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Published bySteven Curtis Modified over 9 years ago
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Structural Risk Models
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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
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Elementary Models Full-Covariance Model –Estimate covariance matrix based upon historical return data –Requires large amount of data –Little confidence in estimates
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Structural Risk Models Assumes return can be explained by a set of common factors plus a factor unique to a given Linear factor model:
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Choosing Factors External Influences –Outside Economic factors –Examples Changes in inflation Changes Exchange rates Changes in industrial production
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Choosing Factors Statistical Factors –Statistical procedure for determining factors –Principal Components Analysis –Factor Analysis
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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
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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
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Risk Indexes Measures the movement of stocks to common investment themes: –Volatility –Momentum –Size –Liquidity –Growth –Value –Leverage
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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
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Portfolio
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Total Risk Decomposition
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Portfolio Risk Factor Exposures
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Portfolio Industry Factor Exposures
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Marginal Contribution to Total Risk
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BARRA Risk Decomposition Total risk –Common Factor: common to all assets –Specific risk factor: uncorrelated with specific risk of other assets Default decomposition
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Total Risk Specific* Risk Common Factor Risk Index Risk Industry Risk *Asset Selection Risk
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DecompositionVarianceStandard Dev. 1. Specific Risk36.80 Common Factor 2. Indexes18.41 3. Industries193.24 4. 2xCOV(51.80) Total Common159.87 Total Risk196.67
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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
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Total Risk Systematic* Risk Residual Risk Residual Common Specific Risk *Market Timing Risk
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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
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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
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Total Risk Benchmark Risk Active Risk* Active Common Specific Risk *Tracking error. Variances do not add
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