# GRA 6551 Quantitative Risk and Asset Management

## GRA 6551 Quantitative Risk and Asset Management

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.

By the end of the course, students are expected to know:

- Common measures of risk.
- Properties of univariate and multivariate time series.
- Tools for univariate and multivariate modelling of skeweness and fat tails.
- The Kelly optimal growth criterion.
- Some popular portfolio management strategies and their connection to mean-variance optimization.

By the end of the course the students are expected to be able to:

- Compute common measures of portfolio risk.
- Explain key properties of univariate and multivariate time series as they related to risk management and portfolio management.
- Model skewed and leptokurtik univariate distributions.
- Explain the assumptions implicit in common strategies for portfolio formation, like risk parity and variance minimization.

The students by the end of the course are expected to be able to reflect on the workings and limitations of risk and asset management.

- 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.

Relevant financial data will be used throughout the course, both in lectures and in assignments. Students will be given regular assignments, focusing on hands-on application of the material covered in class and on software. Some coding will be necessary, and students will receive assistance with aspects of the assignments related to software and coding. These assignments are not compulsory and are not graded, but will be most useful as preparation for the take-home exam.

Labs will be conducted in R, but students are free to use any other programming language (Matlab, Python, Julia etc).

Please note that while attendance is not compulsory in all courses, it is the student’s own responsibility to obtain any information provided in class.

**Both parts of the examination have to be passed in order to obtain a final grade in the course.**

At resit, all exam components must, as a main rule, be retaken during next scheduled course.

__Honour Code__

Academic honesty and trust are important to all of us as individuals, and represent values that are encouraged and promoted by the honour code system. This is a most significant university tradition. Students are responsible for familiarizing themselves with the ideals of the honour code system, to which the faculty are also deeply committed.

Any violation of the honour code will be dealt with in accordance with BI’s procedures for cheating. These issues are a serious matter to everyone associated with the programs at BI and are at the heart of the honour code and academic integrity. If you have any questions about your responsibilities under the honour code, please ask.

All courses in the Masters programme will assume that students have fulfilled the admission requirements for the programme. In addition, courses in second, third and/or fourth semester can have specific prerequisites and will assume that students have followed normal study progression. For double degree and exchange students, please note that equivalent courses are accepted.

**Disclaimer**

Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

Students are expected to be familiar with basic statistics and econometrics (concepts such as “distribution” and “regression”), basic calculus (derivatives, first-order-conditions), basic matrix algebra, and basic programming.

Assessments |
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Exam category: Submission Form of assessment: Written submission Weight: 50 Grouping: Group (1 - 3) Duration: 7 Day(s) Comment: Take-home exam Exam code: GRA65514 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during next scheduled course |

Exam category: Submission Form of assessment: Written submission Invigilation Weight: 50 Grouping: Individual Support materials: - BI-approved exam calculator
- Simple calculator
- Bilingual dictionary
Duration: 2 Hour(s) Comment: Final written examination under supervision Exam code: GRA65514 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during next scheduled course |

Activity | Duration | Comment |
---|---|---|

Teaching | 24 Hour(s) | |

Webinar | 12 Hour(s) | |

Student's own work with learning resources | 25 Hour(s) | |

Prepare for teaching | 40 Hour(s) | |

Examination | 35 Hour(s) |

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 6 ECTS credits corresponds to a workload of at least 160 hours.