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Portfolio Analysis and Capital Markets I

General data

Course ID: 1000-135PK1 Erasmus code / ISCED: 11.923 / (0619) Information and Communication Technologies (ICTs), not elsewhere classified
Course title: Portfolio Analysis and Capital Markets I Name in Polish: Analiza portfelowa i rynki kapitałowe I
Department: Faculty of Mathematics, Informatics, and Mechanics
Course groups:
ECTS credit allocation (and other scores): (not available)
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Language: English
Type of course:

elective courses


Introduction to Mathematical Modelling in Finance 1000-134WMF
Microeconomics 1000-135MIE
Optimization II 1000-135OP2

Short description:

Acquaintance with principles of portfolio analysis (part of financial

mathematics) and with its role in the theory of capital markets.

Full description:

Principles of decision taking under conditions of uncertainty: the expected rate of return, measures of volatility as measures of risk or measures of exposure to danger, VaR, decision criteria, measure of relationship of (random) rates of return, properties of expected utility and indifference curves in the decision taking

model <expected rate of return - risk> (3 lectures).

General Markowitz model: the expected rate of return and risk of a portfolio, feasibility set, extremal and efficient portfolios; minimal, efficient, and maximal frontier; piecewise-linear set of efficient portfolios; kinks on efficient frontier. Maximization of expected utility of portfolio's rate of return and maximization of portfolio's Sharpe coefficient. Estimation of model parameters (4 lectures).

Special models: basic Markowitz, Black, Tobin and modified Tobin, Sharpe. Basic Markowitz and Black models for two stocks in all details (4 lectures).

Capital market hypotheses: - of normality of distribution of rates of return, - of random wandering, - of efficient market, - of fractal market (1 lecture).

The Capital Asset Pricing Model (CAPM): perfect market, equilibrium on a capital market, market portfolio and its relationship to tangent portfolio, the cost of capital formula, applications of CAPM (2 lectures).


E. J. Elton, M. J. Gruber; Modern Portfolio Theory and Investment Analysis, Wiley, 1991.

J. C. Francis; Investments - Analysis and Management, Mc Graw-Hill.

G. J. Alexander, J. C. Francis; Portfolio Analysis, Prentice-Hall, 1986.

H. M. Markowitz [with a chapter and program by G. P. Todd]; Mean-Variance Analysis in Portfolio Choice and Capital Markets, Fabozzi Associates, 2000 (revised reissue with a new chapter).

H. Levy, M. Sarnat; Portfolio and Investment Selection: Theory and Practice, Prentice-Hall, 1984.

This course is not currently offered.
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