parametric pricing models for hedge funds presented at university of stellenbosch business school...
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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
Presenter: Florian BoehlandtUniversity: University of Stellenbosch Business SchoolSupervisor: Prof Eon Smit
Prof Niel KrigeResearch Title: Parametric Pricing Models for Hedge FundsContact: [email protected]
‘In the business world, the rearview mirror is always clearer than the windshield’
- Warren Buffett -
Content
I. Research Approach and MethodologyII. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Research Approach
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Data Sourcing
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Data Treatment
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Data Processing (1/2)
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Data Processing (2/2)
•Code•Fund (Name)•Main Strategy
Information
•MM_DD_YYYY (Date)•Yield•Ptype (ROI or AUM)
Performance
•Leverage (Yes/No)
System Informati
on
Access Database Excel Pivot table report
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Data Import
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Categories
DirectionalDedicated
Short
Bias
Global Macro
Emerging Markets
Global Macro
Long / Short
Equity
Managed Futures Fund of Hedge Funds Market Neutral
Equity Marke
t Neutral
Event Driven
Event Driven
Convertible Arbitrage
Fixed Income
Arbitrage
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Categorization (TASS)
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
t – test (betweenstrategies)
UnbalancedANOVA (withinand betweentreatments)
t – test (leveragevs. no leverage)
t – test forequal means
t – test forequal means
t – test forequal meansModel 1a
Model 2a
t – test forequal means
Model 1b
Model 2b
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Comparative Analysis
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. 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)
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Prediction Models
AR
ARMA
ARIMA
GLS
Univariate
Multivariate
Conditional
PCA Polynomial Fitting
Taylor Series
Higher Co-Moments
Constrained
Lagrange
KKT
Simulation
Prediction ModelsI. Research Approach and
MethodologyII. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. 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
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
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 BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Akaike, H. 1974. A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, 19(6), 716 723.‐ Anil K. Bera & Carlos M. Jarque. 1981. Efficient tests for normality, homoscedasticity and serial independence of regression residuals Monte Carlo Evidence. Economics Letters, 7(4), 313–318. [Online] Available: http://www.sciencedirect.com/science/article/B6V84-45DMS48-6D/2/1f19942c94348a8549c84897ddc4208b. Accessed: 12 June 2009. Box, G. E. P. & Pierce, D. A. 1970. Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models. Journal of the American Statistical Association, 65(332), 1509 1526. [Online] Available: ‐http://www.jstor.org/stable/2284333. Accessed: 12 June 2009.
Dickey, D. A. & Fuller, W. A. 1979. Distribution of the Estimators for Autoregressive Time Series With a Unit Root. Journal of the American Statistical Association, 74(366), 427 431. [Online] Available: ‐ http://www.jstor.org/stable/2286348. Accessed: 12 June 2009.
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Sources (1/4)
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. 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.
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-NFung, 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.pdf
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Sources (2/4)
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. 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.
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
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
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
Sources (3/4)
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
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.
I. Research Approach and Methodology
II. Model BuildingIII. Preliminary FindingsIV. Progress ReportV. Appendix
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