cannot observe the true fair value of a company, they cannot remove inefficiency altogether but may be able to remove the systematic inefficiency that is arguably inherent in capitalization-weighted indices. Equal-weighting is one method to remove this claimed inefficiency but suffers from high turnover, high volatility, and the requirement to invest potentially large sums in illiquid stocks. Weighting by fundamental factors avoids the pitfalls of equal weighting while still removing the claimed systematic inefficiency of capitalization weighting. It weights industries by fundamental factors (also called "Main Street" factors ) such as sales, book value, dividends, earnings, or employees. If a stock’s price gets either too high or too low relative to its fair value, weighting by fundamentals will not reflect this bias as far as there is not perfect correlation between stock prices and economic fundamentals. However, the correlation is quite close since the economic fundamentals used are commonly driving the value of a stock. If we assume no correlation in line with Robert Arnott, this arguably prevents fundamentally based indices from participating in bubbles and crashes and thus reduces its volatility while delivering a higher return. However, the strong underperformance of fundamental indices in 2008 when companies such as banks with large fundamentals crashed has shown that it may not prevent it from participating in stock market crashes. When fundamentals change rapidly so may the stock price. Empirical evidence If the assumptions of the Capital Asset Pricing Model (CAPM) do not hold then there could be three states of the world in line with the so-called joint hypothesis problem explained by Campbell (1997): The capitalization-weighted market portfolio is not efficient. The CAPM model is not an efficient pricing model. 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. Forty years of back-tested Indices weighted by any of several fundamental factors including sales, EBIT, earnings, cash flow, book value, or dividends in U.S. markets outperformed the S&P 500 by approximately 2% per annum with volatility similar to the S&P 500. Thus, fundamentally based indices also had a higher Sharpe ratio than capitalization-weighted indices. In non-U.S. markets, fundamentally based indices outperformed capitalization weighted indices by approximately 2.5% with slightly less volatility and outperformed in all 23