The Market-Based Statistics of 'Actual' Returns of Investors

The paper presents the unified theoretical description of three levels of the market-based statistical moments of “actual” returns, which Investors gain within their market sales. The market-based statistics of “actual” returns takes into account the size of the trade sale values, purchased values and volumes of stocks and that differs it from conventional regular statistics based on frequency analysis of returns time-series. We start with description of statistical moments of returns, which Investor gains via a single sale due to his multiple purchases in the past. The second level describes statistics of returns, which Investor gains performing numerous market sales during the “trading day”. The third level describes statistics of returns that different Investors gain during the “trading day”. We derive dependence of statistical moments of returns on statistical moments of market sale values, purchased values and volumes of stocks. In its turn, statistical moments of trade values and volumes for finite number of market trades during the “trading day” are assessed via regular frequency-based probability