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## The Capital Asset Pricing Model: Some Emprical Tests

The 1972 paper by Black, Jensen and Scholes can be found here or here.

### What are the main questions addressed in the paper:

• the authors revisit one of the most salient empirical objection to the CAPM: that an asset $i$ expected return $R_i$ does not grow proportionally to its $\beta_i$, and constructing portfolios in a certain way leads to non 0 expected $\alpha_i$
• they revisit the relationship between expected risk premium and systematic risk predicted by the CAPM: $$E(R_i) = E(R_M) \beta_i$$
• they point out that if borrowing is risky, an additional risk premium may be charged on high beta names: $$E(R_i) = E(R_Z) (1-\beta_i) + E(R_M) \beta_i$$

### Most evocative table in this paper is the following:

The evidence for a beta factor is shown through portfolios with lowest beta exhibiting positive alpha::

The non stationarity of the $\beta$ factor is illustrated showing the returns by period:

The authors also make the following points:

• aggregating portfolios by $\beta$ quantile helps making less noisy measurements
• $\beta$ for distinct periods are used to construct quantile portfolio in order to prevent errors in the assignment of an asset to a portfolio due to a $\beta$ error from causing systematic bias in the $\alpha$ of the portfolio.
• $\beta$ are non stationary
• asset return distribution have fatter tails than normal distribution, and stable distributions with an exponent lower than 2, and therefore infinite variance would better describe the returns. The authors still expect the normal test to have some validity.

### Conclusion:

High systemic risk names underperform a leveraged portfolio of lower risk name in the period 1931-1965. The effect is not stationary and has become stronger over that period.