The model of the security line or English Capital ate Pricing Model (CAPM) constructs on the Portfoliotheorie of Harry M. Markowitz and ranks among the capital market equilibrium models. The CAPM extends the Portfoliotheorie by the question, which part of the total risk of an investment object is not to be eliminated by Risikostreuung (diversification) and avowedly, how risky investments in the capital market are evaluated. The core of the CAPM, the model of the security line, describes a linear dependence of the net yield of an investment which can be expected on only one risk measured variable (in factor model). A goal of the CAPM is it in the long run, equilibrium courses for individual risky investments (in the following: To deduce securities) in the Portfoliozusammenhang under uncertainty (risk).

The CAPM was independently developed by William F. Sharpe, John Lintner and January Mossin in the 60's.

Structure of the model

The preliminary stage of the CAPM is the model of the capital market line (Capital Market LINE), whereas the model of the security line (Security Market LINE) forms the actual nuclear model. The CAPM develops on the same conditions as the Portfoliotheorie. In addition still highly simplifying acceptance step participants over the capital market and its. In particular it is assumed that

• the capital market in an equilibrium is, so that nobody has cause to shift its security Portfolio,
• a interest rate without risk exists, to which each market participant can take up and invest at any time as many as desired money. The interest rate is thereby under the expected net yield in the following to describing Marktportfolios,
• the investors the same expectations over the future possible net yields and risks of the securities to preserve and that no individual market express taker can change these data,
• no commercial costs (transaction costs), like stock exchange fees, or taxes exist.

From these acceptance it follows that all capital investors an in the same way built up security Portfolio on the basis of the Portfoliotheorie form. In this so-called Marktportfolio all acted securities are present in the relationship of their market values. (The acceptance of the equilibrium meant: If it would give not s efficient securities, then they were sold and against securities to be exchanged. The sales of such securities presses their price (if the Competitivity condition is not accepted), lets thus the net yield of the security concerned rise. In the equilibrium all are already final such transactions, which means that there are no more securities on the regarded capital market, which are not Therefore the Marktportfolio consists only of securities.)

If the expected net yields and the risks of the individual securities are well-known, also the expected net yield and the risk of the Marktportfolios can be computed. The expected net yield of the Marktportfolios is called in the capital market theory "“capital costs under uncertainty"”.

By the possibility of investing or of taking up without risk money, the investor in a next step can produce the desired risk position depending upon degrees of his risk aversion by mixture of the investment without risk with a plant into the risk-efficient Marktportfolio (and/or with smaller risk aversion by raising of credit and plant into the Marktportfolio). This allocation of the capital which can be put on in a always identically structured Marktportfolio independently of the personal risk inclination is called Tobin Separation.

In order to deduce in this model world the expected net yield and/or the course of an individual security in the Portfoliozusammenhang on mathematical-statistic way, the following definitions are met:

The difference between the expected net yield of the Marktportfolios M ("“capital costs under uncertainty"”) and the safe Zinsatz market price for the risk is called. The risk quantity of each security in a probably diversified Portfolio is called beta (ss). The risk of the Marktportfolios M is standardized on 1, i.e. beta = 1. The ss-factor of an individual security is defined as the quotient from the statistic covariance of the security concerned for the Marktportfolios M and the variance of the market portfolio. The beta factor exclusively refers to not far reducible risk in the Portfoliozusammenhang (the so-called "“systematic risk"”) and represents thus the relevant contribution for the risk of each Portfolios.

After one now the central statement of the CAPM results following mathematical optimum regulation:

\ mu_i=r_f+ (\ mu_m-r_f) \ cdot \ beta_i

The expected net yield \ mu_i a risky security (for example share) sits down in the market equilibrium together from the interest rate without risk r_f and to a risk premium. The risk premium is the product from market price for the risk (\ mu_m-r_f) and the risk quantity \ beta_i the regarded investment.

Hereunder applies: The more highly the beta factor of a security, the more highly precipitates its expected net yield and in reverse. In other words: Investors are ready only then to hold a security with a high risk (ss) if an accordingly high net yield is to be expected.

On the set assumption of einperiodiger planning in such a way determined net yield can be transferred in a simple manner into an equilibrium course for each security. The equilibrium course serves as yardstick for it whether an individual security (portfolio) is evaluated in conformity with its risk by the market.

Critical appreciation of the CAPM

The strict premises of the CAPM may appear at first sight unrealistic. However the model could not be falsifiziert in numerous empirical studies. Obvious it is however that at the capital market effects can be observed, in the contradiction to the CAPM. In addition the January effect or the small firm effect belongs depending upon empirical investigation. However already Sharpe expressed in the year 1964 that a theory should be examined not in the reality proximity of its premises, but in the acceptability of their implications. Thus the CAPM does not only supply the most well-known explanation for the exchange relationship (trade off) between net yield and risk, but is e.g. an important instrument during the measuring of performance of unit trust fund. In and the 80's 70's 20. Century were replaced the moreover one some the original model acceptance by more realistic and again set up the model on this basis. It was shown that also on the less strict assumption the core statement of the model of the security line has further existence.

This does not surprise, since the statements derived from models must be inevitably logically true, if no logical mistake in reasoning is present within the model. The CAPM extracts itself from an empirical examination, because the market Portfolio of all net assets cannot be reconstructed. Besides the CAPM the requirement can to explain the stock exchange courses in the reality not become fair, since for material capital markets hardly an equilibrium can be postulated.

Literature

• William Sharpe, Capital ate Prices: A Theory OF Market Equilibrium of under conditions OF Risk, 1964, in: Journal OF Finance, pages 425-442

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