1. Structural Risk Models

2. Elementary Risk Models Single Factor Model –Market Model –Plus assumption residuals are uncorrelated Constant Correlation Model –Assume all asset returns have same pair-wise correlation –Cov(R i, R j ) =  i  j

3. Elementary Models Full-Covariance Model –Estimate covariance matrix based upon historical return data –Requires large amount of data –Little confidence in estimates

4. Structural Risk Models Assumes return can be explained by a set of common factors plus a factor unique to a given Linear factor model:

5. Choosing Factors External Influences –Outside Economic factors –Examples Changes in inflation Changes Exchange rates Changes in industrial production

6. Choosing Factors Statistical Factors –Statistical procedure for determining factors –Principal Components Analysis –Factor Analysis

8. BARRA Method Based on cross-sectional comparison determine exposures Cross-Sectional Comparisons –Comparisons between attributes of stocks –Classified as Fundamental and Market Determine factors based on exposures that best explain the covariance matrix

9. Industry Factors Group Stocks into industries Industry exposures are usually 0/1 variables Large corporation can have fractional exposures to range of industries GE: –39% -- Producers Good –28% -- Aerospace –23% -- Consumer Products –5% -- Miscellaneous Finance –5% -- Media Market: sum of exposures equals one

10. Risk Indexes Measures the movement of stocks to common investment themes: –Volatility –Momentum –Size –Liquidity –Growth –Value –Leverage

11. Risk Indexes Broad categories are broken down into descriptors Risk indexes and descriptors are standardized across universe of stocks (Raw Index – Average)/Stdev So each index has zero average value and unit standard deviation

12. Portfolio

13. Total Risk Decomposition

16. Portfolio Risk Factor Exposures

17. Portfolio Industry Factor Exposures

18. Marginal Contribution to Total Risk

19. BARRA Risk Decomposition Total risk –Common Factor: common to all assets –Specific risk factor: uncorrelated with specific risk of other assets Default decomposition

20. Total Risk Specific* Risk Common Factor Risk Index Risk Industry Risk *Asset Selection Risk

21. DecompositionVarianceStandard Dev. 1. Specific Risk36.80 Common Factor 2. Indexes18.41 3. Industries193.24 4. 2xCOV(51.80) Total Common159.87 Total Risk196.67

22. Systematic-Residual Risk Systematic Risk (Market Timing) - risk associated with market portfolio Residual Risk – risk of component uncorrelated with the market portfolio Select (settings window) –Market: S&P500 –Benchmark: none

23. Total Risk Systematic* Risk Residual Risk Residual Common Specific Risk *Market Timing Risk

24. DecompositionVarianceStandard Dev. 1. Residual Specific Risk32.74 Residual Common Factor 2. Indexes5.57 3. Industries7.13 4. 2xCOV(2.34) 5. Total Residual Common10.38 6. Total Residual43.11 7. Systematic 8. Total Risk 153.56 196.67

25. Active Risk Decomposition Benchmark risk – risk associated with benchmark Active risk – risk associated with deviations from benchmark: tracking error Select – market: none – benchmark: S&P500

26. Total Risk Benchmark Risk Active Risk* Active Common Specific Risk *Tracking error. Variances do not add