Arbitrage pricing theory
The arbitrage pricing theory or English Arbitrage Pricing Theory (APT ) describes a method for determining the cost of equity and the expected return of securities. It was largely developed by Stephen Ross. Ross also used the name Arbitrage Pricing Model ( APM).
Generally
The APT does not demand a more balanced market, but only one arbitrage-free securities market in contrast to the Capital Asset Pricing Model (CAPM). It assumes that the future performance of securities by market factors
Can be explained. Then apply to the yield of the security
The expected return, and stock specific coefficients, which measure the sensitivity of the return relative to the factor. is an unobservable ( interference ) term, which represents the specific securities, unsystematic risk.
Ross has now shown that under the assumption of absence of arbitrage and a perfect capital market, each factor must be associated with a risk premium, so that the expected return of each security as
Results. This is the interest rate of a risk-free investment. This also calls for the APT a linear risk-return relationship.
The APT can be in contrast to the CAPM principle also several factors. A special case is the single- index model, which, like the CAPM is limited to a factor.
Examples of factors
There are basically two approaches to identify the factors of the APT. First, you can use macro-economic indicators. Empirical studies have shown that five factors explain the cost of equity is sufficiently accurate:
- The index of industrial production
- The short-term real interest
- The short-term inflation
- The long-term inflation
- General credit risk
Other possible factors are money supply, oil price, gross domestic product. The relationship between factors and the expected return is then determined by linear regression.
A second approach is to derive a factor analysis of the empirically observed yields of various securities man-made factors.
Motivation
The arbitrage pricing model has been developed on the basis of practical problems in the CAPM. The CAPM meets very strict assumptions about a market equilibrium. It is assumed that all investors hold shares in a market portfolio, ie, that the relative amount of each asset is the same in each vault. For this market equilibrium out results in an equilibrium price for each security, which depends on its correlation with the market portfolio. The CAPM would be the special case of an airport, which knows the price of the market portfolio as a single factor.
These assumptions have proven to be impractical. Firstly, the market portfolio is very difficult to identify, on the other hand, the demand grew econometric models with more than one factor.
Unlike the CAPM
Compared to the CAPM, APT waived on three very critical assumptions:
- Investors need not decide how the CAPM, according to the Bernoulli and ( μ, σ ) principle.
- In the APT no statement about the risk attitude of investors is needed.
- The assumption of capital market equilibrium in the CAPM is attenuated at the APT: on the capital market must be no arbitrage opportunities exist. Therefore, the knowledge of a market portfolio is no longer necessary with the APT.
By way of derogation from the CAPM:
- Asset returns follow a factor model.
- There are " a lot " or " infinitely many" securities on the capital market, so that investors can form through appropriate diversification portfolio with no unsystematic risk.
The crucial assumption of the CAPM that the market is in equilibrium and all investors are allowed to hold only shares in the market portfolio, was toned down and replaced by the assumption that the market is no possibility of arbitrage offers more.
It is a model that has its theoretical background in quantitative analysis (see also Financial Mathematics, arbitrage ). This also allows the APM can be formulated not only in relative returns, but also in absolute performance. In this formulation, the final capital is a function of the influencing factors and the initial capital. The curve is similar to the securities market line of the CAPM. The difference is that in the CAPM is the slope of the security market line from the characteristics of the market portfolio can be calculated. The slope of the curve from the arbitrage pricing model can only be determined empirically. It is a measure of the risk factor. The corresponding beta is a measure of the sensitivity of a company in terms of risk. The evaluation relation can also be applied to portfolios.