That investors expect a higher return than the interest rate as compensation for taking on risks is probably an old insight. The Capital Asset Pricing Model (CAPM) makes two clarifications of this general statement:

1. When it comes to measuring the premium required for assuming risk, then the "risk" must be measured by beta.

2. Sodann ist die in einem gleichgewichtigen Capital market verlangte Risikoprämie proportional zu Beta; der Proportionalitätsfaktor ist gleich der Überrendite des Marktportfolios.

The CAPM was developed by SHARPE in 1964 and is one of the most cited and practically used facts to describe the relationship between expected return and risk in capital markets. The Capital Asset Pricing Model (CAPM) makes a statement about the relationship between the expected return on an individual investment and the beta, which measures the relative systematic risk. The expected return associated with a single investment is initially as high as the interest rate and then there is a premium for the risk that is proportional to beta.

The return to be expected on the individual investment therefore provides the level of the equity costs and is therefore an important parameter for the investment decision.

The CAPM is closely related to the classic portfolio theory as it was created by MARKOWITZ, SHARPE and TOBIN. This theory assumes that the investment results can be fully described by two parameters.

· One parameter covers all useful aspects together. That is the expected return.

· The other parameter summarizes all aspects that reduce the benefit. That's the risk.

The uncertain future investment results are described by probability distributions. So that the probability distributions can be described by two parameters and not three or more parameters are required, only the normal distribution is actually possible as a type if it is considered that one should not leave the framework of the distribution type by creating portfolios. Indeed, stock returns can be viewed as normally distributed.

However, the investment horizon must not be very long. With an investment of 5, 10 or even more years, it becomes clear that the investment results have a pronounced right skew. If a certain random process is assumed, the random walk (discrete time) or the Wiener process (continuous time), then the investment results are lognormally distributed. The logarithm of the investment results is normally distributed. Only if the investment horizon is perhaps only 1/2 year or 1 year or at most 2 years can the investment results, which are actually normally distributed, be regarded as normally distributed without too great a mistake. Consequently, the CAPM is a model for describing the returns for an investment horizon of approximately one year. Accordingly, the interest rate is the one-year interest rate.

Regarding the nature of the CAPM: On the one hand, the model can be theoretically derived (from certain premises) and is therefore valid, i.e. correctly proven, in a model world. On the other hand, despite some criticism from empirical research, it is a sufficiently accepted working basis for practice.

Criticism of whether, from an empirical point of view, beta can be seen as the only and most important factor for explaining return expectations was emphatically expressed by FAMA and FRENCH. The professors at the University of Chicago examined historical time series and came to the conclusion in 1992 that, especially in certain periods of time, two other factors should be given explanatory power for the expected return. On the one hand, there is the size of the company:

Small companies showed higher returns than large companies. On the other hand, the relation between market value and book value has empirical significance. The so-called market-to-book ratio, or M / B for short, is a key figure that is highly regarded by analysts today. The larger the M / B, the lower the expected return.

Despite these and other criticisms, no other model has proven so powerful that it could have ousted the CAPM. The CAPM has remained the dominant model.

**Further remarks:**

The CAPM does not describe the return (as it will actually occur in a year), but the expected return on the plant k, k = 1, 2, ..., n

The CAPM is an equilibrium model. It is assumed that investors can reallocate their portfolios if they notice deviations in the expectations of the returns compared to the numerical values that the CAPM predicts. If the equity securities of a company are not traded in a financial market, then the expected return can of course deviate from the numerical values that correspond to the CAPM. In any case, it is difficult in such cases to formulate expected returns, because the capital investment of the value of the company is not manifested through a price formation but first has to be estimated through a valuation model.

Eine Unternehmung kann nicht „ihr“ Beta schätzen, dann mit Hilfe des CAPM die Renditeerwartung bestimmen und diese als Cost of capital für die Bewertung aller ihrer Projekte heranziehen. Denn die Projekte einer Unternehmung können unterschiedliche Betas und folglich verschiedene Kapitalkosten haben.

The “International Asset Pricing Model” (IAPM) is ideal for investments in an international context. It was developed by SOLNIK in 1974 and has been confirmed comparatively well in empirical tests.