Can Turnover Go to Zero?

Journal of Derivatives & Hedge Funds 20(3) (2014) 157-176

28 Pages Posted: 1 Jun 2014 Last revised: 8 Jan 2015

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Date Written: July 14, 2014


Internal crossing of trades between multiple alpha streams results in portfolio turnover reduction. Turnover reduction can be modeled using the correlation structure of the alpha streams. As more and more alphas are added, generally turnover reduces. In this note we use a factor model approach to address the question of whether the turnover goes to zero or a finite limit as the number of alphas N goes to infinity. We argue that the limiting turnover value is determined by the number of alpha clusters F, not the number of alphas N. This limiting value behaves according to the "power law" ~ F^(-3/2). So, to achieve zero limiting turnover, the number of alpha clusters must go to infinity along with the number of alphas. We further argue on general grounds that, if the number of underlying tradable instruments is finite, then the turnover cannot go to zero, which implies that the number of alpha clusters also appears to be finite.

Keywords: hedge fund, alpha stream, crossing trades, portfolio turnover, factor model, correlation structure, large N limit, transaction costs

JEL Classification: G00

Suggested Citation

Kakushadze, Zura, Can Turnover Go to Zero? (July 14, 2014). Journal of Derivatives & Hedge Funds 20(3) (2014) 157-176, Available at SSRN: or

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

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Stamford, CT 06901
United States
6462210440 (Phone)
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Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159

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