Parametric Pricing Models for Hedge Funds

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

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

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

5. 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

6. 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

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

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

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

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

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

12. 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)

13. 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

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

15. 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)

16. 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

17. 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)

18. 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)

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

20. 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

21. 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)

22. 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)

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

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

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

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