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Parametric Pricing Models for Hedge Funds

This research, presented at the University of Stellenbosch Business School colloquium on November 20, 2009, explores the development of accurate parametric pricing models for hedge funds and fund-of-hedge-funds. Incorporating special statistical properties of alternative investments, it aims to provide practitioners and statisticians a robust framework for assessing and predicting hedge fund investments. Key components include research methodology, model building, preliminary findings, and data treatment, ensuring insights into the complexities and dynamics of hedge fund pricing.

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Parametric Pricing Models for Hedge Funds

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  1. Parametric Pricing Models for Hedge Funds Presented at University of Stellenbosch Business School Colloquium - 20 November 2009 • An Introduction to Quantitative Research into Hedge Fund Investments

  2. ‘In the business world, the rearview mirror is always clearer than the windshield’ - Warren Buffett -

  3. Content • Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix

  4. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Research Purpose • Developing accurate parametric pricing models for hedge funds and fund of hedge funds • Accounting for the special statistical properties of alternative investment funds • Providing practitioners and statisticians with a framework to assess, categorize and predict hedge fund investments

  5. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Research Approach • Research Philosophy • Research Approach • Primary Data Positivistic, deductive research: Postulation of hypotheses that are tested via standard statistical procedures Empirical analysis: Interpreting the quality of pricing models on the basis of historical data External secondary data: Historic time series adjusted for data-bias effects

  6. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Sourcing • DATA POOL

  7. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Treatment • FACTOR ANALYSIS • DATA POOL • MODEL BUILDING • STATISTICAL CLUSTERING

  8. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Processing (1/2)

  9. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Processing (2/2)

  10. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Import Access Database Excel Pivot table report

  11. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Validity • Consistency of performance history across different database providers • Degree of history-backfilling bias • Exclusion of defaulted funds/non-reporting funds from databases (survivorship bias) • Extent of infrequent or inconsistent pricing of assets (managerial bias)

  12. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Data Bias • Survivorship • Self-Selection • Database • Instant History • Look-ahead Inclusion of graveyard funds Multiple databases Rolling-window observation / Incubation period

  13. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Categorization (TASS)

  14. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Statistical tests • Regression Alpha • Average Error term • Information Ratio • Normality (Chi-squared, JarqueBera) • Goodness of fit, phase-locking and collinearity (Akaike Information Criterion, Hannan-Schwartz) • Serial Correlation (Durbin-Watson, Portmanteau) • Non-stationarity (unit root)

  15. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Comparative Analysis • Model 1a • Model 1b Unbalanced ANOVA (within and between treatments) t – test (leverage vs. no leverage) t – test (between strategies) t – test for equal means t – test for equal means t – test for equal means • Model 2a • Model 2b t – test for equal means

  16. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Literature Review (1/2) • Hedge Fund Linear Pricing Models • Sharpe Factor Model (Sharpe, 1992) • Constrained Regression (Otten, 2000) • Fama-French Factor Model (Fama, 1992) • Factor Component Analysis (Fung, 1997) • Simulation of Trading component (lookback straddle)

  17. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Literature Review (2/2) • Statistical Properties • Normality (Jarque & Bera, 1981) • Serial Correlation (Wald, 1943; Durbin & Watson, 1950; Durbin & Watson, 1951; Box & Pierce, 1970; Ljung & Box, 1978)) • Non-stationarity (Dickey & Fuller, 1979) • Goodness of fit • Akaike Information Criterion (Akaike, 1974) • Adapted Criteria (Hannan & Quinn, 1979; Schwartz, 1997)

  18. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Prediction Models

  19. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Empirical Findings • The accuracy of pricing models could be significantly improved when accounting for special statistical properties of hedge funds (Non-normality, non-linearity) • Hedge fund performance can be attributed to location choice as well as trading strategy • A limited number of principal components explains a significant proportion of cross-sectional return variation

  20. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Progress (1/2) • Extensive literature review on alternative investments, recent developments in asset pricing models and Monte Carlo simulation (completed) • Securing access to relevant databases and confidential information (currently access to one of three databases considered in the proposal stage) • Peer-group review of research proposal and research to date (EDAMBA summer academy)

  21. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Progress (2/2) • Publication of preliminary results (in order to confirm current results, access to at least one additional database is required) • Model building and stress testing (completed) • Composition of first draft (introduction and first chapter)

  22. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Sources (1/4)

  23. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Sources (2/4)

  24. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Sources (3/4)

  25. Research Approach and Methodology • Model Building • Preliminary Findings • Progress Report • Appendix Sources (4/4)

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