Alpha factor

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The alpha factor (α) ( Jensen-alpha , Jensen alpha ) referred to in the financial market theory , the measure of an excess return ( positive alpha ), or an insufficient yield ( negative alpha ) of a plant compared with a comparison value (the benchmark ). The alpha factor thus corresponds to the part of the stock return that is independent of the market return.

A stock market index (for example the DAX ) or a well-known investment fund is usually used as a comparison value .

A positive alpha does not necessarily mean that the value of a fund has outperformed its benchmark. Likewise, a negative alpha does not necessarily mean that the value has developed worse than its benchmark.

While this is often the case, there are enough counterexamples. For example, any differences in return compared to the benchmark can be generated. ${\displaystyle \beta =0}$

example

A share produced a return of 13% in period t. However, the forecast based on the CAPM ( Capital Asset Pricing Model ) was 12%. The alpha is therefore 1%. It therefore represents the deviation between the forecast and the empirical return.

Market model

The fundamental equation of the market model or the CAPM is:

${\displaystyle \mu _{i}=\beta _{i}\cdot (\mu _{M}-\mu _{rf})+\mu _{rf}}$

μ _i = predicted return of the i th stock

μ _M = forecast return on the market portfolio M

μ _rf = risk-free market rate

α _J = Jensen alpha of the i th share

β _i = beta factor of the i th share for the market portfolio M

r _i = empirical (actually realized) return on the i th share

However, returns that differ from this model are realized on the market. This deviation is measured by Jensen's Alpha:

${\displaystyle \alpha _{J}=r_{i}-\mu _{i}=(r_{i}-\mu _{rf})-\beta _{i}\cdot (\mu _{M}-\mu _{rf})}$

In words this equation is:

${\displaystyle {\begin{aligned}{\text{Jensens Alpha}}&={\text{realisierte Rendite}}-{\text{prognostizierte Rendite}}\\&={\text{realisierte Risikoprämie}}-{\text{prognostizierte Risikoprämie}}\end{aligned}}}$

meaning

The Jensen Alpha is of particular importance in determining the performance of securities.

In the context of actively managed funds, the fund manager tries to achieve a higher return than the benchmark. To do this, it is essential to use stock analysis to identify stocks with a (future) positive alpha factor.

In the context of stock option plans for executives, as part of a performance-related payment, the option conditions should be chosen so that the options can only be exercised if the alpha factor is positive. This is to prevent the beneficiaries from benefiting from the options simply because the overall stock market has developed positively.

See also

• Beta factor