It was found that under these assumptions Tobin's (1958) super efficient portfolio (it consists of the risk-free asset added to Markowitz's portfolio on the efficient frontier) must also be market portfolio.

Further on, Sharpe (1964) divided portfolio risk into systematic and specific. While systematic risk affects every asset of a portfolio (as the market moves, each individual asset is more or less affected), specific risks are unique to individual assets (it represents the component of an asset's return which is uncorrelated with general market moves) and thus can be diversified in the context of a whole portfolio. In other words, the expected rate of return of a portfolio depends not on specific risks of assets, but on the systematic risk of a portfolio.

where ERi is the expected rate of return on asset i, Rf is a risk-free rate, ERm is the expected rate of return of the market portfolio, and is systematic risk. As can be seen from the SML equation, excess return depends on beta alone and not on systematic risk plus specific risk. Moreover, the connection between rate of return and beta is linear for portfolios.

Obviously, CAPM was designed as a way to determine prices of assets in market portfolios. Indeed, given a systematic risk value and asset's expected rate of return investor can adjust the price of an asset using the SML formula. However, because of its 'ideal' nature CAPM is often seen only as a theoretical tool. In practice its main assumptions are not true, and all investors have different information on risk-return characteristics of assets.

Empirical Tests of CAPM

Since CAPM introduction to nowadays SML equation became a topic of wide academic discussion. Studies performed to assess the validity of CAPM can be divided into three general groups: supporting CAPM (e.g. Black, Jensen, and Scholes 1972; Fama and MacBeth 1973), criticizing CAPM (e.g. Fama and French 1992), and criticizing the critiques of CAPM (e.g. Roll 1977). Abundant empirical data provided on CAPM and SML equation is best reflected with several classical studies. All of the reviewed empirical tests concentrated on whether beta alone can explain historical average returns on portfolios. They took a representative value-weighted index as a market portfolio and examined correlation between the results of SML equation and historical average returns on securities. Since neither expected returns nor betas were unknown all of them had to plot the return and beta data against each other. These fundamental studies are reviewed below in chronological order.

Study by Black, Jensen and Scholes (1972)

Black, Jensen and Scholes (1972) used all of the stocks on New York Stock Exchange (NYSE) during 1926-1965 as 10 market portfolios. They sorted assets into portfolios basing on historical betas, which allowed them to acquire portfolios with different historical beta estimates, increasing the sustainability of the test.

One of the first findings produced by Black-Jensen-Scholes test using linear regression of average monthly ecess returns on beta was the significant difference between the slope and intercept of historical regression line and
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