Skip to main content
SpringerLink
Log in

Random Walks

  • Chapter
  • First Online:
Financial Market Bubbles and Crashes

  • 1016 Accesses

Abstract

Random walk was an early descriptive phrase and plank in what has come to be called modern portfolio theory. It includes the notions of efficient markets and equilibrium economics. This chapter reviews the subject in detail, not because the theory is necessarily correct and useful, but because it provides a benchmark against which newer and better approaches can be developed. Volatility is a key factor in all bubbles and crashes and an extreme events line based on option volatility is introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Adrian, T., and Rosenberg, J. (2005, 2008). “Stock Returns and Volatility: Pricing the Long-Run and Short-Run Components of Market Risk,” Federal Reserve Bank of New York and Journal of Finance, 63(6)(December).

    Google Scholar 

  • Ané, T., and Geman, H. (2000). “Order Flow, Transaction Clock, and Normality of asset Returns,” Journal of Finance, 55(5)(October).

    Google Scholar 

  • Armitage, S. (2005). The Cost of Capital: Intermediate Theory. New York: Cambridge University Press.

    Book  Google Scholar 

  • Appelbaum, B. (2013). “Economists Clash on Theory, but Will Still Share the Nobel,” New York Times, October 15.

    Google Scholar 

  • Arnott, R. D., Harvey, C. R., Kalesnik, V., and Linnainmaa, J. T. (2021). “Reports of Value’s Death May Be Greatly Exaggerated,” Financial Analysts Journal, 77(1).

    Google Scholar 

  • Asness, C., and Liew, J. (2014). “The Great Divide,” Institutional Investor, March.

    Google Scholar 

  • Bailey, R. E. (2005). The Economics of Financial Markets. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. New York: Springer-Verlag.

    Book  Google Scholar 

  • Baker-Said, S (2008). “Flight of the Black Swan,” Bloomberg Markets, May.

    Google Scholar 

  • Bates, D. S. (1996). “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options,” Review of Financial Studies 9(1)(Spring).

    Google Scholar 

  • Beechey, M., Gruen, D., and Vickery, J. (2000). “The Efficient Market Hypothesis: A Survey,” Research Discussion Paper, 2000–2001. Federal Reserve Bank of Australia.

    Google Scholar 

  • Bernstein, P. L. (2007). Capital Ideas Evolving. Hoboken, NJ.:Wiley.

    Google Scholar 

  • ———. (2005). “Capital Ideas: From the Past to the Future,” Financial Analysts Journal, 61(6) (November/December).

    Google Scholar 

  • ———. (2004). “What’s It All About, Alpha?,” Institutional Investor, May.

    Google Scholar 

  • Black, F. (1986). “Noise.” Journal of Finance, 41(3)(July).

    Google Scholar 

  • Black, F., Jensen, M. C., and Scholes, M. (1972). “The Capital Asset Pricing Model: Some Empirical Tests,” in Jensen, M.C., ed., Studies in the Theory of Capital Markets. New York: Praeger.

    Google Scholar 

  • Bookstaber, R. (2017). The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interation. Princeton, NJ: Princeton University Press.

    Book  Google Scholar 

  • Buchanan, M. (2013). Forecast: What Physics, Meteorology, and the Natural Sciences Can Teach Us About Economics. New York: Bloomsbury.

    Google Scholar 

  • Buiter, W. H. (2009). “The Unfortunate Uselessness of Most ‘State of the Art’ Academic Monetary Economics,” Financial Times, March 3.

    Google Scholar 

  • Burton, J. (1998). “Revisiting the Capital Asset Pricing Model,” Dow Jones Asset Manager. http://www.stanford.edu/~wfsharpe/art/djam/djam.htm.

  • Campbell, J. Y., Lo, A. W., and MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press.

    Book  Google Scholar 

  • Cartea, A., and Karyampas, D. (2009). “The Relationship Between the Volatility of Returns and the Number of Jumps in Financial Markets,” Birkbeck Working Paper 0914, Birkbeck, University of London, available at: http://www.ems.bbk.ac.uk/research/wp/PDF/BWPEF0914.pdf.

  • Chan, L., and Lakonishok, J. (2004). “Value and Growth Investing: Review and Update,” Financial Analysts Journal, 60(1) (January/February).

    Google Scholar 

  • Chen, N., Roll, R., and Ross, S. (1986). “Economic Forces and the Stock Market,” Journal of Business, 59(3)(July).

    Google Scholar 

  • Christensen, B. J., and Prabhala, N. R. (1998). “The Relation Between Implied and Realized Volatility,” Journal of Financial Economics, 50.

    Google Scholar 

  • Chua, D. S., Kritzman, M., and Page, S. (2009). “The Myth of Diversification,” Journal of Portfolio Management, 36(1)(fall).

    Article  Google Scholar 

  • Clement, D. (2007). “Interview with Eugene Fama,” The Region, Federal Reserve Bank of Minneapolis available at: www.minneapolisfed.org/publications_papers/pub_display.cfm?id=1134.

  • Conrad, J., and Kaul, G. (1988). “Time-Variation in Expected Returns,” Journal of Business, 61(4)(October).

    Google Scholar 

  • Cont, R., Potters, M., and Bouchaud, J.-P. (1997). “Scaling in Stock Market Data: Stable Laws and Beyond,” available at: http://arxiv.org/pdf/cond-mat/9705087.pdf.

  • Cooper, G. (2008). The Origin of Financial Crises: Central Banks, Credit Bubbles, and the Efficient Market Fallacy. New York: Vintage paperback; UK: Harriman House.

    Google Scholar 

  • Cootner, P. H. (1962). “Stock Prices: Random vs Systematic Changes,” Industrial Management Review, 3(2).

    Google Scholar 

  • Coval, J.D., Hirshleifer, D. A., and Shumway, T. G. (2002). “Can Individual Investors Beat the Market?,” Harvard NOM Working Paper, No. 02–45. Cambridge, MA: Harvard University,

    Google Scholar 

  • Cunningham, S. R. (1993). “Unit Root Testing: A Critique from Chaos Theory,” Review of Financial Economics, 3(1)(Fall).

    Google Scholar 

  • Cuthbertson, K., and Nitzsche, D. (2004). Quantitative Financial Economics, 2nd ed. West Sussex, UK: Wiley.

    Google Scholar 

  • De Long, J. B., and Becht, M. (1992). “‘Excess Volatility’ and the German Stock Market, 1876–1990,” NBER Working Paper No. 4054, Available at www.j-bradford-delong.net/pdf_files/German_Volatility.pdf.

  • De Long, J. B., and Grossman, R. S. (1993). “’Excess Volatility’ on the London Stock Market, 1870–1990,” Working Paper, Department of Economics, Harvard University. Available at www.j-bradford-delong.net/pdf_files/London_Volatility.pdf.

  • Donnelly, B. (1987). “Efficient-Market Theorists Are Puzzled by Recent Gyrations in Stock Market,” Wall Street Journal, October 23.

    Google Scholar 

  • Dufour, J-M., Garcia, R., and Taamouti, A. (2008). “Measuring Causality Between Volatility and Returns with High-Frequency Data,” Madrid: Universidad Carlos III de Madrid, Working paper 08–44, Series 22.

    Google Scholar 

  • Dugan, I. J. (2009). “Sharpe Point: Risk Gauge Is Misused,” Wall Street Journal, August 31.

    Google Scholar 

  • Dunbar, N. (2000). Inventing Money: The Story of Long-Term Capital Management and the Legends Behind It. West Sussex, Chichester, UK: Wiley.

    Google Scholar 

  • Engle, R. F. (1982). “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation,” Econometrica, 50.

    Google Scholar 

  • Estrada, J. (2005). Finance in a Nutshell. London: Pearson/FT Prentice Hall.

    Google Scholar 

  • Evans, L. L., Jr. (2003). Why the Bubble Burst: US Stock Market Performance Since 1982. Cheltenham, UK. Edward Elgar:

    Google Scholar 

  • Fabozzi, F. J., Focardi, S. M., and Jonas, C. (2014). “Investment Management: A Science to Teach or an Art to Learn?,” Research Foundation Review 2015. CFA Institute Research Foundation at www.CFApubs.org/doi/pdf/10.2470.

  • Fama, E. F. (1991). “Efficient Capital Markets: II,” Journal of Finance, XLVI(5)(December).

    Google Scholar 

  • ———. (1970). “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance, 25(2)(May).

    Google Scholar 

  • Fama, E. F., and French, K. (2015). “A Five-Factor Asset Pricing Model,” Journal of Financial Economics, 116(1)(April).

    Google Scholar 

  • ———. (2008). “Dissecting Anomalies,” Journal of Finance, 63(4)(August)

    Google Scholar 

  • ———. (1996). “Multifactor Explanations of Asset Pricing Anomalies,” Journal of Finance, 51 (1)(March).

    Google Scholar 

  • ———. (1992). “The Cross-Section of Expected Stock Returns,” Journal of Finance, 47(2)(June).

    Google Scholar 

  • Fama, E. F., and Litterman, R. (2012). “An Experienced View on Markets and Investing,” Financial Analysts Journal, 68(6)(November/December).

    Google Scholar 

  • French, K. R., Schwert, G. W., and Stambaugh, R. F. (1987). “Expected Stock Returns and Volatility,” Journal of Financial Economics, 19(September).

    Article  Google Scholar 

  • Fox, J. (2009). The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street. New York: HarperCollins.

    Google Scholar 

  • Fraser-Sampson, G. (2014). The Pillars of Finance: The Misalignment of Finance Theory and Investment Practice. New York: Palgrave Macmillan.

    Book  Google Scholar 

  • Fridson, M. S. (2011). “Another Clue to Volatility,” Financial Analysts Journal, 67(3)(May/June).

    Google Scholar 

  • Friedman, B. M. and Laibson, D. I. (1989). “Economic Implications of Extraordinary Movements in Stock Prices,” Brookings Papers on Economic Activity. Washington, DC: Brookings Institute.

    Google Scholar 

  • Gerow, A., and Keane, M. T. (2012). “Mining the Web for the ‘Voice of the Herd’ to Track Stock Market Bubbles,” available at: http://arxiv.org/abs/1212.2676v1.

  • Gopikrishnan, P., Meyer, M., Amaral, L.A.N., and Stanley, H. E. (1998). “Inverse Cubic Law for the Distribution of Stock Price Variations,” The European Physical Journal, 3.

    Google Scholar 

  • Grantham, J. (2021). “Waiting for the Last Dance,” Seeking Alpha, January 6.

    Google Scholar 

  • Gray, W. R., and Vogel, J. R. (2016). Quantitative Momentum. Hoboken, NJ: Wiley.

    Google Scholar 

  • Greene, M., and Fielitz, B. (1977). “Long-Term Dependence in Common Stock Returns,” Journal of Financial Economics, 4.

    Google Scholar 

  • Greenwald, B. C., Kahn, J., Bellissimo, E., Cooper, M. A., and Santos, T. (2021). Value Investing: From Graham to Bubbett and Beyond, 2nd ed. Hoboken, NJ: Wiley.

    Google Scholar 

  • Greenwald, B. C., Kahn, J., Sonkin, P. D., and van Biema, M. (2001). Value Investing From Graham to Bubbett and Beyond. New York: Wiley.

    Google Scholar 

  • Gulko, L. (2005). “Efficient Irrational markets,” Journal of Portfolio Management, 31(2)(Winter).

    Google Scholar 

  • Hagerman, R. L. (1978). “More Evidence on the Distribution of Security Returns,” Journal of Finance, 33(4)(September).

    Google Scholar 

  • Hall, R. E. (2001). “Struggling to Understand the Stock Market,” American Economic Review, May, 91, No. 2 (May).

    Google Scholar 

  • Hassett, K. A. (2002). Bubbleology: The New Science of Stock Market Winners and Losers. New York: Crown.

    Google Scholar 

  • Haug, E. S., and Taleb, N. N., (2009). “Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula,” (fifth version)(26 February 2009). Available at SSRN: http://ssrn.com/abstract=1012075.

  • Heston, S. L. (1993). “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” Review of Financial Studies 6(2)(Summer).

    Google Scholar 

  • Holton, G. (1992). “Time, The Second Dimension of Risk,” Financial Analysts Journal, November/December.

    Google Scholar 

  • Hunter, W. C., Kaufman, G.G., and Pomerleano, M., eds. (2003). Asset Price Bubbles: The Implications for Monetary, Regulatory, and International Policies. Cambridge, MA: MIT Press. , Paperback edition, 2005.

    Google Scholar 

  • Jacobs, B. I. (2018). Too Smart for Our Own Good. New York: McGraw-Hill.

    Google Scholar 

  • Jensen, M. C. (1978). “Some Anomalous Evidence Regarding Market Efficiency,” Journal of Financial Economics, 6(2–3)(June–September).

    Google Scholar 

  • ———. (1972). Studies in the Theory of Capital Markets. New York: Praeger.

    Google Scholar 

  • ———. (1968). “The Performance of Mutual Funds in the Period 1945–1964,” Journal of Finance, 23(2)(May).

    Google Scholar 

  • Jovanovic, F., and Schinckus, C. (2017). Econophysics and Financial Economics: An Emerging Dialog. New York. Oxford University Press.

    Book  Google Scholar 

  • Kaizoji, T., and Sornette, D. (2008). “Market Bubbles and Crashes,” MPRA Paper 15204, University Library Munich, Germany and available at: http://arxiv.org/pdf/0812.2449.

  • Kay, J., and King, M. (2020). Radical Uncertainty: Decision-Making Beyond the Numbers. New York: W. W. Norton.

    Google Scholar 

  • Kim, C-J., Morley, J. C., and Nelson, C. R. (2004). “Is There a Positive Relationship Between Stock Market Volatility and the Equity Premium?,” Journal of Money, Credit and Banking, 36(3)(June).

    Google Scholar 

  • Kleidon, A. W. (1986). “Variance Bounds Tests and Stock Price Valuation Models,” Journal of Political Economy, 94 (October).

    Google Scholar 

  • Kritzman, M., and Rich, D. (2002). “The Mismeasurement of Risk,” Financial Analysts Journal, 58(3)(May/June).

    Google Scholar 

  • LeRoy, S. F., and Parke, W. R. (1992). “Stock Price Volatility: Tests Based on the Geometric Random Walk,” American Economic Review, 82 (September).

    Google Scholar 

  • Lintner, J. (1965). “The Valuation of Risk Assets and the Selection of Risk Investments in Stock Portfolios and Capital Budgets,” Review of Economic Statistics, 47.

    Google Scholar 

  • Liu, Y., Gopikrishnan, P., Cizeau, P., Meyer, M., Peng, C. K., and Sltanley, H. E. (1999). “Statistical Properties of the Volatility of Price Fluctuations,” Physical Review E (60).

    Google Scholar 

  • Lo, A. W. (2017). Adaptive Markets: Financial Evolution at the Speed of Thought. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • ———. (2012). “Adaptive Markets and the New World Order,” Financial Analysts Journal, 68(2)(March/April).

    Google Scholar 

  • ———. (2004). “The Adaptive Markets Hypothesis,” Journal of Portfolio Management, 30(5).

    Google Scholar 

  • ———. (1991). “Long-Term Memory in Stock Market Prices,” Econometrica, 59.

    Google Scholar 

  • Lo, A. W., and MacKinlay, A. C. (1999). A Non-Random Walk Down Wall Street. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Lo, A. W., and Merton, R. C. (2009). “Preface to the Annual Review of Financial Economics,” Annual Review of Financial Economics, vol. 1. Palo Alto, CA: Annual Reviews.

    Google Scholar 

  • Lobato, I. N., and Savin, N. E. (1998). “Real and Spurious Long Memory Properties of Stock Market Data,” The Journal of Business and Economic Statistics, 16 (July).

    Google Scholar 

  • Lorie, J. H., and Hamilton, M. T. (1973). The Stock Market: Theories and Evidence. Homewood, IL: Richard D. Irwin.

    Google Scholar 

  • Lowenstein, R. (2000). When Genius Failed: The Rise and Fall of Long-Term Capital Management. New York: Random House.

    Google Scholar 

  • Mackintosh, J. (2019). “Out-of-Fashion Style Retains Value,” Wall Street Journal, March 18.

    Google Scholar 

  • ———. (2018). “A Historical Tie Breaks, but Trouble Still Lurks,” Wall Street Journal, February 9.

    Google Scholar 

  • Malkiel, B. G. (1999). A Random Walk Down Wall Street, 7th ed., 8th ed. (2003), 9th ed. (2007, 11th ed. (2015). New York: W.W. Norton

    Google Scholar 

  • Mallaby, S. (2010). More Money Than God: Hedge Funds and the Making of a New Elite. New York, Penguin/Random House.

    Google Scholar 

  • Mandelbrot, B. (1972). “Statistical Methodology for Non-periodic Cycles: From Covariance to R/S Analysis,” Annals of Economic and Social Measurement, 1.

    Google Scholar 

  • Mandelbrot, B., and Hudson, R. L. (2004). The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books.

    Google Scholar 

  • Mantegna, R. N. (1991). “Lévy Walks and Enhanced Diffusion in Milan Stock Exchange,” Physica A, 179 (2).

    Google Scholar 

  • Mantegna, R. N., and Stanley, H. E. (2000). An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Markowitz, H. M. (1952). “Portfolio Selection,” Journal of Finance, 7.

    Google Scholar 

  • Marks, H. (2018). Mastering the Market Cycle: Getting the Odds on Your Side. Boston: Houghton Mifflin Harcourt.

    Google Scholar 

  • Mauboussin, M. J. (2006). More Than You Know: Finding Financial Wisdom in Unconventional Places. New York: Columbia University Press.

    Google Scholar 

  • Mehrling, P. (2005). Fischer Black and the Revolutionary Idea of Finance. Hoboken, NJ: Wiley.

    Google Scholar 

  • Merton, R. C. (1992). Continuous-Time Finance, rev. ed. Oxford, UK: Blackwell.

    Google Scholar 

  • Mills, T. C. (1993). The Econometric Modelling of Financial Time Series. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Modigliani, F., and Pogue, G. A. (1974). “An Introduction to Risk and Return,” Financial Analysts Journal, 30(2)(March/April).

    Google Scholar 

  • Montier, J. (2002). Behavioural Finance: Insights into Irrational Minds and Markets. Chichester, UK and Hoboken, NJ: Wiley.

    Google Scholar 

  • Mossin, J. (1966). “Equilibrium in a Capital Asset Market,” Econometrica, 34.

    Google Scholar 

  • Munk, C. (2013). Financial Asset Pricing Theory. Oxford, UK: Oxford University Press.

    Book  Google Scholar 

  • Orlowski, L. T. (2012). “Financial Crisis and Extreme Market Risks: Evidence from Europe,” Review of Financial Economics, 21(3)(September).

    Google Scholar 

  • Penman, S., and Reggiani, F. (2018). “Fundamentals of Value versus Growth Investing and an Explanation for the Value Trap.” Financial Analysts Journal, 74(4)(Fourth Quarter).

    Google Scholar 

  • Peters, E. E. (1996). Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility, 2nd ed. New York: Wiley.

    Google Scholar 

  • ———. (1994). Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. New York: Wiley.

    Google Scholar 

  • ———. (1991). “A Chaotic Attractor for the S&P 500,” Financial Analysts Journal, 47(2)(March/April).

    Google Scholar 

  • ———. (1989). “Fractal Structure in the Capital Markets,” Financial Analysts Journal, 45(4)(July/August).

    Google Scholar 

  • Poterba, J., and Summers, L. H. (1988). “Mean Reversion in Stock Returns: Evidence and Implications,” Journal of Financial Economics, 22(1)(October).

    Google Scholar 

  • ———. (1986). “The Persistence of Volatility and Stock Market Fluctuations,” American Economic Review, 76.

    Google Scholar 

  • Prechter, R. R, Jr. (2016). The Socionomic Theory of Finance. Gainsville, GA: Socionomics Institute Press.

    Google Scholar 

  • Radner, R. (1968). “Competitive Equilibrium Under Uncertainty,” Econometrica, 36(1)(January).

    Google Scholar 

  • Rahman, A., and Saadi, S. (2008). “Random Walk and Breaking Trend in Financial Series: An Econometric Critique of Unit Root Tests,” Review of Financial Economics, 17(3)(August).

    Google Scholar 

  • Redleaf, A., and Vigilante, R. (2010). Panic: The Betrayal of Capitalism by Wall Street and Washington. Minnepolis, MN: Richard Vigilante Books.

    Google Scholar 

  • Ridley, M. (1993). “Frontiers of Finance: On the Edge,” The Economist, October 9.

    Google Scholar 

  • Rockel, N. (2010). “Evolutionary Road: The Enduring Popularity of MPT Hasn’t Stopped Practitioners from Trying to Improve It,” Institutional Investor, May.

    Google Scholar 

  • Ross, S. M. (2003). An Elementary Introduction to Mathematical Finance, Options and Other Topics, 2nd ed. New York and Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • ———. (1976). “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, 13.

    Google Scholar 

  • Scalas, E., and Kim, K. (2006). “The Art of Fitting financial Time Series with Lévy Stable Distributions,” MPRA Paper No. 336 available at: http://mpra.ub.uni-muenchen.de/336/.

  • Schwert, G. W. (1989). “Business Cycles, Financial Crises, and Stock Volatility,” Working Paper No. 2957, NBER (May).

    Google Scholar 

  • Segal, J. (2013). “Is Alpha Dead?,” Institutional Investor, September.

    Google Scholar 

  • Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 19.

    Google Scholar 

  • Shiller, R. J. (2000, 2005, 2015). Irrational Exuberance. Princeton, NJ: Princeton University Press 3rd ed, 2015.

    Google Scholar 

  • ———. (1992). Market Volatility. Cambridge, MA: MIT Press.

    Google Scholar 

  • Shleifer, A. (2000). Inefficient Markets: An Introduction to Behavioral Finance. Oxford, UK: Oxford University Press.

    Book  Google Scholar 

  • Silver, N. (2012). The Signal and the Noise: Why So Many Predictions Fail -- but Some Don’t. New York: Penguin.

    Google Scholar 

  • Skidelsky, R. (2009). Keynes: The Return of the Master. New York: Public Affairs (Perseus).

    Google Scholar 

  • Smant, D. J. C. (2003). “The Variance-Bound Fallacy,” Rotterdam: Erasmus University, Rotterdam School of Economics. Available at www.few.eur.nl/few/people/smant.

  • Sommer, J. (2013). “Eugene Fama, King of Predictable Markets,” New York Times, October 27.

    Google Scholar 

  • Statman, M. (1995). “Behavioral Financie versus Standard Finance,” in Behavioral Finance and Decision Theory in Investment Management. Charlottesville, VA: Association for Investment Management and Research.

    Google Scholar 

  • Strasburg, J., and Pulliam, S. (2011). “Hedge Funds’ Pack Behavior Magnifies Swings in Market,” Wall Street Journal, January 14.

    Google Scholar 

  • Summers, L. H. (1986). “Does the Stock Market Rationally Reflect Fundamental Values?,” Journal of Finance, 41(3).

    Google Scholar 

  • Taylor, J. B. (2010). “The Fed and the Crisis: A Reply to Ben Bernanke,” Wall Street Journal, January 11.

    Google Scholar 

  • Taylor, S. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Thaler, R., H. (2016). “Behavioral Economics: Past, Present, and Future,” American Economic Review, 106(7)(July).

    Google Scholar 

  • ———. (2015). Misbehaving: The Making of Behavioral Economics. New York: W.W. Norton.

    Google Scholar 

  • Tobin, J. (1958). “Liquidity Preference as Behavior Toward Risk,” Review of Economic Studies, 67(February).

    Google Scholar 

  • Todorov, V. (2010). “Variance Risk Premium Dynamics: The Role of Jumps,” Review of Financial Studies, 23(1).

    Google Scholar 

  • Todorov, V., and Tauchen, G. (2010). “Volatility Jumps,” Working Paper, Northwestern University, Kellogg School of Management, Evanston, IL.

    Google Scholar 

  • Tooze, A. (2018). Crashed: How a Decade of Financial Crises Changed the World. New York: Viking.

    Google Scholar 

  • Treynor, J. L. (1965). “How to Rate Management of Investment Funds,” Harvard Business Review, 43(January/February).

    Google Scholar 

  • Triana, P. (2009). Lecturing Birds on Flying: Can Mathematical Theories Destroy the Financial Markets? Hoboken, NJ:Wiley

    Google Scholar 

  • Tsay, R. (2005). Analysis of Financial Time Series, 2nd ed. Hoboken, NJ: Wiley.

    Book  Google Scholar 

  • Turner, A. L., and Weigel, E.J. (1990). “An Analysis of Stock Market Volatility,” Russell Research Commentaries. Tacoma, WA: Frank Russell Company.

    Google Scholar 

  • Vandewalle, N., Ausloos, M., Boveroux, P., and Minguet, A. (1999). “Visualizing the Log-Periodic Pattern Before Crashes,” European Physical Journal B, 9(2)(May).

    Article  Google Scholar 

  • Vogel, H. L., and Werner, R. A. (2015). “An Analytical Review of Volatility Metrics for Bubbles and Crashes,” International Review of Financial Analysis, 38 (March).

    Google Scholar 

  • Wallace, C. (2010). “Mind Over Markets,” Institutional Investor, May.

    Google Scholar 

  • Weatherall, J. O. (2013). The Physics of Wall Street: A Brief Histoty of Predicting the Unpredictable. Boston: Houghton Mifflin Harcourt.

    Google Scholar 

  • Willoughby, J. (2010). “Did Investors Learn Anything from 2008’s Crash?,” Barron’s, July 26.

    Google Scholar 

  • Wilmott, P., and Orrell, D. (2017). The Money Formula: Dodgy Finance, Psuedo Science, and How Mathematicians Took Over the Markets. Hoboken, NJ: Wiley.

    Book  Google Scholar 

  • Zweig, J. (2018). “Patience Is a Virtue for the Value Investor,” Wall Street Journal, April 28.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. New York, NY, USA

    Harold L. Vogel

Authors
  1. Harold L. Vogel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vogel, H.L. (2021). Random Walks. In: Financial Market Bubbles and Crashes. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-79182-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-79182-7_6

  • Published:

  • Publisher Name: Palgrave Macmillan, Cham

  • Print ISBN: 978-3-030-79181-0

  • Online ISBN: 978-3-030-79182-7

  • eBook Packages: Economics and FinanceEconomics and Finance (R0)

Publish with us

Policies and ethics

Search

Navigation