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# Optimal Investment Horizons

## Author

Listed:
• Ingve Simonsen
• Mogens H. Jensen
• Anders Johansen

## 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.

## Suggested Citation

• Ingve Simonsen & Mogens H. Jensen & Anders Johansen, 2002. "Optimal Investment Horizons," Papers cond-mat/0202352, arXiv.org.
• Handle: RePEc:arx:papers:cond-mat/0202352
as

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

## References listed on IDEAS

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1. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
2. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
3. 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.
4. A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 1(2), pages 141-143, January.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. 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.
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. T. Bisig & A. Dupuis & V. Impagliazzo & R. B. Olsen, 2012. "The scale of market quakes," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 501-508, July.
4. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo & Rosario Mantegna, 2009. "Diffusive behavior and the modeling of characteristic times in limit order executions," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 547-563.
5. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
6. 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.
7. Kei Katahira & Yu Chen & Gaku Hashimoto & Hiroshi Okuda, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Papers 1902.02040, arXiv.org.
8. Johannes Vitalis Siven & Jeffrey Todd Lins, 2009. "Temporal structure and gain/loss asymmetry for real and artificial stock indices," Papers 0907.0554, arXiv.org.
9. Zhou, Wei-Xing & Yuan, Wei-Kang, 2005. "Inverse statistics in stock markets: Universality and idiosyncracy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 433-444.
10. Ingve Simonsen & Anders Johansen & Mogens H. Jensen, 2005. "Investment horizons : A time-dependent measure of asset performance," Papers physics/0504150, arXiv.org.
11. Niu, Hongli & Wang, Jun & Lu, Yunfan, 2016. "Fluctuation behaviors of financial return volatility duration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 30-40.
12. Katahira, Kei & Chen, Yu & Hashimoto, Gaku & Okuda, Hiroshi, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 503-518.
13. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.
14. 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.

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