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. Presenter:Florian Boehlandt University:University of Stellenbosch Business School Supervisor:Prof Eon Smit Prof Niel Krige Research Title:Parametric Pricing Models for Hedge Funds Contact:14959747@sun.ac.za

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

4. Content I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

5. Research Purpose 1.Developing accurate parametric pricing models for hedge funds and fund of hedge funds 2.Accounting for the special statistical properties of alternative investment funds 3.Providing practitioners and statisticians with a framework to assess, categorize and predict hedge fund investments I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

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

7. Data Sources Hedge Fund Databases CISDM/MAR Financial Databases Risk Simulation Monte Carlo (Solver) Confidence (RiskSim) DATA POOL I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Data Sourcing

8. FACTOR ANALYSIS Data Treatment Risk Simulation Statistical Processing Excel / VBA Statistica EViews DATA POOL MODEL BUILDING STATISTICAL CLUSTERING I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Data Treatment

9. Data Import Extract relevant data from Access (SQL) Import data as Pivot table report Data Treatment Test for serial correlation /databias Calculate adjusted excess returns Data Analysis Select funds with consistent data series Determine statistical model I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Data Processing (1/2)

10. Weighting Estimate weighted average parameters Construct style indices Comparative Analysis Calculate within-group variation Calculate between-group variation Data Output Tabular display of aggregate results Construction of line - bar charts I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Data Processing (2/2)

11. Code Fund (Name) Main Strategy Information MM_DD_YYYY (Date) Yield Ptype (ROI or AUM) Performance Leverage (Yes/No) System Information Access DatabaseExcel Pivot table report I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Data Import

12. 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) I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

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

14. Categories Directional Dedicated Short Bias Global Macro Emerging Markets Global Macro Long / Short Equity Managed Futures Fund of Hedge Funds Market Neutral Equity Market Neutral Event Driven Convertible Arbitrage Fixed Income Arbitrage I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Categorization (TASS)

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

16. t – test (between strategies) Unbalanced ANOVA (within and between treatments) t – test (leverage vs. no leverage) t – test for equal means t – test for equal means t – test for equal means Model 1aModel 2a t – test for equal means Model 1bModel 2b I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Comparative Analysis

17. 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) I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

18. 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) I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

19. Prediction Models AR ARMA ARIMA GLS Univariate Multivariate Conditional PCA Polynomial Fitting Taylor Series Higher Co- Moments Constrained Lagrange KKT Simulation Prediction Models I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

20. 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 I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

21. Progress (1/2) Extensive literature review on alternative investments, recent developments in asset pricing models and Monte Carlo simulation (completed) x 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) I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

22. Progress (2/2) x 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) I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix

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24. Durbin, J. & Watson, G. S. 1950. Testing for Serial Correlation in Least Squares Regression: I. Biometrika, 37(3/4), 409‐428. [Online] Available: http://www.jstor.org/stable/2332391. Accessed: 12 June 2009. http://www.jstor.org/stable/2332391 Durbin, J. & Watson, G. S. 1951. Testing for Serial Correlation in Least Squares Regression. II. Biometrika, 38(1/2), 159‐177. [Online] Available: http://www.jstor.org/stable/2332325. Accessed: 12 June 2009. http://www.jstor.org/stable/2332325 Fama, E.F. & French, K.R. 1992. The Cross-Section of Expected Stock Returns. Journal of Finance, 47(2), June, 427-465. [Online] Available: http://links.jstor.org/sici?sici=0022- 1082%28199206%2947%3A2%3C427%3ATCOESR%3E2.0.CO%3B2-N http://links.jstor.org/sici?sici=0022- 1082%28199206%2947%3A2%3C427%3ATCOESR%3E2.0.CO%3B2-N Fung, W. & Hsieh, D.A. 1997. Empirical characteristics of dynamic trading strategies: the case of hedge funds. Review of Financial Studies, 10(2), Summer, 275-302. [Online] Available: http://faculty.fuqua.duke.edu/~dah7/rfs1997.pdfhttp://faculty.fuqua.duke.edu/~dah7/rfs1997.pdf I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Sources (2/4)

25. Hannan, E. J. & Quinn, B. G. 1979. The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society. Series B (Methodological), 41(2), 190‐195. [Online] Available: http://www.jstor.org/stable/2985032. Accessed: 12 June 2009.http://www.jstor.org/stable/2985032 Ljung, G. M. & Box, G. E. P. 1978. On a Measure of Lack of Fit in Time Series Models. Biometrika, 65(2), 297‐303. [Online] Available: http://www.jstor.org/stable/2335207. Accessed: 12 June 2009. http://www.jstor.org/stable/2335207 Otten, R. & Bams, D. 2000. Statistical Tests for Return-Based Style Analysis. Paper delivered at EFMA 2001 Lugano Meetings, July. [Online] Available: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=277688 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=277688 Sharpe, W.F. 1992. Asset allocation: management style and performance measurement. Journal of Portfolio Management, Winter, 7-19. [Online] Available: www.uic.edu/classes/fin/fin512/Articles/sharpe.pdf www.uic.edu/classes/fin/fin512/Articles/sharpe.pdf I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Sources (3/4)

26. Sharpe, W.F. 1992. Asset allocation: management style and performance measurement. Journal of Portfolio Management, Winter, 7-19. [Online] Available: www.uic.edu/classes/fin/fin512/Articles/sharpe.pdf www.uic.edu/classes/fin/fin512/Articles/sharpe.pdf Wald, A. 1943. Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large. Transactions of the American Mathematical Society, 54(3), 426‐482. [Online] Available: http://www.jstor.org/stable/1990256. Accessed: 12 June 2009. http://www.jstor.org/stable/1990256 I.Research Approach and Methodology II.Model Building III.Preliminary Findings IV.Progress Report V.Appendix Sources (4/4)