Beta factor in financial theory

The Greek letter ß, a small beta, denotes the no longer diversifiable risk associated with a single investment and puts it in relation to the risk of the market portfolio. Beta is therefore a measure of the relative systematic risk. The importance of beta as a measure of risk lies in the Capital Asset Pricing Model (CAPM).

The risk associated with an investment in stocks has been understood since the definition of MARKOWITz within the financial theory as fluctuations in the return and therefore measured with the spread (standard deviation, square root of the variance) of the return.
Diese Rendite kommt durch die Käufe und Verkäufe an der Börse zustande. Selbstverständlich handeln die Investoren in der Regel rational: Käufe und Verkäufe, damit also die Kurse, spiegeln deshalb im Regelfall die „inneren“ Vorgänge der Untemehmung wieder. Diese, als Information efficiency bezeichnete Hypothese koppelt die „objektive“ Performance einer Unternehmung an die gelegentlich „subjektiv“ wirkenden Käufe und Verkäufe von Aktien.

The definition of beta and the CAPM go back to SHARPE and the time around 1965. Consider the return rk that will be associated with buying and holding a share in company k for the coming year. Since this size is uncertain, the name should be given a tilde. It is a random variable because it indicates knowledge gained from certain information about the probability distribution of the return for the coming year.

In general, beta is defined as a measure of future, uncertain returns. However, historical time series are used for the estimation and the calculated values are called historical betas. The attempt was made to average between betas that were estimated on the basis of “short-term” data and “long-term” betas in order to arrive at better estimates for the future beta actually sought.

For example, it was discovered that very high historical betas (greater than 1) often overestimated the true beta, while very low betas (less than 1) often underestimated the true beta. Adjustments have been suggested to compensate for such errors. They have been developed by companies that offer financial data such as Blume, Bloomberg, Merill-Lynch, BARRA and others.

Weil Beta und das CAPM eine Bestimmung der Cost of capital erlauben, wurde das Konzept auf einzelne Investitionsprojekte übertragen, auch auf solche, die vielleicht als Teil einer Unternehmung nicht als Investitionsmöglichkeiten der Aktionärsöffentlichkeit direkt zugänglich sind. Die Frage, wie hoch die Kapitalkosten eines einzelnen Projekts seien, soll dann über die Bestimmung des jeweiligen Beta beantwortet werden.

The question that is asked again and again is how the beta of an investment project or a company division can be estimated if this part is not specifically traded on the stock exchange and therefore returns cannot be calculated using historical price changes, the fluctuations of which would then lead to beta. The answer: Then analogy conclusions are recommended.

The beta of a single system also depends on the market portfolio. The market portfolio is a theoretical construct and in practice a “proxy” must be chosen. A “market index” will be chosen, but indices from national and international markets are available. It can also be seen that the known indices practically only consider the large stock corporations as investments, while many investors hold investments that are not included here.

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