# Quantitaive Methods in Finance (3061)

### Quantitative Methods in Finance (3061, 6 ECTS Credits)

Workload and its composition (self-study, contact time):

Contact time (Lecture, tutorial etc.): 15 h; self-study: 165 h

Methods and duration of examination:

The written seminar paper on the one of the proposed topics and the presentation of the chosen topic at the end of the semester.

Emphasis of the grade for the final grade: 70% - paper, 30% - presentation.

Aim of the module (expected learning outcomes and competencies to be acquired):

Asset prices are determined by investors' risk preferences and by the distribution of assets' risky future payments. Economists refer to these two bases of prices as investors "tastes" and the economy's "technologies" for generating asset returns. A satisfactory theory of asset valuation must consider how individuals allocate their wealth among assets having different future payments. This course explores the development of expected utility theory, the standard approach for modelling investor choices over risky assets. We first analyze the conditions that an individual's preferences must satisfy to be consistent with an expected utility function. We then consider the link between utility and risk aversion and how risk aversion leads to risk premia for particular assets. Our final topic examines how risk aversion affects an individual’s choice between a risky and a risk-free asset.

Next topics will be considered in the course:

1. Stock prices. Returns and log-returns.

2. Statistical analysis of the data.

3. Markowitz mean-variance analysis.

4. Utility optimization: quadratic, exponential and power functions.

5. Numerical solution for the utility optimization.

Teaching and learning methods:

Formal lectures will be supported by materials including visual aids, plus interactive sessions with R programming language.

Literature (compulsory reading, recommended literature):

· Pennacchi, George Gaetano. Theory of asset pricing. Boston: Pearson/Addison-Wesley, 2008.

· Brandt, Michael W. "Portfolio choice problems." Handbook of financial econometrics: Tools and techniques. North-Holland, 2010. 269-336.

· Bodnar, Taras, Nestor Parolya, and Wolfgang Schmid. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function." Annals of Operations Research 229.1 (2015): 121-158.

· Bodnar, Taras, Nestor Parolya, and Wolfgang Schmid. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability." European Journal of Operational Research 246.2 (2015): 528-542.

· Bodnar, Taras, et al. "Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios." arXiv preprint arXiv:1806.08005 (2018).

· Ivasiuk, Dmytro. "An approximate solution for the power utility optimization under predictable returns." arXiv preprint arXiv:1911.06552 (2019).

Further information:

Registration in Moodle Viadrina required.