Inhalt

Abstract:

"Risk is the possibility of a negative deviation from the target" - this is a common definition of risk in the context of business management. It reflects the fact that a risk can occur, but does not necessarily have to, and that things can go worse (negatively) than they were planned. All this supposes that targets have been defined previously.

 

This is where risk management comes in, by supporting organizations in identifying possible dangers at an early stage in order to keep any deviations from targets as low as possible. Of course, this presupposes that risks are actually identified and correctly assessed, and that the "right" measures (in terms of effectiveness and costs) are taken in good time to manage them.

 

The Covid 19 pandemic, with which the entire world has been confronted since the beginning of March 2020, shows that things can fail to run according to previous plans. It can be assumed that most companies have probably included a pandemic risk in their risk universe. However, the Covid 19 pandemic is certainly far beyond everything imagined before.

 

There are often considerable methodological deficits in risk management, for example when, in a popular but simplistic approach, risks are assessed as a mathematical product of probability of occurrence and impact of damage. If a very low probability and a very high impact of damage are used to quantify the current situation, this would result in a low to moderate risk. It is obvious that such risk measures are illusive. In practice, there are still considerable differences between existing risk management and effective risk management.

 

Effective risk management therefore goes far beyond simplistic approaches and requires - in addition to a practiced risk culture in the company – a deeper understanding and correct use of quantitative risk assessment procedures. Quantitative assessment procedures and simulations based thereon can provide valid statements about a company's overall risk position (e.g., in the form of risk measures). Only then the company's capital requirements (= risk buffer) required for the risk situation can reasonably be determined.

 

However, this requires that risk managers are also familiar with the necessary mathematical-statistical procedures. This challenge is addressed by the present course "Elementary Quantitative Risk Assessment" (EQRA), which teaches these competencies at a basic level for bachelor students.

Gliederung:

Learning module 1 | Concepts and terminology of quantitative risk modeling.
- Central terms of risk modelling
- Variables of loss and profit type
- Upside and downside risks
- Risks in learning of risks

Learning module 2 | Mathematical and Statistical Foundations of Risk Modelling
A) Data

B) Mathematical and statistical principles of risk modelling
- Statistical distributions in context of risk
- Basic concept of statistical distributions
- Density and distribution functions
- Probability distributions in risk context

C) Distribution parameters as risk indicators
- Risk measures and loss functions
- Distribution parameters in risk context: location, dispersion, shape
- Parameter estimation
- Basic concept of interval estimation
- Confidence intervals

D) Right tail behaviour of distributions
- Tail classification of distributions

Learning module 3 | Stochastic Risk Measures
A) The purpose of stochastic risk measures
- The pitfall of the mean
- Theoretical and empirical quantiles

B) The Value at Risk
- Basel I, II, III regulations
- The Value at Risk for loss variables
- Value at Risk estimation
>- Distribution-free estimation of VaR
>- Distribution-based VaR estimation
>- VaR estimation - Peaks over Threshold (PoT) and Hill-Weissman

C) Conditional Value at Risk (CVaR)
- Subadditivity of VaR and CVaR
- Distribution-free CVaR estimation
- Distribution-based CVaR estimation
- Peaks over Theshold CVaR estimation

Detaillierter Inhalt:

Learning module 1 | Concepts and terminology of quantitative risk modelling.
The central concepts and schemes in the context of risk modelling are introduced and explained, especially terminologies such as risk phenomenon, risk object, direct risk, indirect risk, loss type and profit type risk variable, upside and downside risks, risk indicator and risk measure.

Learning module 2 | Mathematical and statistical basics of risk modelling.
This learning module covers mathematical and statistical foundations for describing risk phenomena and related data in four parts A, B, C, and D.

A) Data
This submodule communicates basic characteristics of data sets and the mechanisms creating data.

B) Mathematical and statistical principles of risk modelling
This submodule considers the topics i) purpose of probability distributions in risk modelling, ii) basic concept of probability distributions, iii) densities and cumulative distribution functions, iv) special probability distributions for risk modelling.

C) Distribution parameters as risk parameters.
For a simple description of risk phenomena, location measures and dispersion measures as well as their estimation are presented and demonstrated. In addition, the construction of confidence intervals for these measures is shown.

D) Right Tail behaviour of distributions
Stochastic inequalities such as those due to Chebycheff or Camp-Meidell are discussed. These can be used to establish inequalities for quantiles and to build parameter-free confidence intervals for quantiles. The concepts of a light-tailed and a heavy-tailed distribution defined. With these concepts, the multitude of distributions from A) can be assessed with regard to their suitability for the respective risk assessment.

Learning module 3) Special stochastic risk measures
The risk measures Value at Risk (VaR) and Conditional Value at Risk are paramount for sound and effective risk assessment and risk management. These measures are basic in capital adequacy regulations such as Basel III, and are therefore of high practical relevance. Methods of estimating VaR and CVaR are a core focus of the course.

A) The purpose of stochastic risk measures
This submodule discusses the mean and its flaws in risk assessment. The quantile is subsequently motivated as a basis for better risk measures explored in submodules B) and C).

B) Value at Risk (VaR)
This submodule discusses the definition, interpretation, use and estimation of Value at Risk. Three common methods for estimating VaR are presented, and their strengths and weaknesses are explained: distribution-free, distribution-based, and peaks over threshold (POT) methods. In the case of the distribution-based and POT methods, particular attention is paid to fitting probability distributions to the data. Both point and interval estimation techniques are provided.

 
C) Conditional Value at Risk (CVaR)
In this submodule, the definition, interpretation, use and estimation of the Conditional Value at Risk (CVaR) are discussed. Common methods for estimating CVaR, including both point and interval estimation, are presented and illustrated.

 

Learning Goals:

The Students
- become familiar with the methods of quantitative model building and  quantitative analysis, for applications in risk management.
- are able to describe risk phenomena and related data in an analytic, formal way.
- get acquainted with basic procedures of descriptive data analysis.
- familiarize themselves with a variety of probability distributions and their applicability in describing risk phenomena.
- are able to fit distributions to data.
- possess knowledge on the theoretical definitions and applications of central stochastic risk measures.

Schwierigkeitsgrad:

Einsteiger

Lehr-/Lernform:

Virtuelle Vorlesung

Interaktionsformen mit dem System/Betreuer:

Chat, E-Mail

Interaktionsformen mit Mitlernenden:

Forum

Kursdemo:

zur Kursdemo

Schlagworte:

Risiko, Datenanalyse, Verteilungen, Statistik, Empirische Methoden

Nutzung

Zielgruppe:

Wirtschaftswissenschaften für FH-Studierende, Wirtschaftsinformatik für Uni-Studierende, Wirtschaftsinformatik für FH-Studierende, Wirtschaftswissenschaften für Uni-Studierende

Nutzbar im Studiengang:

Universität Würzburg: Bachelor Wirtschaftsmathematik

OTH Amberg-Weiden: Bachelor Betriebswirtschaft

Hochschule Coburg: Bachelor Betriebswirtschaft

Universität Erlangen-Nürnberg (FAU): Bachelor Wirtschaftswissenschaften

Geeignet für Berufsfeld:

Graduates in economics, mathematics or sciences

Formale Zugangsvoraussetzungen:

Course enrolment via the Virtuelle Hochschule Bayern (vhb)

Erforderliche Vorkenntnisse:

none

Erforderliche Vorkenntnisse bzgl. Handhabung der Lernplattform:

-

Verantwortlich

Trägerhochschule:

Uni Würzburg

Anbieter:

Prof. Dr. Rainer Göb

Autoren:

Jens Bischoff, Andrew Easton, Philipp Fröhlich, Rainer Göb

Betreuer:

Prof. Dr. Rainer Göb

Prüfung

Exam for the course (part 1: 30 minutes closed book + part 2: 60 minutes open book = 90 minutes)

Art der Prüfung:

schriftlicher Leistungsnachweis (Klausur)

Prüfer:

Prof. Dr. Rainer Göb

Anmeldeverfahren:

Die Anmeldung erfolgt über das WWW.

Prüfungsanmeldefrist:

01.10.2024 00:00 Uhr bis 31.01.2025 23:59 Uhr

Prüfungsabmeldefrist:

01.10.2024 00:00 Uhr bis 31.01.2025 23:59 Uhr

Kapazität:

–

Prüfungsdatum:

–

Prüfungszeitraum:

–

Prüfungsdauer:

90 Minuten

Prüfungsort:

Würzburg

Zustündiges Prüfungsamt:

Examination office of the students' home university

Zugelassene Hilfsmittel:

part 1 (30 minutes closed book): none
part 2 (60 minutes open book): all printed material and portable calculator. No laptops, no devices that enable communication

Formale Voraussetzungen für die Prüfungsteilnahme:

Timely registration for the exam via the vhb portal

Inhaltliche Voraussetzungen für die Prüfungsteilnahme:

Course content

Zertifikat:

Ja (Graded certificate)

Anerkennung an folgenden Hochschulen:

Uni Würzburg, Uni Erlangen-Nürnberg (FAU), FH Coburg, FH Amberg-Weiden

Sonstige Anerkennung:

noch nicht bekannt

Online-Prüfungsan-/-abmeldung:

Ja

Bemerkung:

The exam is divided into two parts: closed book part (30 minutes) and open book part (60 minutes)

Erforderliche Technik

Browser:

Current version of a common web browser (e.g., Chrome, Edge, Firefox)

Nutzungsbedingungen

Gebühren:

Nein

Nutzungsentgelte:

für andere Personen als (reguläre) Studenten der vhb Trägerhochschulen nach Maßgabe der Benutzungs- und Entgeltordnung der vhb

Copyright:

-

Hinweise zur Nutzung:

-