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 2-day programme, 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
• Understand the implications of dependency in various investment risk management applications
• 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 the Modern Portfolio Theory and portfolio risk analysis

Introduction to Correlation and Dependency Concepts

• Correlation versus dependency
• Correlation versus causation
• The many interpretations of correlations
• Correlation and networks
• Behavioural aspects of correlation
• Why are assets correlated
• Correlation in Modern Portfolio Theory: diversification, hedging, factor models

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?
• Correlation analysis of correlation: the Fisher Transformation

Workshop: Calculating tail and downside correlations

Mathematical Properties of Correlation and the Correlation Matrix

• Validity of a correlation matrix
• Fixing an invalid or singular correlation matrix
• Geometric interpretation of correlation and correlation matrices
• Synchronisation issues & solutions
• Spectral decomposition of a correlation matrix
  • Principal Component Analysis (PCA), eigenvalues and eigenvectors
  • Applications: fixing a broken correlation matrix, generating random correlation matrices
  • Singular value decomposition of correlations
• Autocorrelation: dependency over time

Alternative Approaches to Correlation and Dependency

• Spearman Rank Correlation
• Kendall's Tau
• Gerber Index
• Co-integration
• Conditional correlation: scenarios-based, downside and tail
• Distance measures: Euclidian, Manhattan, Chebyshev, Minowski
• Graph Theory: representing dependency as un-directional networks and applications in ML, AI

Workshop: Examining the validity of a correlation matrix

Scenario Analysis and Stress Testing

• Tweaking individual entries in a correlation matrix
• Changing blocks of correlation values
• Changing individual values
• Extrapolating and reverting trends in correlations
• "Risk on/off" scenarios
• Biased correlations due to illiquidity

A General Theory of Dependency – Copulas

• Introduction to Copula Theory
• Applications of Copula Theory
  • Data analysis
  • Stress testing
• Limitations of Copula Theory
• Copula application:
  • Modelling defaults as Bernoulli variables
  • Default dependence: multivariate defaults
  • Implications for the Joint Default Probability: independent, linear correlation and non-linear Clayton Copula Default Dependency in comparison

Workshop: Identifying copulas in an international asset class universe

Simulating Correlated Data

• Cholesky Decomposition & Covariance Whitening
• Multivariant normal data
• Solutions for non-normal data

Stochastic Process Models for the Correlation Coefficient

• Jacobi process: simulating paths
• Beta distribution: randomizing a correlation coefficient
• Wishart distribution: randomizing a correlation matrix

Time Series Models for Correlations

• Historical estimators and exponentially-weighted correlations
• Vectorisation of correlation matrices: vec, vecl
• Robust estimators: average correlations, denoising with insights from Random Matrix Theory
• Bayesian shrinkage estimators: Jorion, Ledoit/Wolf
• Implied correlations from derivatives instruments
• Deriving asset correlations from factor correlations
• Scenario-based correlations and (Markov) regime-switching models for correlation
• GARCH approach: Multivariate GARCH, Constant Conditional Correlation (CCC), Scalar BEKK, Dynamic Conditional Correlation (DCC), Dynamic Equi-Correlation (DECO)

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