Presented at EDAMBA summer school, Soreze (France)
23 July – 27 July 2009
Data Sourcing, Statistical Processing
and Time Series Analysis
An Example from Research into
Hedge Fund Investments
Presenter:
University:
Supervisor:
Research Title:
Contact:
Florian Boehlandt
University of Stellenbosch – Business School
Prof Eon Smit
Prof Niel Krige
A Risk-Return Assessment of Fund of Hedge
Funds in Comparison to Single Hedge Funds
– An Empirical Analysis
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
Research Philosophy
Positivistic, deductive research:
Postulation of hypotheses that are tested via standard statistical procedures
Research Approach
Empirical analysis:
Interpreting the quality of pricing models on the basis of historical data
Primary Data
External secondary data:
Historic time series adjusted for data-bias effects
Data Sourcing
Data
Sources
Hedge Fund
Databases
Financial
Databases
Risk
Simulation
Monte Carlo
(Solver)
Confidence
(RiskSim)
CISDM/MAR
DATA
POOL
Data Treatment
Data
Treatment
DATA
POOL
Risk
Simulation
Statistical
Processing
Excel / VBA
Statistica
EViews
FACTOR
ANALYSIS
STATISTICAL
CLUSTERING
MODEL
BUILDING
STATISTICAL SIGNIFICANCE
Data Processing (1/2)
Data Import
Data
Treatment
Data
Analysis
• Extract relevant data from Access (SQL)
• Import data as Pivot table report
• Test for serial correlation /databias
• Calculate adjusted excess returns
• Select funds with consistent data series
• Determine statistical model
Data Processing (2/2)
Weighting
Comparative
Analysis
Data Output
• Estimate weighted average parameters
• Construct style indices
• Calculate within-group variation
• Calculate between-group variation
• Tabular display of aggregate results
• Construction of line - bar charts
Data Import
Access Database
Information
• Code
• Fund (Name)
• Main Strategy
Performance
• MM_DD_YYYY (Date)
• Yield
• Ptype (ROI or AUM)
System
Information
• Leverage (Yes/No)
Excel Pivot table report
Access Database Management
1.
2.
3.
4.
5.
6.
Introduce Autonumber as primary keys
Define foreign keys for data queries
Define table relationships (one-to-many)
Build junction tables (many-to-many)
Write SQL queries to display relevant data
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
Inclusion of graveyard funds
SelfSelection
Multiple databases
Database
Instant
History
Look-ahead
Rolling-window observation / Incubation
period
Hedge Fund Categories (TASS)
Categories
Dedicated Short
Bias
Directional
Managed Futures
Fund of Hedge
Funds
Market Neutral
Global Macro
Long / Short
Equity
Equity Market
Neutral
Event Driven
Emerging Markets
Global Macro
Event Driven
Fixed Income
Arbitrage
Convertible
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)
Comparative Analysis
Unbalanced
ANOVA (within
and between
treatments)
Strategy 1
Leverage
Strategy 2
Leverage
t – test for
equal means
Strategy 1
No
Leverage
Strategy 2
No
Leverage
t – test for
equal means
t – test (leverage t – test for
vs. no leverage) equal means
t – test for
equal means
t – test (between
strategies)
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 crosssectional 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
GLS
PCA
Polynomial
Fitting
Constrained
ARMA
Univariate
Taylor Series
Lagrange
ARIMA
Multivariate
Higher CoMoments
KKT
Conditional
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=00221082%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