Can beta be negative funding

Capital Asset Pricing Model

The Capital Asset Pricing Model or short CAPM describes the relationship between systematic risk and the expected return one share in the investment and finance account. In the following article we describe the background of the CAPM via the Capital Market Line and the Security Market Line and explain the formula.

Would you rather have the topic explained in a relaxed manner? Then sit back and check out ours Video to the CAPM at.

CAPM assumptions simply explained, formula and definition

  • The central assumption of the CAPM is a perfect capital market. In a perfect capital market it is possible to both raise and invest capital at the same risk-free interest rate.
  • In addition, unlike the Portfolio theory , in the CAPM model it is assumed that all investors have a homogeneous return expectation in terms of future returns.
  • The prerequisite for this is that on the capital market Market efficiency is present. Due to market efficiency, it can be assumed that all investors are the same curved efficiency line have.

At the CAPM The portfolio theory is expanded to include the aspect that the systematic part of the overall risk cannot be eliminated through diversification. The model also explains how investors can evaluate their risky investment opportunities on the capital market. The idea behind this is that investors are rewarded for their investment on two levels with returns on their investment. Once for the Time value of money , so that they do not just put the money in a risk-free investment and on the other hand for the Risksthat they enter into with an investment in the portfolio. The model is based on the fact that the expected return on a security is a linear function of the risk premium of the market portfolio.

CAPM model

The CAPM determines theoretical equilibria that arise when the risk-averse investmentr their portfolios according to the Portfolio theory put together efficiently. This means the following: If there were inefficient securities, then these would be sold by the market participants and exchanged for efficient ones.

In the equilibrium state, all these transactions are already done. So there is no inefficient securities more in the market. The Market portfolio Only consists of efficient securities and must therefore be efficient itself.

Capital Market Line vs. Security Market Line

The representation of the CAPM can be divided into two parts. Part one, so to speak Prepress of the model, deals with the Derivation of the Capital Market Line, which are also called Capital market line or CML for short. To do this, we first deal with the question of which risk-return combinations actually deliver an efficient portfolio.

The second part deals with the Security Market Line, which represents the actual core model. The Security Market Line serves to make the assessment relevant risk with the expected values ​​of return to connect the financial stocks.

Capital Market Line Definition

As a consequence of these assumptions, there is a certain optimal portfolio of risky financial stocks for all investors, regardless of their risk attitude. This is known as Market portfolio. Depending on their risk preference, investors now choose a combination of this market portfolio and the risk-free investment or financing. These results in the risk-return combinations. The Capital market line depicts this.

Let's take a look at this using a graph. This drawing corresponds to the drawing for portfolio theory with short sales and the possibility of investing at the risk-free interest rate. The only difference is that the straight line in this case represents the capital market line and the portfolio at the touch point represents that Market portfolio and is not an individual investor's portfolio.

When we look for a market portfolio other assume, then the expected value of the return on a portfolio can be determined as follows:

The return from a investment is made up of the Time value of money and the Risk premium together:

The Tobin separation describes the situation in which there is no dependency between the risk attitude and the composition of the risky securities. So that all investors despite being different Risk attitude select the same efficient market portfolio.

CAPM - Security Market Line Definition

Up to this point, the procedure is basically the same as with the one Portfolio theory. So we come to the second step: connecting the Expected values of returns with the appropriate Risk measure. To do this, we should first deal with the question of what is the expected return on investment Security or would have to have a portfolio if all investors manage their portfolios according to the Capital market line put together.

For this it is very important that the financial stock-specific risk one Financial stock does not have to be remunerated, as it is through a suitable Portfolio composition can be eliminated. So only those risks may be reimbursed that are not through Portfolio creation be diversified away. The Security Market Line, also called Wertpapierlinie or SML for short, forms this central statement of the CAPMmodel from. This line is obtained by reshaping the Capital Market Line. The result for the security line is the formula:

The expected return of a security results from the market return minus the risk-free interest multiplied by the Beta factor. The risk-free interest rate is then added to this value. This formula also represents the central one CAPM equation It looks like this in the drawing. The Stock line looks almost exactly like the Capital Market Line, but the yields shown on the ordinates are completely different! In the Security Market Line, the abscissa is Beta factor and not that volatility pictured.

In addition, the security line shows the risk-return combinations of individual securities in the market portfolio and not, as with the capital market line, of the entire market portfolio. The Security Market Line thus indicates the relationship between the expected return of a correctly valued portfolio and the systematic risk of this portfolio. The systematic risk denotes those risks caused by Fluctuations at the Capital markt arise.

CAPM beta factor

The Beta factor indicates how closely a stock is linked to the index. The CAPM Beta quantifies the systematic risk and says nothing about the unsystematic risk. At a Beta factor a one out of one makes the stock neutral because that means that the Eexpected value of the return is identical to that of the market return. However, this does not mean that the variance is also identical. This is because this differs from that of the market return.

Is the Beta factor a share is considered greater than one aggressivebecause it reacts particularly strongly to market fluctuations. If it is less than one, it counts as defensive. Incidentally, it can also be negative Beta factors give. The negative interest rate on the financial instrument can then be more or less than the one to be paid Risk premium for the non-diversifiable systematic risk. The larger the beta, the more risk premium a company has to pay. Since beta is the only one Risk factor is we speak of one One factor model.

The Risk premium is generally called the difference between the expected return on the market and the risk-free interest of the systems defined.

This means that a company whose share has a beta factor greater than one - that is, greater than that of the market portfolio - has to pay a higher annual dividend to its shareholders. Those who have more risk also want to be better rewarded. The only efficient one Portfolio so is that Market portfolio. This then has to go to individual shares be put in relation.

Summary and criticism of CAPM

Here you can see them again central formula for the CAPM:


However, the assumptions of the CAPM are problematic, in particular the homogeneous expectations and the consideration of past developments when determining return values. The latter, however, implies that securities have constant properties over time. In reality, however, there are many changes here, which is why the assessment based on historical data is often incorrect. Therefore, depending on the basis, there are also different in different securities funds Market portfolios and not using THE ONE market portfolio.