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

  • Emanuel Derman
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    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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    File URL: http://arxiv.org/pdf/cond-mat/0201345
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    Paper provided by arXiv.org in its series Papers with number cond-mat/0201345.

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    Date of creation: Jan 2002
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    Handle: RePEc:arx:papers:cond-mat/0201345
    Contact details of provider: Web page: http://arxiv.org/

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    1. 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 637-54, May-June.
    2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
    3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    4. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    5. Sam Howison & David Lamper, 2001. "Trading volume in models of financial derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 119-135.
    6. Vasiliki Plerou & Parameswaran Gopikrishnan & Luis. A. Nunes Amaral & Xavier Gabaix & H. Eugene Stanley, 1999. "Economic Fluctuations and Diffusion," Papers cond-mat/9912051, arXiv.org.
    7. U. A. Muller & M. M. Dacorogna & R. D. Dave & O. V. Pictet & R. B. Olsen & J.R. Ward, . "Fractals and Intrinsic Time - a Challenge to Econometricians," Working Papers 1993-08-16, Olsen and Associates.
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