GRA 6551 Quantitative Risk and Asset Management

GRA 6551 Quantitative Risk and Asset Management

Course code: 
GRA 6551
Course coordinator: 
Paolo Giordani
Course name in Norwegian: 
Quantitative Risk and Asset Management
Product category: 
MSc in Quantitative Finance
2021 Spring
Active status: 
Level of study: 
Teaching language: 
Course type: 
One semester

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.

Learning outcomes - Knowledge

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.
Learning outcomes - Skills

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.
General Competence

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.

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.
Teaching and learning activities

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).

Software tools
Additional information

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.


Due to the Covid-19 pandemic, there may be deviations in teaching and learning activities as well as exams, compared with what is described in this course description.

Required prerequisite knowledge

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.  Qualifications: Add required pre-requisite knowledge for the students to know what they need before taking the course, e.g. basic finance theory, statistics, basic time series modelling, distributions, etc.

Exam category: 
Form of assessment: 
Written submission
Group (1 - 2)
7 Day(s)
Take-home exam
Exam code: 
Grading scale: 
Examination when next scheduled course
Exam category: 
Form of assessment: 
Written submission
Support materials: 
  • BI-approved exam calculator
  • Simple calculator
  • Bilingual dictionary
3 Hour(s)
Final written examination under supervision
Exam code: 
Grading scale: 
Examination when next scheduled course
Type of Assessment: 
Ordinary examination
All exams must be passed to get a grade in this course.
Total weight: 
Sum workload: 

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.