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

[email protected]

‘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 POOL

Data Treatment

Data Treatment Risk Simulation Statistical Processing Excel / VBA Statistica EViews FACTOR ANALYSIS STATISTICAL CLUSTERING MODEL BUILDING

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

Excel Pivot table report Access Database

Information • Code • Fund (Name) • Main Strategy Performance • MM_DD_YYYY (Date) • Yield • Ptype (ROI or AUM) System Information • Leverage (Yes/No)

Access Database Management

1. Introduce Autonumber as primary keys 2. Define foreign keys for data queries 3. Define table relationships (one-to-many) 4. Build junction tables (many-to-many) 5. Write SQL queries to display relevant data 6. 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)

Survivorship Self Selection Database Instant History Look-ahead

Data Bias

Inclusion of graveyard funds Multiple databases Rolling-window observation / Incubation period

Hedge Fund Categories (TASS)

Categories Directional Dedicated Short Bias Global Macro Managed Futures Fund of Hedge Funds Market Neutral Long / Short Equity Equity Market Neutral Event Driven Fixed Income Arbitrage Emerging Markets Global Macro Event Driven 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

Strategy 1 Leverage Unbalanced ANOVA (within and between treatments) Strategy 1 No Leverage t – test (leverage vs. no leverage) t – test for equal means Strategy 2 Leverage Strategy 2 No Leverage t – test for equal means t – test for 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 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

AR ARMA ARIMA GLS Univariate Multivariate PCA Prediction Models Polynomial Fitting Constrained Simulation Taylor Series Lagrange Higher Co Moments KKT Conditional

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