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Dynamics of a Well-Diversified Equity Index

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Abstract

The paper derives a parsimonious model for the long-term dynamics of a well-diversified stock index, the S&P500. The index is modeled as growth optimal portfolio. Its normalized value evolves, in some market time, as a square root process. The derivative of market time is a linear function of the squared derivative of a smoothed proxy of the single driving Brownian motion. The model explains the feedback effects from index moves typically observed for monthly and daily S&P500 values. It is highly tractable, permits almost exact simulation and leads beyond classical assumptions in finance.

Suggested Citation

  • Eckhard Platen & Renata Rendek, 2019. "Dynamics of a Well-Diversified Equity Index," Research Paper Series 398, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:398
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    More about this item

    Keywords

    long-term index model; growth optimal portfolio; square root process; market time; leverage effect puzzle; benchmark approach;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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