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On The Role Of The Growth Optimal Portfolio In Finance

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  • ECKHARD PLATEN

Abstract

The paper discusses various roles that the growth optimal portfolio (GOP) plays in finance. For the case of a continuous market we show how the GOP can be interpreted as a fundamental building block in financial market modeling, portfolio optimisation, contingent claim pricing and risk measurement. On the basis of a portfolio selection theorem, optimal portfolios are derived. These allocate funds into the GOP and the savings account. A risk aversion coefficient is introduced, controlling the amount invested in the savings account, which allows to characterize portfolio strategies that maximise expected utilities. Natural conditions are formulated under which the GOP appears as the market portfolio. A derivation of the intertemporal capital asset pricing model is given without relying on Markovianity, equilibrium arguments or utility functions. Fair contingent claim pricing, with the GOP as numeraire portfolio, is shown to generalise risk neutral and actuarial pricing. Finally, the GOP is described in various ways as the best performing portfolio. Copyright Blackwell Publishing Ltd/University of Adelaide and Flinders University 2005..

Suggested Citation

  • Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
  • Handle: RePEc:bla:ausecp:v:44:y:2005:i:4:p:365-388
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    References listed on IDEAS

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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    4. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Computational Statistics, Springer, vol. 18(3), pages 355-373, September.
    5. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Eckhard Platen, 2004. "Modeling The Volatility And Expected Value Of A Diversified World Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 511-529.
    8. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    9. Fleming, Wendell H. & Stein, Jerome L., 2004. "Stochastic optimal control, international finance and debt," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 979-996, May.
    10. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
    11. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    14. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    15. 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.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    17. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
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    Citations

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    Cited by:

    1. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, january-d.
    2. Rei[ss], Oliver & Schoenmakers, John & Schweizer, Martin, 2007. "From structural assumptions to a link between assets and interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 593-612, February.
    3. Christopoulos, Andreas D., 2017. "The composition of CMBS risk," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 215-239.
    4. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 180, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Liao Wang & Johannes Wissel, 2013. "Mean-variance hedging with oil futures," Finance and Stochastics, Springer, vol. 17(4), pages 641-683, October.
    6. David R. Banos & Giulia Di Nunno & Frank Proske, 2013. "Sensitivity analysis in a market with memory," Papers 1312.5116, arXiv.org, revised Jan 2017.
    7. Stein, Jerome L., 2007. "United States current account deficits: A stochastic optimal control analysis," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1321-1350, May.
    8. repec:wsi:ijtafx:v:13:y:2010:i:06:n:s0219024910006054 is not listed on IDEAS
    9. Baldeaux Jan & Ignatieva Katja & Platen Eckhard, 2014. "A tractable model for indices approximating the growth optimal portfolio," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 1-21, February.
    10. repec:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003360 is not listed on IDEAS
    11. David Heath & Eckhard Platen, 2005. "Currency Derivatives Under A Minimal Market Model With Random Scaling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1157-1177.
    12. Eckhard Platen, 2005. "Investments for the Short and Long Run," Research Paper Series 163, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Pablo Castañeda & Heinz Rudolph, 2010. "Portfolio Choice, Minimum Return Guarantees, and Competition in DC Pension Systems," Working Papers 39, Superintendencia de Pensiones, revised Feb 2010.
    14. Muteba Mwamba, John & Suteni, Mwambi, 2010. "An alternative to portfolio selection problem beyond Markowitz’s: Log Optimal Growth Portfolio," MPRA Paper 50240, University Library of Munich, Germany.
    15. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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