Quantitative Risk and Asset Management

Introduction

This course focuses on statistical aspects related to the management of financial risk and the construction of portfolios, issues that are paramount for banks, asset managers, and other financial institutions and international supervisory authorities. We start with the fundamental concepts of financial risk management. The course emphasis is on non-Gaussian returns, estimation error, model errors, skewness and fat tails, non-linear exposures, and dynamic portfolio choice. These concepts are first explored in a univariate setting and then extended to a multivariate portfolio. We wish to understand when portfolio optimization is more likely to succeed and fail, and why popular portfolio strategies like risk parity and factor modelling have abandoned or severely constrained the optimization process. Standard and Bayesian approaches are presented and compared.

Course content

• Introduction to quantitative risk and asset management. Useful ways to think about risk and where it originates.
• Risk measures.
• Statistical tools: maximum likelihood and approximate Bayesian inference.
• Properties of univariate financial time series. Skew and thick tails vanish very slowly (if at all) in financial series
• Some useful univariate distributions.
• Modelling skew and thick tails with univariate mixtures.
• Introduction to univariate models of time-varying volatility.
• Dynamic portfolio sizing with one risky asset: Introduction to the Kelly optimal growth criterion.
• Connections between the Kelly criterion and some popular trading strategies.
• Properties of multivariate financial time series.
• Some useful multivariate distributions.
• Modelling skew and thick tails with multivariate mixtures.
• Introduction to copulas.
• Model error and dimensionality.
• Introduction to multivariate models of time-varying volatility.
• Dimensionality reduction: shrinkage methods and factor methods.
• The Kelly optimal growth criterion with multiple assets.
• When and why Modern Portfolio Theory works poorly in practice. Improving the performance of MPT.
• Some popular portfolio management strategies and their connection to MPT: risk-parity, minimum variance, maximum diversification.