Data Sourcing, Statistical Processing and Time Series Analysis

Presented at EDAMBA summer school, Soreze (France) 23 July – 27 July 2009

An Example from Research into Hedge Fund Investments

Presenter: Florian BoehlandtUniversity: University of Stellenbosch – Business SchoolSupervisor: Prof Eon Smit

Prof Niel KrigeResearch Title: A Risk-Return Assessment of Fund of Hedge

Funds in Comparison to Single Hedge Funds – An Empirical Analysis

Contact: 14959747@sun.ac.za

‘In the business world, the rearview mirror is always clearer than the windshield’

- Warren Buffett -

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

Research Approach

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

Data Sources

Hedge Fund Databases

CISDM/MAR

Financial Databases Risk Simulation

Monte Carlo (Solver)

Confidence (RiskSim)

Data Sourcing

DATA POOL

FACTOR ANALYSIS

Data Treatment

Risk Simulation Statistical Processing

Excel / VBA

Statistica

EViews

Data Treatment

DATA POOL

MODEL BUILDING

STATISTICAL CLUSTERING

STATISTICAL SIGNIFICANCE

Data Processing (1/2)

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

Data Processing (2/2)

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

Data Import

•Code•Fund (Name)•Main Strategy

Information

•MM_DD_YYYY (Date)•Yield•Ptype (ROI or AUM)

Performance

•Leverage (Yes/No)System

Information

Access Database Excel Pivot table report

Access Database Management

1. Introduce Autonumber as primary keys2. Define foreign keys for data queries3. Define table relationships (one-to-many)4. Build junction tables (many-to-many)5. Write SQL queries to display relevant data6. Integrate SQL in VBA code

Why Access?

• Avoiding duplicate entries• Cross-referencing data from various sources• Combining and aggregating different databases• Efficient storage due to relational data management• Queries allow for retrieval/display of specific data• Linked-in with Microsoft VBA and Excel (data

displayable as Pivot table reports)• Searching for specific entries via SQL

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)

Data Bias

Survivorship

Self-Selection

Database

Instant History

Look-ahead

Inclusion of graveyard funds

Multiple databases

Rolling-window observation / Incubation period

Hedge Fund Categories (TASS)

Categories

DirectionalDedicated

Short

Bias

Global Macro

Emerging Markets

Global Macro

Long /

Short Equity

Managed Futures Fund of Hedge Funds Market Neutral

Equity Market

Neutral

Event Driven

Event Driven

Convertible Arbitrage

Fixed Income

Arbitrage

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)

t – test (betweenstrategies)

UnbalancedANOVA (withinand betweentreatments)

t – test (leveragevs. no leverage)

t – test forequal means

t – test forequal means

t – test forequal means

Comparative Analysis

Strategy 1Leverage

Strategy 1No

Leverage

t – test forequal means

Strategy 2Leverage

Strategy 2No

Leverage

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

Literature Review

• 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)

Prediction Models

Prediction Models

AR

ARMA

ARIMA

GLS

Univariate

Multivariate

Conditional

PCA Polynomial Fitting

Taylor Series

Higher Co-Moments

Constrained

Lagrange

KKT

Simulation

Sources

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

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.pdf

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