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Randomly walking through Wall Street

Author

Listed:
  • Braselton, James
  • Rafter, John
  • Humphrey, Patricia
  • Abell, Martha

Abstract

The daily closing values of the S&P 500 Index from January 1, 1926 through June 11, 1993, a total of 17,610 values, were entered into Mathematica, and the day-to-day percent changes were calculated. Using the Standard Mathematica Package Statistics ‵ContinuousDistributions‵ and the built-in function NonLinearFit, procedures were developed to find the probability distribution that best models these daily changes. Although the log-normal distribution has been used traditionally, we found that a logistic distribution provides the best model, having a coefficient of determination 0.998. Using this model and Mathematica to simulate stock market performance we have found that, although the short-term changes in the stock market can often be explained by world events, longer-term behavior of the market can be modeled with accuracy. Simulations for time periods between 6 months and 10 years show that, although dollar-cost average investing has less volatility, the long-term investor can expect a higher return from a lump-sum investment.

Suggested Citation

  • Braselton, James & Rafter, John & Humphrey, Patricia & Abell, Martha, 1999. "Randomly walking through Wall Street," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(4), pages 297-318.
    • Handle: RePEc:eee:matcom:v:49:y:1999:i:4:p:297-318
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    References listed on IDEAS

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    1. Goldenberg, David H. & Schmidt, Raymond J., 1996. "On Estimating the Expected Rate of Return in Diffusion Price Models with Application to Estimating the Expected Return on the Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(4), pages 605-631, December.
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    Cited by:

    1. Kirkby, J. Lars & Mitra, Sovan & Nguyen, Duy, 2020. "An analysis of dollar cost averaging and market timing investment strategies," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1168-1186.
    2. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.

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