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Portföljoptimering med courtageavgifter
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2014 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Portfolio optimization with brokerage fees (English)
Abstract [en]

Ever since it was first introduced in an article in the Journal of Finance 1952, Harry Markowitz’ mean - variance model for portfolio selection has become one of the best known models in finance. The model was one of the first in the world to deal with portfolio optimization mathematically and have directly or indirectly inspired the rest of the world to develop new portfolio optimization methods. Although the model is one of the greatest contributions to modern portfolio theory, critics claim that it may have practical difficulties. Partly because the Markowitz model is based on various assumptions which do not necessarily coincide with the reality. The assumptions which are based on the financial markets and investor behavior contain the simplification that there are no transaction costs associated with financial trading. However, in reality, all financial products are subject to transaction costs such as brokerage fees and taxes. To determine whether this simplification leads to inaccurate results or not, we derive an extension of the mean-variance optimization model which includes brokerage fees occurred under the construction of an investment portfolio. We then compare our extension of the Markowitz model, including transaction costs, with the standard model. The results indicate that brokerage fees have a negligible effect on the standard model if the investor's budget is relatively large. Hence the assumption that no brokerage fees occur when trading financial securities seems to be an acceptable simplification if the budget is relatively high. Finally, we suggest that brokerage fees are negligible if the creation of the portfolio and hence the transactions only occurs once. However if an investor is active and rebalances his portfolio often, the brokerage fees could be of great importance.

Abstract [sv]

Harry Markowitz portföljoptimeringsmodell har sedan den publicerades år 1952 i en artikel i the journal of Finance, blivit en av de mest använda modellerna inom finansvärlden. Modellen var en av dem första i världen att hantera portföljoptimering matematiskt och har direkt eller indirekt inspirerat omvärlden att utveckla nya portföljoptimeringsmetoder. Men trots att Markowitz modell är ett av de största bidragen till dagens portföljoptimeringsteori har kritiker hävdat att den kan ha praktiska svårigheter. Detta delvis på grund av att modellen bygger på olika antaganden som inte nödvändigtvis stämmer överens med verkligheten. Antagandena, som är baserad på den finansiella marknaden och individers investeringsbeteende, leder till förenklingen att transaktionskostnader inte förekommer i samband med finansiell handel. Men i verkligheten förekommer transaktions-kostnader som courtageavgifter och skatter nästintill alltid vid handel av finansiella produkter som t.ex. värdepapper. För att avgöra om modellen påvisar felaktiga resultat på grund av bortfallet av courtageavgifter härleds en utvidgning av Markowitz modell som inkluderar courtageavgifter. Utvidgningen av Markowitz modell jämförs sedan med originalmodellen. Resultaten tyder på att courtageavgifter har en försumbar effekt på originalmodellen om investeraren har en stor investeringsbudget. Slutsatsen är därför att, förenklingen att inga courtageavgifter förekommer är en acceptabel förenkling om investeringsbudgeten är stor. Det föreslås slutligen att courtageavgiften är försumbar om transaktionen av aktier endast sker en gång. Men om en investerare är aktiv och ombalanserar sin portfölj flitigt, kan courtageavgifterna vara av stor betydelse.

 

Place, publisher, year, edition, pages
2014.
Series
TRITA-MAT-K, 2014:15
Keyword [en]
Portfolio optimization, brokerage fees, mean-variance portfolio optimization, Markowitz, efficient frontier
Keyword [sv]
Portföljoptimering, courtageavgifter, Markowitz, mean-variance portfolio optimization, effektiv front.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-146748OAI: oai:DiVA.org:kth-146748DiVA: diva2:725419
Subject / course
Applied Mathematical Analysis
Educational program
Master of Science in Engineering - Industrial Engineering and Management
Supervisors
Examiners
Available from: 2014-06-16 Created: 2014-06-15 Last updated: 2014-06-16Bibliographically approved

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