William F. Sharpe Style Analysis May 20, 2016 A Multi-factor Model - - PowerPoint PPT Presentation

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William F. Sharpe Style Analysis May 20, 2016 A Multi-factor Model - - PowerPoint PPT Presentation

Feb 09, 2024 438 likes •783 views

William F. Sharpe Style Analysis May 20, 2016 A Multi-factor Model Factors: Returns on mutually exclusive and exhaustive market capitalization-weighted portfolios U.S. Stock Indices Barra U.S. Stock Index Performance Regression Analysis

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William F. Sharpe Style Analysis

May 20, 2016

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A Multi-factor Model

Factors: Returns on mutually exclusive and exhaustive market capitalization-weighted portfolios

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U.S. Stock Indices

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Barra U.S. Stock Index Performance

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Regression Analysis

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Regression Analysis with a Constraint

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Quadratic Programming

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“An Algorithm for Portfolio Improvement”

Advances in Mathematical Programming and Financial Planning, 1987

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Asset Classes “Determining a Fund's Effective Asset Mix”

(Dec. 1988)

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In-sample R2 Values

388 Pension Fund Manager Accounts

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Asset Classes

“Asset Allocation: Management Style and Performance Measurement” Winter 1992

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R2 = 89.0 %

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Mean: 0.18 %/mo Standard Deviation = 1.48 %/mo t(avg) = 0.84

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Mean: 0.57 %/mo Standard Deviation = 1.05 %/mo t(avg) = 3.76

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Mean = -0.074 %/mo (annualized: 0.888% /year)

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Style and Performance Analysis

l Performance in month t vs. Style at end of

month t-2

l Out-of-sample R2 values l Style Analysis

  • number of months utilized
  • exponential weighting of monthly observations

l Aggregate results for individual funds

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A Large Pension Fund

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Holdings-based vs. Returns-based Style Analysis Models

(from Morningstar website)

Holdings-based

  • Uses characteristics of underlying securities

Returns-based

  • More widely used among financial professionals, because

the input data (monthly returns) is (sic) widely available Morningstar has long been a proponent of holdings-based style analysis but recognizes that there may be situations where returns-based analysis can also be helpful. The company's institutional research platform … combines advanced holdings-based and returns-based style analysis. Ideally, practitioners should use both approaches.