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: 14959747@sun.ac.za

‘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

Sources (4/4)