Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus reverse-engineering attempts. This work is a contribution to the building of a set of stylized facts about the traders themselves. Using the client database of Swissquote Bank SA, the largest on-line Swiss broker, we find empirical relationships between turnover, account values and the number of assets in which a trader is invested. A theory based on simple mean-variance portfolio optimization that crucially includes variable transaction costs is able to reproduce faithfully the observed behaviors. We finally argue that our results bring into light the collective ability of a population to construct a mean-variance portfolio that takes into account the structure of transaction costs
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