# Optimal Investment Horizons

## Author Info

Listed author(s):
• Ingve Simonsen
• Mogens H. Jensen
• Anders Johansen
Registered author(s):

## 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

## Bibliographic Info

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

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 Length: Date of creation: Feb 2002 Publication status: Published in Eur. Phys. J. B 27, 583, (2002). Handle: RePEc:arx:papers:cond-mat/0202352 Contact details of provider: Web page: http://arxiv.org/

## References

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1. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
2. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
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.
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