Modeling the Optimal Portfolio: the Case of the Largest European Stock Exchanges

Florin Aliu; Artor Nuhiu; Besnik Krasniqi; Fisnik Aliu

doi:10.18778/1508-2008.23.11

Authors

Florin Aliu Faculty of Economics, University for Business and Technology (UBT)
Artor Nuhiu Faculty of Law, University of Prishtina
Besnik Krasniqi Faculty of Economics, University of Prishtina
Fisnik Aliu Faculty of Computer Science and Engineering, University for Business and Technology (UBT)

DOI:

https://doi.org/10.18778/1508-2008.23.11

Keywords:

Portfolio diversification, stock exchanges, correlation coefficient, volatility

Abstract

Portfolio optimization is the main concern for portfolio managers. Financial securities are placed within the portfolio based on the investor’s risk tolerance. The study measures the risk-reward relationship when the number of stocks in the portfolio increases. Six diverse portfolios have been created with a different number of stocks, such as portfolios with 47 stocks, 95 stocks, 142 stocks, 190 stocks, 239 stocks, and 287 stocks. Stock prices and trading volume were collected on a weekly basis from the six largest European stock exchanges (FTSE100, CAC40, FTSE MIB, IBEX35, DAX, and MDAX). Markowitz’s (1952) diversification formula has been used to measure the risk level of the individual portfolios. The results of the study show that the diversification risk constantly decreases when we move from the portfolios with 47 stocks to the portfolios with 287 stocks. The weighted average returns increase on the portfolios with a higher number of stocks, which is contrary to the standard portfolio theories. The results of the study indicate managerial implications for financial investors that are focused exclusively on the largest European stock exchanges.

Downloads

Download data is not yet available.

References

Abid, F., Leung, P., Mroua, M., Wong, W. (2014), International diversification versus domestic diversification: Mean-variance portfolio optimization and stochastic dominance approaches, “Journal of Risk and Financial Management”, Vol. 7 (2). https://doi.org/10.3390/jrfm7020045
Google Scholar DOI: https://doi.org/10.3390/jrfm7020045

Aliu, F., Krasniki, B., Knapkova, A., Aliu, F. (2019), Interdependence and Risk Comparison of Slovak, Hungarian and Polish Stock Markets: Policy and Managerial Implications, “Acta Oeconomica”, Vol. 69 (2). https://doi.org/10.1556/032.2019.69.2.6
Google Scholar DOI: https://doi.org/10.1556/032.2019.69.2.6

Aliu, F., Pavelkova, D., Dehning, B. (2017), Portfolio risk-return analysis: The case of the automotive industry in the Czech Republic, “Journal of International Studies”, Vol. 10 (4). https://doi.org/10.14254/2071-8330.2017/10-4/5
Google Scholar DOI: https://doi.org/10.14254/2071-8330.2017/10-4/5

Bali, T., Cakici, N., Levy, H. (2008), A model-independent measure of aggregate idiosyncratic risk, “Journal of Empirical Finance”, Vol. 15 (5).
Google Scholar DOI: https://doi.org/10.1016/j.jempfin.2008.02.002

Bartram, S., Taylor, S., Wang, Y. (2007), The Euro and European financial market dependence, “Journal of Banking & Finance”, Vol. 31 (5). https://doi.org/10.1016/j.jbankfin.2006.07.014
Google Scholar DOI: https://doi.org/10.1016/j.jbankfin.2006.07.014

Berrill, J., Kearney, C., O’Hagan-Luff, M. (2019), Measuring the diversification benefits of investing in highly internationalised firms, “International Business Review”, Vol. 28 (4). https://doi.org/10.1016/j.ibusrev.2019.01.005
Google Scholar DOI: https://doi.org/10.1016/j.ibusrev.2019.01.005

Brands, S., Gallagher, D. (2005), Portfolio selection, diversification and fund‐of‐funds: a note, “Accounting & Finance”, Vol. 45 (2). https://doi.org/10.1111/j.1467-629x.2004.00130.x
Google Scholar DOI: https://doi.org/10.1111/j.1467-629x.2004.00130.x

Burzala, M. (2016), Contagion Effects in Selected European Capital Markets During the Financial Crisis of 2007–2009, “Research in International Business and Finance”, Vol. 37 (May). https://doi.org/10.1016/j.ribaf.2016.01.026
Google Scholar DOI: https://doi.org/10.1016/j.ribaf.2016.01.026

Cai, F., Warnock, F. (2012), Foreign exposure through domestic equities, “Finance Research Letters”, Vol. 9 (1). https://doi.org/10.1016/j.frl.2011.12.001
Google Scholar DOI: https://doi.org/10.1016/j.frl.2011.12.001

Christoffersen, P., Errunza, V., Jacobs, K., Langlois, H. (2012), Is the potential for international diversification disappearing? A dynamic copula approaches, “The Review of Financial Studies”, Vol. 25 (12). https://doi.org/10.1093/rfs/hhs104
Google Scholar DOI: https://doi.org/10.1093/rfs/hhs104

Damodaran, A. (2012), Damodaran on valuation: security analysis for investment and corporate finance, John Wiley & Sons, New York. https://doi.org/10.1002/9781119201786
Google Scholar DOI: https://doi.org/10.1002/9781119201786

Driessen, J., Laeven, L. (2007), International portfolio diversification benefits: Cross-country evidence from a local perspective, “Journal of Banking & Finance”, Vol. 31 (6). https://doi.org/10.1016/j.jbankfin.2006.11.006
Google Scholar DOI: https://doi.org/10.1016/j.jbankfin.2006.11.006

Elton, E.J., Gruber, M.J. (1977), Risk reduction and portfolio size: An analytical solution, “The Journal of Business”, Vol. 50 (4). https://doi.org/10.1086/295964
Google Scholar DOI: https://doi.org/10.1086/295964

Errunza, V., Hogan, K., Hung, M.W. (1999), Can the gains from international diversification be achieved without trading abroad?, “The Journal of Finance”, Vol. 54 (6). https://doi.org/10.1111/0022-1082.00182
Google Scholar DOI: https://doi.org/10.1111/0022-1082.00182

Evans, J.L., Archer, S.H. (1968), Diversification and the reduction of dispersion: an empirical analysis, “The Journal of Finance”, Vol. 23 (5). https://doi.org/10.2307/2325905
Google Scholar DOI: https://doi.org/10.2307/2325905

Fama, E.F. (1968), Risk return and equilibrium: some clarifying comments, “The Journal of Finance”, Vol. 23 (1). https://doi.org/10.1111/j.1540-6261.1968.tb02996.x
Google Scholar DOI: https://doi.org/10.1111/j.1540-6261.1968.tb02996.x

Farooqi, J., Huerta, D., Ngo, T. (2015), Should you globally diversify or let the globally diversified firm do it for you?, “The Quarterly Review of Economics and Finance”, Vol. 57. https://doi.org/10.1016/j.qref.2015.02.005
Google Scholar DOI: https://doi.org/10.1016/j.qref.2015.02.005

French, K.R., Poterba, J.M. (1991), Investor diversification and international equity markets, National Bureau of Economic Research, Working Paper No. 3609. https://www.nber.org/papers/w3609.pdf (accessed: 23.01.2019).
Google Scholar DOI: https://doi.org/10.3386/w3609

Gup, B.E. (1983), The Basics of Investing (2nd ed.), Wiley & Sons, New York.
Google Scholar

Kacperczyk, M., Sialm, C., Zheng, L. (2005), On the industry concentration of actively managed equity mutual funds, “The Journal of Finance”, Vol. 60 (4). https://doi.org/10.1111/j.1540-6261.2005.00785.x
Google Scholar DOI: https://doi.org/10.1111/j.1540-6261.2005.00785.x

Kumar, A. (2007), Do the diversification choices of individual investors influence stock returns?, “Journal of Financial Markets”, Vol. 10 (4). https://doi.org/10.1016/j.finmar.2007.06.003
Google Scholar DOI: https://doi.org/10.1016/j.finmar.2007.06.003

Lintner, J. (1965), Security prices, risk, and maximal gains from diversification, “The Journal of Finance”, Vol. 20 (4). https://doi.org/10.2307/2977249
Google Scholar DOI: https://doi.org/10.2307/2977249

Markowitz, H. (1952), Portfolio selection, “The Journal of Finance”, Vol. 7 (1). https://doi.org/10.2307/2975974
Google Scholar DOI: https://doi.org/10.2307/2975974

Meucci, A. (2009), Managing diversification, “Risk”, Bloomberg Education & Quantitative Research and Education Paper, http://ssrn.com/abstract=1358533 (accessed: 30.01.2019).
Google Scholar

Reilly, F.K. (1985), Investment Analysis and Portfolio Management (2nd ed.), Dryden Press, San Francisco.
Google Scholar

Roll, R. (2013), Volatility, correlation, and diversification in a multi‐factor world, “Journal of Portfolio Management”, Vol. 39 (2). https://doi.org/10.3905/jpm.2013.39.2.011
Google Scholar DOI: https://doi.org/10.3905/jpm.2013.39.2.011

Sharpe, W.F. (1964), Capital asset prices: A theory of market equilibrium under conditions of risk, “The Journal of Finance”, Vol. 19 (3). https://doi.org/10.2307/2977928
Google Scholar DOI: https://doi.org/10.2307/2977928

Skintzi, V.D., Refenes, A.P.N. (2005), Implied correlation index: A new measure of diversification, “Journal of Futures Markets: Futures, Options, and Other Derivative Products”, Vol. 25 (2). https://doi.org/10.1002/fut.20137
Google Scholar DOI: https://doi.org/10.1002/fut.20137

Solnik, B.H. (1974), Why not diversify internationally rather than domestically?, “Financial Analysts Journal”, Vol. 30. https://doi.org/10.2469/faj.v30.n4.48
Google Scholar DOI: https://doi.org/10.2469/faj.v30.n4.48

Statman, M. (1987), How many stocks make a diversified portfolio?, “Journal of Financial and Quantitative Analysis”, Vol. 22 (3). https://doi.org/10.2307/2330969
Google Scholar DOI: https://doi.org/10.2307/2330969

Stevenson, R.A., Jennings, E.H. (1984), Fundamentals of Investments (3rd ed.), West Publ. Co., San Francisco.
Google Scholar

Van Nieuwerburgh, S., Veldkamp, L. (2009), Information immobility and the home bias puzzle, “The Journal of Finance”, Vol. 64 (3). https://doi.org/10.1111/j.1540-6261.2009.01462.x
Google Scholar DOI: https://doi.org/10.1111/j.1540-6261.2009.01462.x