What is the definition of price pressure and what does it imply? In a number of paper I read that the price pressure can influence the portfolio returns; can you explain why and in which way it can do that?
If you want to learn more about price pressure, you should look after market impact of metaorders, which is a more adequate term.
Because of the microstructure (i.e. the mix of orderbboks dynamics, trading rules, participants behaviours and habits, etc), the more you buy or sell, the more you influence the price an unfavorable way (for your trades).
In Market Microstructure in Practice, we provide a picture of empirical market impact measured on more than 300000 metaorders (during at least 4 hours each):
The y-axis is the price move (expressed in a generic unit). Before 100%, note the concavity of the impact on price, after 100% of the metaorder, you can see the relaxation.
More recently a new paper provided more insight of price impact, splitting price moves between impact and investor's predictions (i.e. alpha): Market impacts and the life cycle of investors orders, by Emmanuel Bacry, Adrian Iuga, Matthieu Lasnier, Charles-Albert Lehalle.
According to the literature in market microstructure, the price pressure is defined as "the change in price when large quantities of a security are traded". Here you can find an example of how price pressure influences the bond market and in which the authors provide a complete definition of the phaenomenon and the relative problem of the information effects. Other suggestions and help will be grateful.