Minimally Constrained Long-Short (L-S) Portfolio • More Constrained L-S Portfolio • Long-Only Portfolio • Partial L-S Portfolio (130/30) • Constraints, Penalties, Overrides • The Costs of Constraints • Consider Using Penalties Over Constraints • Overrides – What Am I Doing to My Portfolio? • Summary • Glossary • References

  4. 1) Overview of the Portfolio Management Process

  5. 1. Overview of the Portfolio Management Process Optimization Market Model ( σ Model ) • Market • Prices • Earn Ests • Financials • Measurement • Performance • Attribution • Risk decomp Control Models ( α + T-cost Models )

  6. A Simple Alpha Model Univ: US large & mid-caps Raw Factor: BP (Book/Price) Std Industry Neutralization Final α

  7. Other Assumptions • Our Other Tools • Third party structural factor risk model • Risk Factors – e.g., momentum, volatility, leverage … • Industry factors • Single country model – US • Third party optimizer • No transaction costs • The Client • Wants large-mid cap US equity exposure. • Willing to consider long-only or long-short portfolios. • Can tolerate • L-S total risk of 5% and gross gearing of 200% or, • L-O tracking error of 5%.

  8. 2) Optimal Portfolios

  9. 2a. Optimal Portfolios: The Characteristic Portfolio A characteristic portfolio has an unit exposure to only one attribute and minimum risk. Setup: Minimize σp2 s.t.α = 1. Why isn’t my TC = 1? It should since, w=σp2 V-1α and TC = correl (V-1α, w)

  10. 2b. Optimal Portfolios: Minimally Constrained Long-Short Portfolio Setup: Maximize αs.t.σp= 5% Long Gearing = Short Gearing = 100% -10% < wi < 10% Am I comfortable with these exposures?

  11. 2c. Optimal Portfolios: More Constrained Long-Short Portfolio Setup: Maximize αs.t.σp= 5% Long Gearing = Short Gearing = 100% -5% < wi < 5% -5% < Industry Group < 5% Am I comfortable with the security concentration? I.e., how much does specific risk contribute to my overall risk?

  12. 2d. Optimal Portfolios: Long-Only Constrained Portfolio Setup: Maximize αs.t.σt.e.= 5% Long-Only -5% < active_wti < 5% -5% < active_wtInd Group < 5% I hold a 23 stock long-only portfolio. Any stock I own below benchmark weight or do not own is an active underweight.

  13. 2e. Optimal Portfolios: Partial LS (130/30)Portfolio Setup: Maximize αs.t.σt.e.= 5% Long Gearing = 130%, Short Gearing = 30% -5% < active_wti < 5% -5% < active_wtInd Group < 5%

  14. 3) Constraints, Penalties, Overrides

  15. 3a. The Costs of Constraints Different Portfolio Construction Methodologies (Base Case) Characteristic Ptf IR TC Value 1.01 0.86 % Diff v Base - - LS Constrained Ptf IR TC Value 0.63 0.68 % Diff v Base -37% -21% 130-30 Ptf IR TC Value 0.48 0.47 % Diff v Base -53% -45% LS Simple Ptf IR TC Value 0.69 0.68 % Diff v Base -32% -21% Long Only Ptf IR TC Value 0.28 0.30 % Diff v Base -73% -65%

  16. 3b. Consider Using Penalties over Constraints Piecewise Penalties Constraint Utility Utility Weight Weight

  17. 3c. Overrides – What Am I Doing to My Portfolio? • You’re in the early stages of the Financial Crisis. Subprime loans are defaulting. • Should you override your model? Which one? How? • You decided that you don’t trust your alpha model on the home builders or the diversified financials. Set these alphas to zero. Optimize and examine your portfolio. α Override Long-only portfolio Long-only portfolio Why?

  18. 4) Summary • Understand the models you are using. Make sure your models and metrics are aligned. • The optimizer is a just a tool. Make sure you have the right problem formulation. • Constraints can be expensive • The long-only constraint is very expensive. • Our examples are even before implementation (e.g., borrowing, trading, etc.) • Consider using penalties instead of constraints. • Be careful of unintended consequences from constraints and overrides.

  19. Glossary Alpha: Forecast of excess return. Factors: Characterizations or attributes that may be used to describe a group of securities and explain its returns. Factors may be fundamental or statistical. Gearing: The notional exposure of a portfolio to risky assets divided by the total capital invested in the portfolio. Information Ratio (IR): Measure of risk-adjusted return calculated by dividing active return by active risk. Leverage: Use of capital in excess of the original investment to structure a portfolio. Gearing and leverage are sometimes used interchangeably. Neutralization: Eliminating the influence of other factors on a given factor by calculating its orthogonal component. Return, Active:The return of an asset or a portfolio, relative to a benchmark. Return, Total: The percentage gain or loss of an asset or a portfolio over a defined period of time. Returns may be calculated ex-ante or measured ex-post. Risk, Active: The risk of an asset or portfolio, relative to a benchmark. Risk, Total: Standard deviation of total returns of an asset or portfolio. Risks may be calculated ex-ante or measured ex-post. Short: Selling securities one doesn’t own with the intent of buying it back in the future at a lower price. Shorting rules vary by countries. Standardization: Creating a Z-score by subtracting the sample mean and dividing by the sample standard deviation. Tracking Error: Active risk. These two terms are used interchangeably. Transfer Coefficient: Correlation of the active weights of the assets in a one’s portfolio to one’s risk-adjusted alpha model. It is a measure of how efficiently research ideas are translated into a portfolio. Weight, Active The weight of a security in a portfolio, relative to a benchmark. Weight, Total The currency value of a security in a portfolio divided by the capital invested in the portfolio.

  20. References Active Portfolio Management, 2nd edition, R.C. Grinold & R.N. Kahn, McGraw-Hill, 2000 Linear Algebra and Its Applications, 3rd edition, G. Strang, Harcourt Brace Jovanovich, Publishers 1988 Quantitative Equity Portfolio Management, Modern Techniques and Applications, E.E. Qian, R.H. Hua & E.H. Sorenson, Chapman & Hall / CRC, 2007

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