Dynamics of a Well-Diversified Equity Index

Eckhard Platen () and Renata Rendek

No 398, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: long-term index model; growth optimal portfolio; square root process; market time; leverage effect puzzle; benchmark approach (search for similar items in EconPapers)
JEL-codes: C10 C15 G10 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2019-01-01
New Economics Papers: this item is included in nep-rmg
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