A market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market (with the necessary assumption that these assets are infinitely divisible). A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more of a weight than others. ... In business and accounting an asset is anything owned, whether in possession or by right to take possession, by a person or a group acting together, e. ... The concept of infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). ...

Richard Roll's critique (1977) states that this is only a theoretical concept, as to create a market porfolio for investment purposes in practice would necessarily include every single possible available asset, including real estate, precious metals, stamp collections, jewelry, and anything with any worth, as the theoretical market being referred to would be the world market. As a result, proxies for the market (such as the FTSE100 in the UK or the S&P500 in the US) are used in practice by investors. Roll's critique states that these proxies cannot provide an accurate representation of the entire market.

The concept of a market portfolio plays an important role in many financial theories and models, including the Capital asset pricing model where it is the only fund in which investors need to invest, to be supplemented only by a risk-free asset (depending upon each investor's attitude towards risk). The capital asset pricing model (CAPM) is used in finance to determine a theoretically appropriate price of an asset such as a security. ...