In 1972 three researchers (Fischer Black, Michael Jensen and Myrton Scholes) divided the stocks listed on the New York Stock Exchange into ten portfolios. The first portfolio contained 10% of the securities with the lowest betas, the second the 10% with the next lowest betas, and so on. The study found that over 35 years there was an almost exactly straight-line relationship between a portfolio's beta and its average return, just as predicted by the CAPM

However, niggling doubts remain. Stocks with a beta of zero tended to have a higher return than treasury bills, contrary to the CAPM'S predictions. This suggests that investors do expect to be compensated for taking on unsystematic risk. Also, stocks with high betas tended to do slightly worse than predicted by the CAPM.
The CAPM works only in the long run. The returns of America's mutual funds in the 1980s bore no relation to their betas; if anything, in fact, there was a slight tendency for low-beta funds to outperform high-beta ones. And the betas of individual stocks vary a good deal over time. (The beta of a portfolio of stocks is more stable, though, because changes in the betas of individual stocks tend to cancel each other out.) Despite these doubts, the CAPM passed most of its early tests with honours. Then in 1977 it was dealt a more serious blow, by Richard Roll of the University of California at Los Angeles.

According to the original CAPM, all investors choose to hold the market portfolio. Taking this idea literally, the market portfolio would include every financial asset in the world. The trouble with tests of the CAPM, suggested Mr Roll, is that they use a bad proxy for this market portfolio-eg, the 500 biggest companies listed on the New York Stock Exchange.
Roll showed that the CAPM will always look true if the market proxy (such as the S&P 500) is "efficient" in the sense defined by Mr Markowitz-ie, if no combination of the shares would give a higher return for the same risk. But this does not prove that each share's expected return is affected only by its correlation with the true market portfolio.
Conversely, even if share returns were unrelated to betas derived from the S&P 500, shares might still be correctly priced in relation to the true market portfolio. This objection might look like a quibble. But Mr Roll showed that a small change in the market proxy (eg, from the S&P 500 to the Wilshire list of 5,000 listed stocks) can completely alter the expected returns of a stock as predicted by the CAPM. Since nobody knows what the true market portfolio is, nobody can say whether the CAPM holds.