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Portfolio Selection – A Technical Note

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  • Ana Paula Martins

Abstract

This note develops the solutions of the static portfolio optimization problem in explicit matrix form. Three cases are contemplated and connected, with the derivation of relevant corner solutions: the unconstrained problem in the presence of risky assets only, the constrained one, and the presence of a risk-free asset. The use of a generalised form for the budget constraint allows us to use the structure to study the behaviour of a complete borrower – subject or not to liquidity constraints – and infer the price of pure risk. Some properties of the several solutions are highlighted. The rationale for a linear relation between the standard deviation and the expected return of the unitary application in an efficient portfolio is derived. Requirements for useful existence in the market of any given security are established. Additionally, we infer the expected co-movement properties of efficient and the global market – or any other – portfolio.

Suggested Citation

  • Ana Paula Martins, 2012. "Portfolio Selection – A Technical Note," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 55(3), pages 78-99.
  • Handle: RePEc:eei:journl:v:55:y:2012:i:3:p:78-99
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    1. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    2. Tsangyao Chang, 2012. "Nonlinear adjustment to purchasing power parity in China," Applied Economics Letters, Taylor & Francis Journals, vol. 19(9), pages 843-848, June.
    3. Lumengo Bonga-Bonga & Alain Kabundi, 2011. "Monetary Policy Action and Inflation in South Africa: An Empirical Analysis," The African Finance Journal, Africagrowth Institute, vol. 13(2), pages 25-37.
    4. Joseph Kargbo, 2003. "Food prices and long-run purchasing power parity in Africa," Development Southern Africa, Taylor & Francis Journals, vol. 20(3), pages 321-336.
    5. Enders, Walter & Siklos, Pierre L, 2001. "Cointegration and Threshold Adjustment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 166-176, April.
    6. Taylor, Alan M, 2001. "Potential Pitfalls for the Purchasing-Power-Parity Puzzle? Sampling and Specification Biases in Mean-Reversion Tests of the Law of One Price," Econometrica, Econometric Society, vol. 69(2), pages 473-498, March.
    7. Yu‐shao Liu & Chi‐wei Su, 2011. "Purchasing Power Parity With Rank Tests For Nonlinear Cointegration In African Countries," South African Journal of Economics, Economic Society of South Africa, vol. 79(1), pages 17-26, March.
    8. Darby, Michael R., 1981. "Does purchasing power parity work?," Proceedings, Federal Reserve Bank of San Francisco, pages 136-173.
    9. Mark Holmes & Ping Wang, 2006. "Asymmetric adjustment towards long-run PPP: Some new evidence for Asian economies," International Economic Journal, Taylor & Francis Journals, vol. 20(2), pages 161-177.
    10. Chang, Tsangyao & Lee, Chia-Hao & Liu, Wen-Chi, 2012. "Nonlinear adjustment to purchasing power parity for ASEAN countries," Japan and the World Economy, Elsevier, vol. 24(4), pages 325-331.
    11. Frankel, Jeffrey A. & Rose, Andrew K., 1996. "A panel project on purchasing power parity: Mean reversion within and between countries," Journal of International Economics, Elsevier, vol. 40(1-2), pages 209-224, February.
    12. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    13. Alan M. Taylor & Mark P. Taylor, 2004. "The Purchasing Power Parity Debate," Journal of Economic Perspectives, American Economic Association, pages 135-158.
    14. Mohsen Bahmani-Oskooee & Abera Gelan, 2006. "Testing the PPP in the non-linear STAR Framework: Evidence from Africa," Economics Bulletin, AccessEcon, vol. 6(17), pages 1-15.
    15. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    16. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-174, March.
    17. Seref Bozoklu & Sinem Kutlu, 2012. "Linear and Nonlinear Cointegration of Purchasing Power Parity: Further Evidence from Developing Countries," Global Economic Review, Taylor & Francis Journals, vol. 41(2), pages 147-162, June.
    18. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-511, August.
    19. Cheung, Yin-Wong & Lai, Kon S., 1993. "Long-run purchasing power parity during the recent float," Journal of International Economics, Elsevier, vol. 34(1-2), pages 181-192, February.
    20. Schnabl, Gunther & Baur, Dirk, 2002. "Purchasing power parity: Granger causality tests for the yen-dollar exchange rate," Japan and the World Economy, Elsevier, pages 425-444.
    21. Menon, Jayant, 1995. " Exchange Rate Pass-Through," Journal of Economic Surveys, Wiley Blackwell, vol. 9(2), pages 197-231, June.
    22. Azali, M. & Habibullah, M. S. & Baharumshah, A. Z., 2001. "Does PPP hold between Asian and Japanese economies? Evidence using panel unit root and panel cointegration," Japan and the World Economy, Elsevier, vol. 13(1), pages 35-50, January.
    23. Frederic Bec & Melika Ben Salem & Marine Carrasco, 2004. "Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 382-395, October.
    24. Oludele Akinloye Akinboade & Daniel Makina, 2006. "Mean reversion and structural breaks in real exchange rates: South African evidence," Applied Financial Economics, Taylor & Francis Journals, pages 347-358.
    25. Kim, Hyeongwoo & Moh, Young-Kyu, 2010. "A century of purchasing power parity confirmed: The role of nonlinearity," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1398-1405, November.
    26. Brissimis, Sophocles N. & Sideris, Dimitris A. & Voumvaki, Fragiska K., 2005. "Testing long-run purchasing power parity under exchange rate targeting," Journal of International Money and Finance, Elsevier, vol. 24(6), pages 959-981, October.
    27. Liew, Venus Khim-Sen & Ling, Tai-Hu & Chia, Ricky Chee-Jiun & Yoon, Gawon, 2012. "On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea," Economic Modelling, Elsevier, vol. 29(2), pages 326-332.
    28. Andrew Phiri, 2012. "Threshold effects and inflation persistence in South Africa," Journal of Financial Economic Policy, Emerald Group Publishing, vol. 4(3), pages 247-269, July.
    29. Fred S. McChesney & William F. Shughart & David D. Haddock, 2004. "On the Internal Contradictions of the Law of One Price," Economic Inquiry, Western Economic Association International, vol. 42(4), pages 706-716, October.
    30. repec:ebl:ecbull:v:6:y:2006:i:17:p:1-15 is not listed on IDEAS
    31. Siyue Liu & Tsangyao Chang & Chia-Hao Lee & Pei-I Chou, 2012. "Nonlinear adjustment to purchasing power parity: the ADL test for threshold cointegration," Applied Economics Letters, Taylor & Francis Journals, vol. 19(6), pages 569-573, April.
    32. Oh, Keun-Yeob, 1996. "Purchasing power parity and unit root tests using panel data," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 405-418, June.
    33. Shady Kholdy & Ahmad Sohrabian, 1990. "Exchange Rates and Prices: Evidence from Granger Causality Tests," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 13(1), pages 71-78, September.
    34. Baum, Christopher F. & Barkoulas, John T. & Caglayan, Mustafa, 2001. "Nonlinear adjustment to purchasing power parity in the post-Bretton Woods era," Journal of International Money and Finance, Elsevier, vol. 20(3), pages 379-399, June.
    35. Tsangyao Chang & Chia-Hao Lee & Pei-I Chou, 2012. "Nonlinear adjustment to purchasing power parity in G-7 countries," Applied Economics Letters, Taylor & Francis Journals, vol. 19(2), pages 123-128, February.
    36. Nakagawa, Hironobu, 2010. "Investigating nonlinearities in real exchange rate adjustment: Threshold cointegration and the dynamics of exchange rates and relative prices," Journal of International Money and Finance, Elsevier, vol. 29(5), pages 770-790, September.
    37. Guneratne Wickremasinghe, 2009. "Are real exchange rates of Papua New Guinea mean-reverting? Evidence from panel unit root tests," Applied Economics Letters, Taylor & Francis Journals, vol. 16(2), pages 157-161.
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    Cited by:

    1. William H. Greene & Ana P. Martins, 2002. "Striking Features of the Labor Market," EERI Research Paper Series EERI RP 2002/08, Economics and Econometrics Research Institute (EERI), Brussels.
    2. William H. Greene & Ana P. Martins, 2013. "Striking Features of the Labor Market: Empirical Evidence," Journal of Economics and Econometrics, Economics and Econometrics Society, pages 25-53.
    3. William H. Greene & Ana P. Martins, 2013. "Striking Features of the Labor Market: Theory," Journal of Economics and Econometrics, Economics and Econometrics Society, pages 1-24.

    More about this item

    Keywords

    Portfolio Choice; Mean Variance; CAPM; Quadratic Programming; Price of Risk.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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