Ite, Beta Est

Thirty years already and not a wrinkle. The beta is still here and certainly here. A concept of both academic and practical interest, sometimes contested, it serves nevertheless as a reference in finance. The beta and the theory associated with it (CAPM or Capital Asset Pricing Model) certainly merit an issue of Quants. We judged it useful to recall the theoretical basis of the concept and to show its ruitfulness. It provides astonishingly simple answers, robust to variations in the underlying financial and mathematical hypotheses. This very simplicity has in fact provoked regular criticism and exhaustive empirical tests. One of the most recent tests (1992), that of Fama and French, has even dealt a severe blow to the credibility of CAPM, in showing that, more than the beta, it is a "size" effect which explains the average returns of american stocks over the past 40 years. Thus it appears to be an opportune moment to examine what in the theory can be tested effectively, and to carry out certain of these tests in the case of the Paris stock market. The results of these tests lead us to conclude, in agreement with the theory, that in the medium term (over periods of investment between 5 and 10 years), the specific risk of french stocks is not remunerated, and to note that the average return of portfolios is indeed proportional to their beta. However, these tests emphasize the importance of the composition of the "risk-less portfolio", with respect to whose return the risk premium of a financial asset is calculated. This portfolio is too often identified with a monetary fund. Furthermore, from an operational point of view, the historical beta (obtained by linear regression on the near past) appears, for portfolios with a great number of securities, to be the best parameter by which to select portfolios that will beat the market, assuming its upswings and downswings are correctly anticipated. The practical applications of the beta and the extensions of CAPM are legion. A small User‘s Guide is included at the end of the document. We have considered moreover other forms of the beta that are either original or attractive, like an extension to stable laws or multi-factorial models such as the BARRA-CCF French Stocks model. But we had to limit our scope, issues number 3, 5, 7 and 10 of Quants having already mentioned CAPM. To be continued ...