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Structural Risk Models

Structural Risk Models. 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. Elementary Models. Full-Covariance Model

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Structural Risk Models

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  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(Ri, Rj) = 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

  7. 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

  8. 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

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

  10. 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

  11. Portfolio

  12. Total Risk Decomposition

  13. Portfolio Risk Factor Exposures

  14. Portfolio Industry Factor Exposures

  15. Marginal Contribution to Total Risk

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

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

  18. 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

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

  20. 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

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

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