Correlation in Investment Management

Despite the very well-known facts that dependencies in financial markets are time-variable and can have a major impact on the overall risk of portfolios and balance sheets, information regarding advanced methodologies in dependency analysis is hard to find and often fragmentary.

In this intensive program, correlation and related dependency concepts take centre stage. After a systematic introduction to empirical and mathematical properties of the traditional correlation concept, more recent methodologies are presented and examined in detail. This will help practitioners to derive deeper insights into real-word dependency structures, and solve practical issues in working with scenario-based approaches and deriving forward-looking estimators.

Participants will solve exercises based on typical situations encountered in applied dependency analysis, allowing them to find new inspiration and to take home practical tools to further improve their practice.

• Buy-side and sell-side risk managers
• Investment managers of traditional and alternative assets
• All staff involved with quantitative analysis
• Programmers and application developers

• Understand the limitations of traditional linear correlation analysis
• Gain familiarity with modern dependency concepts beyond correlation
• Learn how to apply scenario analysis to correlation forecasting and stress-testing
• Analyze the implications of dependency on portfolio risk
• Gain a deeper understanding of the advantages, and disadvantages, of quantitative methods in investment decision making

• Basic understanding in statistics, especially linear regression
• Familiarity with modern portfolio theory and portfolio risk analysis

Introduction to Correlation and Dependency Concepts

Stylized Facts about Correlations and Dependencies in Financial Market Data

• Contagion effects in stock correlations
• Globalization in global equity investing
• Bonds as a safe haven asset
• Is gold a safe haven?

Workshop: Calculating tail and downside correlations

Mathematical Properties of Correlation and the Correlation Matrix

• Validity of a correlation matrix
• Fixing a broken correlation matrix
• Alternative correlation concepts
• Spearman’s Rank Correlation
• Kendall's T
• Spectral decomposition of a correlation matrix: eigenvalues and eigenvectors
• Singular value decomposition of correlations
• Autocorrelation: dependency over time
• Co-integration and its use in trading

Workshop: Examining the validity of a correlation matrix

Correlation in Modern Portfolio Theory – Diversification

Scenario Analysis and Stress Testing

• Tweaking individual entries in a correlation matrix
• Changing blocks of correlation values
• Extrapolating trends in correlations: "Risk On" and "Risk Off" scenarios
• Randomizing a correlation matrix
• Handling the additivity of conditional correlations

A General Theory of Dependency – Copulas

• Introduction to Copula Theory
• Applications of Copula Theory
  • Data analysis
  • Stress testing

Workshop: Identifying copulas in an international asset class universe

Simulating Correlated Data

• Multivariant normal data
• Solutions for non-normal data

Stochastic Process Models for the Correlation Coefficient

Forecasting Correlations

• Historical estimators
• Robust estimators
• Bayesian shrinkage estimators: Jorion, Ledoit/Wolf
• Implied correlations from derivatives instruments
• Deriving asset correlations from factor correlations

Time Series Models for Correlations

• Exponential smoothing
• Multivariate GARCH
• Dynamic Conditional Correlation (DCC)

Workshop: Analyzing the volatility risk of a multi-asset-class portfolio based on robust correlation scenarios