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Factor Models

Factor Models. Riccardo Colacito. Diversification and Portfolio Risk. Market risk Systematic or Nondiversifiable Firm-specific risk Diversifiable or nonsystematic. Portfolio Risk as a Function of the Number of Stocks. Portfolio Risk as a Function of Number of Securities.

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Factor Models

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  1. Factor Models Riccardo Colacito

  2. Diversification and Portfolio Risk • Market risk • Systematic or Nondiversifiable • Firm-specific risk • Diversifiable or nonsystematic

  3. Portfolio Risk as a Function of the Number of Stocks

  4. Portfolio Risk as a Function of Number of Securities

  5. A single factor Model

  6. What is M? • Anything that can be regarded as a proxy for macroeconomic risk • Commonly used factor: a broad market index like the S&P500 • Call it Rm

  7. Commonly Run Regression

  8. Scatter Diagram for Dell

  9. Various Scatter Diagrams

  10. Coca Cola: another example

  11. Regression statistics Dependent Variable: KO Method: Least Squares Sample: 1962:02 2007:10 Included observations: 549 Variable Coefficient Std. Error t-Statistic Prob. C -0.005508 0.004206 -1.309559 0.1909 SP 0.816898 0.098425 8.299663 0.0000 R2 = 0.111846

  12. A more recent sample Dependent Variable: KO Method: Least Squares Sample: 1990:01 2007:10 Included observations: 214 Variable Coefficient Std. Error t-Statistic Prob. C -0.004975 0.006378 -0.780066 0.4362 SP 0.523387 0.158603 3.299976 0.0011 R2 = 0.048858

  13. Some Betas of S&P500 companies

  14. Measuring Components of Risk si2 = bi2sm2 + s2(ei) Where: si2 = total variance bi2sm2 = systematic variance s2(ei) = unsystematic variance

  15. Decomposition of Risk • Total variability of the rate of return depends on two components • The variance attributable to the uncertainty common to the entire market • The variance attributable to firm specific risk factors

  16. Systematic and idiosyncratic risk with many securities • Two assets • Portfolio weights are w1 and (1-w1) • What is the portfolio b? • What is the systematic risk of the portfolio? • What is the idiosyncratic risk of the portfolio?

  17. Portfolio b • because

  18. Systematic Risk • A good strategy would select securities with smallest b’s

  19. Idiosyncratic Risk • Benefits from diversification if idiosyncratic risk is less than perfectly correlated

  20. Advantages of the Single Index Model • Reduces the number of inputs for diversification • Easier for security analysts to specialize

  21. What risk should be priced? • What risk should be priced? • Idiosyncratic risk: no • Aggregate risk: yes • Only aggregate/macro risk commands a premium

  22. Why? Because: • idiosyncratic risk can be diversified away • Macro risk affects all assets and cannot be diversified

  23. Example: two assets

  24. What is the portfolio variance? Systematic Risk Idiosyncratic Risk

  25. Example: three assets

  26. What is the portfolio variance? Systematic Risk Idiosyncratic Risk • Systematic risk: unchanged • Idiosyncratic risk: decreased • Can you guess what would happen if we had an infinite number of assets?

  27. Infinite assets • For a well diversified portfolio • That is: we got rid of any idiosyncratic shock and we are left only with systematic risk

  28. What lesson did we learn? • The only source of risk that we are entitled to ask a compensation for is aggregate risk. • Idiosyncratic risk does not entitle to any compensation because it can be diversified away.

  29. Risk compensation

  30. This opens up to our next topic • The Capital Asset Pricing model!

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