IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.10253.html
   My bibliography  Save this paper

The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory

Author

Listed:
  • Ignas Gasparaviv{c}ius
  • Andrius Grigutis

Abstract

This survey article is dedicated to the life of the famous American economist H. Markowitz (1927--2023). We do revisit the main statements of the portfolio selection theory in terms of mathematical completeness including all the necessary auxiliary details.

Suggested Citation

  • Ignas Gasparaviv{c}ius & Andrius Grigutis, 2024. "The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory," Papers 2402.10253, arXiv.org.
    • Handle: RePEc:arx:papers:2402.10253
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.10253
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    3. Mark Rubinstein, 2002. "Markowitz's “Portfolio Selection”: A Fifty‐Year Retrospective," Journal of Finance, American Finance Association, vol. 57(3), pages 1041-1045, June.
    4. Andrius Grigutis, 2023. "Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche," Papers 2303.06148, arXiv.org.
    5. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    7. Carole Bernard & Corrado De Vecchi & Steven Vanduffel, 2021. "When do two- or three-fund separation theorems hold?," Quantitative Finance, Taylor & Francis Journals, vol. 21(11), pages 1869-1883, November.
    8. André F. Perold, 2004. "The Capital Asset Pricing Model," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 3-24, Summer.
    9. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    10. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    11. Bick, Avi, 2004. "The mathematics of the portfolio frontier: a geometry-based approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 337-361, May.
    12. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    13. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    14. Jan Wenzelburger, 2010. "The two-fund separation theorem revisited," Annals of Finance, Springer, vol. 6(2), pages 221-239, March.
    15. Roman Vershynin, 2012. "How Close is the Sample Covariance Matrix to the Actual Covariance Matrix?," Journal of Theoretical Probability, Springer, vol. 25(3), pages 655-686, September.
    16. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Merton, Robert, 1990. "Capital market theory and the pricing of financial securities," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 11, pages 497-581, Elsevier.
    2. Haim Levy, 2010. "The CAPM is Alive and Well: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 16(1), pages 43-71, January.
    3. Zabarankin, Michael & Pavlikov, Konstantin & Uryasev, Stan, 2014. "Capital Asset Pricing Model (CAPM) with drawdown measure," European Journal of Operational Research, Elsevier, vol. 234(2), pages 508-517.
    4. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    5. Syed Mohammad Faisal & Ahmad Khalid Khan & Omar Abdullah Al Aboud, 2018. "Estimating Beta (¦Â) Values of Stocks in the Creation of Diversified Portfolio - A Detailed Study," Applied Economics and Finance, Redfame publishing, vol. 5(3), pages 89-99, May.
    6. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    7. Javid, Attiya Yasmin, 2008. "Time Varying Risk Return Relationship: Evidence from Listed Pakistani Firms," MPRA Paper 37561, University Library of Munich, Germany.
    8. J. Christopher Westland, 2017. "An empirical investigation of analytical procedures using mixture distributions," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 24(4), pages 111-124, October.
    9. Rostagno, Luciano Martin, 2005. "Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index," ISU General Staff Papers 2005010108000021878, Iowa State University, Department of Economics.
    10. Zied Ftiti & Aviral Tiwari & Amél Belanès & Khaled Guesmi, 2015. "Tests of Financial Market Contagion: Evolutionary Cospectral Analysis Versus Wavelet Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 575-611, December.
    11. David Morelli, 2002. "The robustness of tests of structural change in equity returns using factor analysis," Applied Economics, Taylor & Francis Journals, vol. 34(2), pages 241-251.
    12. Stefan Lutz, 2012. "Effects of taxation on European multi-nationals’ financing and profits," Economics Discussion Paper Series 1214, Economics, The University of Manchester.
    13. Saggese, Pietro & Belmonte, Alessandro & Dimitri, Nicola & Facchini, Angelo & Böhme, Rainer, 2023. "Arbitrageurs in the Bitcoin ecosystem: Evidence from user-level trading patterns in the Mt. Gox exchange platform," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 251-270.
    14. Jeonggyu Huh, 2018. "Measuring Systematic Risk with Neural Network Factor Model," Papers 1809.04925, arXiv.org.
    15. John G. Cragg & Burton G. Malkiel, 1982. "References, Index," NBER Chapters, in: Expectations and the Structure of Share Prices, pages 167-176, National Bureau of Economic Research, Inc.
    16. Moon K. Kim & Chunchi Wu, 1987. "Macro-Economic Factors And Stock Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(2), pages 87-98, June.
    17. Ali Habibnia & Esfandiar Maasoumi, 2021. "Forecasting in Big Data Environments: An Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 363-381, December.
    18. Miranda Sarmento, J. & Renneboog, L.D.R., 2014. "Public-Private Partnerships : Risk Allocation and Value for Money," Other publications TiSEM b9218010-a357-4c0a-805a-7, Tilburg University, School of Economics and Management.
    19. Jon Poynter & James Winder & Tzu Tai, 2015. "An analysis of co-movements in industrial sector indices over the last 30 years," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 69-88, January.
    20. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2015. "Down-side Risk Metrics as Portfolio Diversification Strategies across the GFC," Documentos de Trabajo del ICAE 2015-19, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2402.10253. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.