In order to maximize their utility function, investors select some assets over others by choosing the ideal portfolio that will maximize their wealth. Each asset is chosen taking into account the relationship between the risk of that particular investment (usually measured by variance)- and the return it can offer, as well as the risk between this and other assets (as measured by covariance).
The purpose of this work was to build an optimal portfolio using data on PSI-20's stock prices (2008-2016) where investors are aware of risk and want to minimize it. For this purpose, an optimal portfolio’s comparison in the period between 2004-2007 was conducted. This period was referred to as the financial pre-crisis, compared to the optimal portfolio obtained in the period after the financial crisis (2008-2016).
The methodology used to estimate the expected profitability of each asset that makes up the PSI-20 was obtained by extracting the historical quotations from the Euronext Lisbon website. The Elton & Gruber model was used in order to determine the optimal portfolio, as well as the assets that should be part of it.
In the period after the financial crisis, it can be verified in the optimal portfolio’s composition that, in the periods after the financial crisis and the financial crisis, there were no stocks to be included in the optimal portfolio, and an analysis in smaller periods was made. In the post financial crisis period actions were found with an attractiveness index superior to the cut-off point, which would lead them to be included in the optimal portfolio, and it was verified that the large distribution sector with (32.15%) has the greatest weight in the optimal portfolio, considering also the Oil and Gas (19.95%), Banking (11.84%) and Production (8.09%) sectors. While addressing shorter periods in pre financial crisis period, no asset was included in the optimal portfolio’s constitution.
AHARONI, G., GRUNDY, B., ZENG, Q, (2013), Stock returns and the Miller Modigliani valuation formula: Revisiting the Fama French analysis. Unpublished working paper. University of Melbourne.
CHAN, L. K. C., HAMAO, Y., LAKONISHOK, J. (1991), Fundamentals and stock returns in Japan. Journal of Finance 46, pp. 1739–1764.
CHORDIA, T., GOYAL, A., SHANKEN, J. (2015). Cross-sectional asset pricing with individual stocks: Betas versus characteristics.
ELTON, E. J., GRUBER, M. J., PADBERG, M. W. (1976), Simple Criteria for Optimal Portofolio Selection. Journal of Finance, XI, number. 5 Dec.
ELTON, E. J., GRUBER, M. J., (1995), Modern Portfolio Theory and Investment Analysis, 5th ed. New York: John Wiley & Sons, Inc.
ELTON, E. J., GRUBER, M. J., BROWN, S. J., GOETZMANN, W. N. (2011), Modern Portfolio Theory and Investment Analysis, 8th ed. Asia: John Wiley & Sons, Inc,
FAMA, E. F., FRENCH, K. R. (1993), Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics, Vol. 33 (1), pp. 3-56.
FAMA, E. F., FRENCH, K. (1998), Value versus growth: the international evidence. Journal of Finance 53, pp. 1975–1999.
FAMA, E. F., FRENCH, K. (2012), Size, value, and momentum in international stock returns. Journal of Financial Economics 105, pp. 457–472.
FAMA, E. F., FRENCH, K. R. (2015), A Five-factor asset pricing model, Journal of Financial Economics 116, pp. 1-22;
FAMA, E., FRENCH, K. (2016), Dissecting anomalies with a five-factor model. Review of Financial Studies 29, 70–103.
FERNANDES, C. e MARTINS, A. (2003), A Teoria Financeira Tradicional e a Psicologia dos Investidores: Uma síntese, Boletim de Ciências Económicas, vol. XLVI, pp. 201-292.
GRIFFIN, J. (2002), Are the Fama and French factors global or country specific? Review of Financial Studies 15, pp. 783–803.
HOU, K., KAROLYI, G., KHO, B. (2011), What factors drive global stock returns? Review of Financial Studies 24, pp. 2527–2574.
LINTNER, J. (1965), The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, Review of Economics and Statistics, 47:1, pp. 13-37.
MARKOWITZ, H. (1952), Portfolio Selection. The Journal of Finance, Vol. 7, No. 1, pp. 77-91.
MARKOWITZ, H. (1959), Portfolio Selection. Efficient Diversification of Investments. Yale University Press, New Haven.
MOSSIN, J. (1966), Equilibrium in a Capital Asset Market, Econometrica, 34, pp. 768-783.
NEVES, M. E., QUELHAS, A. P. (2013), Carteiras de Investimento: Gestão e Avaliação do Desempenho. Almedina, Coimbra.
NOVY-MARX, R. (2013), The other side of value: The gross profitability premium. Journal of Financial Economics, vol. 108, pp. 1-28.
PINHO, C., MELO, A. (2017), The financial crisis impact on the composition of an optimal portfolio on in the stock market – study applyied to Portuguese index PSI-20. International Journal of Business and Social Science, Vol. 8 (10), pp. 38-47.
REILLY, F. Y., NORTON, E. A. (2008), Investimentos. 7ª ed. São Paulo: Cengage Learning, pp 181.
SAMANEZ, C. P. (2006), Gestão de Investimentos e Geração de Valor. Pearson - Prentice Hall. São Paulo.
SHARPE, W. F. (1963), A simplified model for portfolio analysis. Management Science, pp. 277-293.
SHARPE, W. F. (1964), Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk, The Journal of Finance, Vol. 19 (3), pp. 425-442.
SUN, L., WEI, C., XIE, F. (2013), On explanations for the gross profitability effect: insights from international equity markets. Manuscript. Hong Kong University of Science and Technology.
TITMAN, S., WEI, C., Xie, F. (2013), Market development and the asset growth effect: international evidence. Journal of Financial and Quantitative Analysis 48, pp. 1405–1432.
TOSTA DE SÁ, G. (1999), Administração de Investimentos: Teoria de Carteiras e Gerenciamento do Risco. Rio de Janeiro: Qualitymark Ed. pp 376.
WATANBE, A., YU, Y., YAO, T., YU, T. (2013), The asset growth effect: insights from international equity markets. Journal of Financial Economics 108, pp. 529–563.