MPF_TEPO Portfolio Theory

Faculty of Economics and Administration
Spring 2025
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Ing. Luděk Benada, Ph.D. (lecturer)
Ing. Luděk Benada, Ph.D. (seminar tutor)
Mgr. Silvie Zlatošová, Ph.D. (seminar tutor)
Guaranteed by
Ing. Luděk Benada, Ph.D.
Department of Finance – Faculty of Economics and Administration
Contact Person: Iva Havlíčková
Supplier department: Department of Finance – Faculty of Economics and Administration
Prerequisites
! MPF_APOT Portfolio Theory && !NOWANY( MPF_APOT Portfolio Theory )
Knowledge in Microeconomics, Macroeconomics, Mathematics, Statistics and Financial Mathematics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 140 student(s).
Current registration and enrolment status: enrolled: 0/140, only registered: 27/140, only registered with preference (fields directly associated with the programme): 13/140
fields of study / plans the course is directly associated with
Course objectives
In the course, students will get acquainted with the basic mathematical methods used in the field of evaluation of investment opportinities, portfolio optimization and valuation of risky and non-risky assets.
The course is especially important for students who intend to work in the field of asset management at financial institutions.
The content is divided into two thematic areas.
The subject of the first part is the Markowitz model in the standard form, which is further extended by risk-free deposits and risk-free loans.
The content of the second thematic area is the model of capital asset valuation, risk diversification and arbitrage valuation theory.

The main objectives of the course are:
-understanding the basics of portfolio theory,
-understanding the valuation of securities yield and risk;
-understanding the basic approaches to compiling a portfolio of securities;
-the ability to apply the acquired knowledge to problem areas that are not directly discussed in the course.
Learning outcomes
Student will be able to:
- apply knowledge of the key characteristic (return, risk, liquidity) of traded equity securities
- quantify the expected price price development of a security
- valuate securities
- create a portfolio in the line with Markowitz´s and Sharpe concept
- solve the portfolio problem with weight restricktion (short sell, max. weight of a security)
Syllabus
  • Structure of the lectures:
  • 1. Introduction to Theory of portfolio.
  • 2. Assets in Theory of portfolio, revenue, risk, changes of its revenue.
  • 3. expected revenue, change of portfolio revenue.
  • 4. Markowitz model, system of acceptable portfolios in the area of revenue and risk
  • 5. Group of effective portfolios in Sharpe and Markowitz
  • 6. Non-risk assets, sell short, borrowing and lending
  • 7. Math models for defining ofweights in portfolio, optimal portfolio, risk minimizing
  • 8. Model of appreciation capital assets CAPM, capital market line
  • 9. Model of appreciation capital assets SML, capital market line
  • 10. One index model and defining of share of stocks in portfolio (sell short, or not , Elton-Gruber)
  • 11. Factor models, consolidation of CAPM and APT
  • 12. “Morefactors” models, influence of inflation, stock revenue, portfolio revenue
  • Thematic plan of seminars:
  • 1. Initial seminar – working methods in seminars, clause of classification
  • 2 Kvantification of revenue and risk of assets (revenue and risk of assets, historical attitudes, expert attitudes)
  • 3. Kvantification of expected revenue and risk of portfolio (revenue and risk of portfolio if you know shares, stock exchange trading, risk of change of revenue if you know shares)
  • 4. Permissible and effective group of portfolios construction, indifferent curves (grafical solutions)
  • 5. Control test I
  • 6. Non-risk assets, lending and borrowing (construction portfolio group with non-risk assets (...) revenue in perfect competition, or in non-perfect competition)
  • 7. Defining shares of assets in portfolio (defining shares by Lagrange multiplier, using of stock exchange datas
  • 8. Capital assets appreciation, capital market curve (CML curve; bond market curve)
  • 9. Capital assets market in SML, using of the bond market curve, deciding to buy and sell, systematic and non- systematic risk, one- index model...)
  • 10. Control test II
  • 11. Determining factors of assets revenue, CAPM and APT merging
  • 12. Factor models, beta-factor, revenue and risk of factor portfolios, inflation in the Czech Republic
Literature
    required literature
  • ELTON, Edwin J. Modern portfolio theory and investment analysis. 8th ed. Hoboken, N.J.: John Wiley & Sons, 2011, xviii, 727. ISBN 9780470505847. info
    recommended literature
  • STEWART, Scott Dudley, Christopher Dixon PIROS and Jeffrey HEISLER. Portfolio management : theory and practice. Second edition. Hoboken, New Jersey: Wiley, 2019, xvi, 703. ISBN 9781119397410. info
  • SCHULMERICH, Marcus, Yves-Michel LEPORCHER and Ching-Hwa EU. Applied asset and risk management : a guide to modern portfolio management and behavior-driven markets. Berlin: Springer, 2015, xvii, 476. ISBN 9783642554438. info
    not specified
  • BERK, Jonathan and Peter DEMARZO. Corporate Finance. 4th Edition. Pearson, 2016. ISBN 978-1-292-16016-0. info
Teaching methods
Lectures, during the seminars - solving of problems related to expected return and risk counting of assets, portfolio selection under different conditions, equilibrium pricing models.
Assessment methods
Teaching structure: 2/2 (lectures/seminars)
Examination: Written
Control test I and Control test II in seminars will be written by students following the schedule (concrete information will be given at the begining of semester). If student can not participate in one of two tests (not both) he or she can apologize (but only teacher will decide if the apology is authorized). There can be one repetitional test at the beginning of the exam period (there can be everything for whole year, that was taught). Classification will be the same as for the standard tests.
The final grade is determined on the basis of the result in seminars (with minimal partitipation of 70 %) and the achieved results from two tests. To successfully graduate, it is necessary to have on average 60 % of both tests. Failur to meet this condition presupposes a repetition of the course.
Each test consists of three problems of different difficulty.

Then final classification is following:
A= [27, 30]
B= [25, 27)
C= [23, 25)
D= [21, 23)
E=[18, 21)
F= [0, 18)

If student will cheat or copy or plagiarize, or do enything else tht is forbidden, teacher would interupt the exam and student will be classified by F, FF, or FFF. Further, there could be made an applictaion for disciplinary proceedings.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Tento předmět je obsahově ekvivalentní s předmětem MPF_APOT vyučovaném v anglickém jazyce.
Credit evaluation note: k=1.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
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