The Structure of Financial Returns

14 Pages Posted: 5 Jun 2020

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

King Wang

Morgan Stanley

Date Written: December 24, 2019


Financial returns at unit time are modeled as non-Gaussian limit laws. They may reflect random walks or additive processes reflecting some predictability. Mixtures of these two constructions are formulated and estimated on one minute data. It is observed that the random walk fraction is generally below 10%. The results argue against a strict random walk in favor of the presence of a predictable component representing returns as perpetual motion machines responding to past price movements.

Keywords: Bilateral Gamma, CGMY, Sato Process, Random Walk

JEL Classification: G10, G17, G19

Suggested Citation

Madan, Dilip B. and Wang, King, The Structure of Financial Returns (December 24, 2019). Available at SSRN: or

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

King Wang

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

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