Capital Asset Pricing Model (CAPM)

What is the CAPM?

From Wikipedia: In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

Basically, is a model that describes the  required return of a asset to compensate the non-diversifiable risk premium.

What is diversifiable  and non-diversifiable risk?

The non-diversifiable risk is the intrinsic risk of the market (i.e.: the standard deviation of the returns of big indexes like the SP500).

The diversifiable risk is the risk of a portfolio that can be diversified away. It happens because when the portfolio is very large, the ups and downs of the assets compensates each other.

Which is the equation of the CAMP?
$$r=r_{f}+\beta(r_{m}-r_{f})$$

Explanation:

$r$: Return of the analysed asset.

$r_{f}$: Risk-free rate; return that is possible to achieve without risk (for example, government bonds of germany).

$\beta$: It measures the sensivity of the asset to the market, the exposure to general market movements. If $\beta$>1, when the market goes up, the asset goes higher, and when the market goes down, the asset goes lower. Therefore the volatility of the asset is higher than the volatility of the market. If $\beta$<1, the volatility of the asset is lower than the volatility of the market. Thus, $\beta$ is a mesure of risk. Theorically, the $\beta$ of a risk-free asset is zero (no risk).

$r_{m}-r_{f}$: Premium return of the market over the risk-free asset because the market has no non-diversifiable risk.

How is possible to mesure the beta coefficient?
The theorical expresion for the beta coefficient is:
$$\beta=\frac{Cov(r_{asset}, r_{market})}{Variance (r_{market})}$$

The covariance is a measure of how much two random variables change together. If they move in the same direction, the covariance is positive. If they move in opposite directions, the covariance is negative.

In practice, the beta coeficient is estimated doing a linear regression between the premium return of the asset ($r-r_{f}$) against the premium return of the market $r_{m}-r_{f}$. The data for doing the regression is obtained from historical values.

Why is important the CAPM?
It was the first model to quantify the relation between risk and return. Although new models have come up, the CAPM is still widely used. Is very intuitive and easy.