1. Factor Models Riccardo Colacito

2. Foundations of Financial Markets 2 Diversification and Portfolio Risk Market risk –Systematic or Nondiversifiable Firm-specific risk –Diversifiable or nonsystematic

3. Foundations of Financial Markets 3 Portfolio Risk as a Function of the Number of Stocks

4. Foundations of Financial Markets 4 Portfolio Risk as a Function of Number of Securities

5. Foundations of Financial Markets 5 A single factor Model

6. Foundations of Financial Markets 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 R m

7. Foundations of Financial Markets 7 Commonly Run Regression

8. Foundations of Financial Markets 8 Scatter Diagram for Dell

9. Foundations of Financial Markets 9 Various Scatter Diagrams

10. Foundations of Financial Markets 10 Coca Cola: another example

11. Foundations of Financial Markets 11 Regression statistics Dependent Variable: KO Method: Least Squares Sample: 1962:02 2007:10 Included observations: 549 VariableCoefficientStd. Errort-StatisticProb. C-0.0055080.004206-1.3095590.1909 SP 0.8168980.0984258.2996630.0000 R 2 = 0.111846

12. Foundations of Financial Markets 12 A more recent sample Dependent Variable: KO Method: Least Squares Sample: 1990:01 2007:10 Included observations: 214 VariableCoefficientStd. Errort-StatisticProb. C-0.0049750.006378-0.7800660.4362 SP0.5233870.1586033.2999760.0011 R 2 = 0.048858

13. Foundations of Financial Markets 13 Some Betas of S&P500 companies CompanyBeta Apple1.3 Amazon1.6 Cisco1.1 Coca Cola0.8 Countrywide Financial1.8 Goldman Sachs1.7 Johnson & Johnson0.5 McDonald's0.8 Microsoft0.9

14. Foundations of Financial Markets 14 Measuring Components of Risk  i 2 =  i 2  m 2 +  2 (e i ) Where:  i 2 = total variance  i 2  m 2 = systematic variance  2 (e i ) = unsystematic variance

15. Foundations of Financial Markets 15 Decomposition of Risk Total variability of the rate of return depends on two components 1.The variance attributable to the uncertainty common to the entire market 2.The variance attributable to firm specific risk factors

16. Foundations of Financial Markets 16 Systematic and idiosyncratic risk with many securities Two assets Portfolio weights are w 1 and (1-w 1 ) What is the portfolio  ? What is the systematic risk of the portfolio? What is the idiosyncratic risk of the portfolio?

17. Foundations of Financial Markets 17 Portfolio  because

18. Foundations of Financial Markets 18 Systematic Risk A good strategy would select securities with smallest  ’s

19. Foundations of Financial Markets 19 Idiosyncratic Risk Benefits from diversification if idiosyncratic risk is less than perfectly correlated

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

21. Foundations of Financial Markets 21 What risk should be priced? –Idiosyncratic risk: no –Aggregate risk: yes Only aggregate/macro risk commands a premium

22. Foundations of Financial Markets 22 Why? Because: 1.idiosyncratic risk can be diversified away 2.Macro risk affects all assets and cannot be diversified

23. Foundations of Financial Markets 23 Example: two assets

24. Foundations of Financial Markets 24 What is the portfolio variance? Systematic Risk Idiosyncratic Risk

25. Foundations of Financial Markets 25 Example: three assets

26. Foundations of Financial Markets 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. Foundations of Financial Markets 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. Foundations of Financial Markets 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. Foundations of Financial Markets 29 Risk compensation

30. Foundations of Financial Markets 30 This opens up to our next topic The Capital Asset Pricing model!