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Optimal Investment Horizons

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Author Info

  • Ingve Simonsen
  • Mogens H. Jensen
  • Anders Johansen
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    Abstract

    In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established that the distribution of returns exhibits ``fat tails'' indicating that large returns occur more frequently than what is expected from standard Gaussian stochastic processes (Mandelbrot-1967,Stanley1,Doyne). Instead of estimating this ``fat tail'' distribution of returns, we propose here an alternative approach, which is outlined by addressing the following question: What is the smallest time interval needed for an asset to cross a fixed return level of say 10%? For a particular asset, we refer to this time as the {\it investment horizon} and the corresponding distribution as the {\it investment horizon distribution}. This latter distribution complements that of returns and provides new and possibly crucial information for portfolio design and risk-management, as well as for pricing of more exotic options. By considering historical financial data, exemplified by the Dow Jones Industrial Average, we obtain a novel set of probability distributions for the investment horizons which can be used to estimate the optimal investment horizon for a stock or a future contract.

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    File URL: http://arxiv.org/pdf/cond-mat/0202352
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0202352.

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    Date of creation: Feb 2002
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    Publication status: Published in Eur. Phys. J. B 27, 583, (2002).
    Handle: RePEc:arx:papers:cond-mat/0202352

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    Web page: http://arxiv.org/

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 1(2), pages 141-143, January.
    2. Maslov, Sergei & Zhang, Yi-Cheng, 1999. "Probability distribution of drawdowns in risky investments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 232-241.
    3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    4. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
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    Cited by:
    1. Johannes Vitalis Siven & Jeffrey Todd Lins, 2009. "Temporal structure and gain/loss asymmetry for real and artificial stock indices," Papers 0907.0554, arXiv.org.
    2. Johannes Vitalis Siven & Jeffrey Todd Lins & Jonas Lundbek Hansen, 2008. "A multiscale view on inverse statistics and gain/loss asymmetry in financial time series," Papers 0811.3122, arXiv.org.
    3. Zou, Yongjie & Li, Honggang, 2014. "Time spans between price maxima and price minima in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 303-309.
    4. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.
    5. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
    6. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    7. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    8. Ingve Simonsen & Anders Johansen & Mogens H. Jensen, 2005. "Investment horizons : A time-dependent measure of asset performance," Papers physics/0504150, arXiv.org.

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