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The Perception of Time, Risk and Return During Periods of Speculation

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  • Emanuel Derman

Abstract

What return should you expect when you take on a given amount of risk? How should that return depend upon other people's behavior? What principles can you use to answer these questions? In this paper, we approach these topics by exploring the consequences of two simple hypotheses about risk. The first is a common-sense invariance principle: assets with the same perceived risk must have the same expected return. The second hypothesis concerns the perception of time. We conjecture that in times of speculative excitement, short-term investors may instinctively imagine stock prices to be evolving in a time measure different from that of calendar time. They may instead perceive and experience the risk and return of a stock in intrinsic time, a dimensionless time scale that counts the number of trading opportunities that occur. The most noteworthy result is that, in the short-term, a stock's trading frequency affects its expected return. We show that short-term stock speculators will expect returns proportional to the temperature of a stock, where temperature is defined as the product of the stock's traditional volatility and the square root of its trading frequency. We hope that this model will have some relevance to the behavior of investors expecting inordinate returns in highly speculative markets.

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  • Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/0201345
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    References listed on IDEAS

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    1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    4. Vasiliki Plerou & Parameswaran Gopikrishnan & Luis. A. Nunes Amaral & Xavier Gabaix & H. Eugene Stanley, 1999. "Economic Fluctuations and Diffusion," Papers cond-mat/9912051, arXiv.org.
    5. U. A. Muller & M. M. Dacorogna & R. D. Dave & O. V. Pictet & R. B. Olsen & J.R. Ward, "undated". "Fractals and Intrinsic Time - a Challenge to Econometricians," Working Papers 1993-08-16, Olsen and Associates.
    6. Sam Howison & David Lamper, 2001. "Trading volume in models of financial derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 119-135.
    7. 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.
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    Cited by:

    1. Siddiqi, Hammad, 2014. "Analogy Making and the Structure of Implied Volatility Skew," MPRA Paper 60921, University Library of Munich, Germany.
    2. Dieter Hendricks & Tim Gebbie & Diane Wilcox, 2015. "Detecting intraday financial market states using temporal clustering," Papers 1508.04900, arXiv.org, revised Feb 2017.
    3. Siddiqi, Hammad, 2013. "Mental Accounting: A Closed-Form Alternative to the Black Scholes Model," MPRA Paper 50759, University Library of Munich, Germany.
    4. Siddiqi, Hammad, 2015. "Anchoring Heuristic in Option Pricing," MPRA Paper 63218, University Library of Munich, Germany.
    5. Hervé OTT, 2012. "Fertilizer markets and its interplay with commodity and food prices," JRC Working Papers JRC73043, Joint Research Centre (Seville site).
    6. Zapart, Christopher A., 2009. "On entropy, financial markets and minority games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1157-1172.
    7. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.

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