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The Market-Based Statistics of “Actual” Returns of Investors

Olkhov, Victor (2023): The Market-Based Statistics of “Actual” Returns of Investors.

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Abstract

We describe three successive approximations of market-based statistical moments of “actual” return that investors gain within their market trade sales. We derive how the market-based statistical moments of “actual” return depend on the statistical moments of the sale values, the purchase values, and the trade volumes of stocks. That differs from the conventional assessments of returns’ statistical moments based on the frequency analysis of the time series of investors’ returns. We start with the statistical moments of return that investors gain from a single trade sale after making multiple purchases in the past. Then we describe the statistical moments of return that an investor gains from numerous trade sales during the “trading day.” Finally, we introduce the trading day portfolio composed of stocks, which were sold by all investors during the “trading day”. We derive the statistical moments of return of the trading day portfolio and the statistical moments of average returns of different investors. That describes the distribution of the “actual” profitability of market trade over all “selling” investors during the “trading day” and can serve as a benchmark for “purchasing” investors.

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