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A capitalization-weighted (or cap-weighted) index, also called a market-value-weighted index is a stock market index whose components are weighted according to the total market value of their outstanding shares. Every day an individual stock's price changes and thereby changes a stock index's value.
The market return is defined as the wealth-weighted sum of all investment returns in the economy. Roll's critique makes two statements regarding the market portfolio: 1. Mean-variance tautology: Any mean-variance efficient portfolio satisfies the CAPM equation exactly:
The excess growth rate of the market portfolio admits the representation () = = () as a capitalization-weighted average relative stock variance. This quantity is nonnegative; if it happens to be bounded away from zero, namely
For example, if Company A had 20 million shares outstanding and a share price of $500, its market cap is as follows: $500 x 20,000,000 = $10,000,000,000 market capitalization
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Both the cap-weighted market portfolio and the CAPM model are inefficient. If we assume that the capitalization-weighted market portfolio is not efficient, assuming a pricing inefficiency, capitalization-weighting might be sub-optimal and the degree of sub-performance might be proportional to the degree of random noise. [3] [10] [11]
Stock market indices may be categorized by their index weight methodology, or the rules on how stocks are allocated in the index, independent of its stock coverage. For example, the S&P 500 and the S&P 500 Equal Weight each cover the same group of stocks, but the S&P 500 is weighted by market capitalization, while the S&P 500 Equal Weight places equal weight on each constituent.