## Multivariate Methods

### Lehrinhalte

probability calculus: multivariate distributions with a focus on the bivariate normal distribution, covariance and correlation; estimation of the moments and distributions of linear combinations of random variables. inferential statistics: fundamentals of estimation and desirable properties of estimators (unbiasedness, efficiency and consistency); Maximum Likelihood estimator, estimation of the expected value, proportion, variance, covariance and correlation; foundation of test procedures: structure of tests (Null-hypothesis, test statistic, acceptance or rejection of null hypothesis), type I and type II errors (alpha and beta errors); test for proportion and expected value; structure and assumption of a simple linear regression: estimation of parameters and testing for significance. multivariate regression: estimation of the parameters, goodness-of-fit measures (R2 and adjusted R2) and important tests (t-test and F-test; regression diagnostics); factor models and principal components analysis: introduction with an example from asset and risk management (e.g. forecasting for an equity portfolio); logistic regression: estimation of the parameters, assessing the goodness-of-fit (e.g. ROC- or CAP-curve, Brier-Score), important tests and areas of application in asset or risk management (e.g. for rating models); Neural networks: Estimation of parameters, goodness-of-fit, important tests and areas of application in asset or risk management (e.g. forecasting models for equity or FX)

### Art der Vermittlung

Präsenzveranstaltung

Pflichtfach

### Empfohlene Fachliteratur

Alexander, C., 2008, Quantitative Methods in Finance, Wiley & Sons; Hair, J., Black, W., Babin, B., Anderson, R., 2013, Multivariate Data Analysis, 7th edition, Pearson Education Limited; Peng, C., 2008, Data analysis using SAS, SAGE publications

### Lern- und Lehrmethode

Interactive teaching (lecture and discussion), blended learning (online exercises are mandatory), application of models on practical problem sets

### Prüfungsmethode

49% assignment projects and online-quizzes, 51% final exam

### Voraussetzungen laut Lehrplan

FOEC10, FUFI10, FUMS10, PRDA10

### Schnellinfos

#### Studiengang

Quantitative Asset and Risk Management (Master)

Master

5.00

Englisch

Berufsbegleitend

2024

1 WS

Ja

#### Lernergebnisse der Lehrveranstaltung

After the successful completion of the course, students are able to decide on appropriate statistical techniques (e.g. regression and classification models) and they can apply and interpret them: they can calibrate, interpret and analyse models’ parameter estimates and goodness-of-fit measures in detail and they can hence judge the accuracy of these models. They can apply the calibrated models to estimate the value of dependent variables (regressand) on the basis of the values of explanatory variables (regressors). As the statistical concepts are always taught on the basis of practical examples, the students know in which areas of asset and risk management these advanced multivariate models are used: return distributions and risks of portfolios of assets, models to estimate the default probability of obligors etc.

#### Kennzahl der Lehrveranstaltung

0613-09-01-BB-EN-05