Trade Volumes

Market-Based Variance of Market Portfolio and of Entire Market ArXiv ID: 2510.13790 “View on arXiv” Authors: Victor Olkhov Abstract We present the unified market-based description of returns and variances of the trades with shares of a particular security, of the trades with shares of all securities in the market, and of the trades with the market portfolio. We consider the investor who doesn’t trade the shares of his portfolio he collected at time t0 in the past. The investor observes the time series of the current trades with all securities made in the market during the averaging interval. The investor may convert these time series into the time series that model the trades with all securities as the trades with a single security and into the time series that model the trades with the market portfolio as the trades with a single security. That establishes the same description of the returns and variances of the trades with a single security, the trades with all securities in the market, and the market portfolio. We show that the market-based variance, which accounts for the impact of random change of the volumes of consecutive trades with securities, takes the form of Markowitz’s (1952) portfolio variance if the volumes of consecutive trades with all market securities are assumed constant. That highlights that Markowitz’s (1952) variance ignores the effects of random volumes of consecutive trades. We compare the market-based variances of the market portfolio and of the trades with all market securities, consider the importance of the duration of the averaging interval, and explain the economic obstacles that limit the accuracy of the predictions of the returns and variances at best by Gaussian distributions. The same methods describe the returns and variances of any portfolio and the trades with its securities. ...

Expressions of Market-Based Correlations Between Prices and Returns of Two Assets ArXiv ID: 2412.13172 “View on arXiv” Authors: Unknown Abstract This paper derives the expressions of correlations between prices of two assets, returns of two assets, and price-return correlations of two assets that depend on statistical moments and correlations of the current values, past values, and volumes of their market trades. The usual frequency-based expressions of correlations of time series of prices and returns describe a partial case of our model when all trade volumes and past trade values are constant. Such an assumptions are rather far from market reality, and its use results in excess losses and wrong forecasts. Traders, banks, and funds that perform multi-million market transactions or manage billion-valued portfolios should consider the impact of large trade volumes on market prices and returns. The use of the market-based correlations of prices and returns of two assets is mandatory for them. The development of macroeconomic models and market forecasts like those being created by BlackRock’s Aladdin, JP Morgan, and the U.S. Fed., is impossible without the use of market-based correlations of prices and returns of two assets. ...