Arbitraj fiyatlama teorisi ve Türkiye’de uygulanabilirliği - Önalan, Deniz (My University, 2001)
ARBITRAGE PRICING THEORY AND APPLICABILITY IN TURKEY The Arbitrage Pricing Theory (APT) , orginally formulated by Ross (1976), is an asset pricing model that explains the cross - sectional variation in asset returns . It attempts to provide a model that explains asset pricing better than the original CAPM . The appeal of the APT is that it is a more genaral model whose derivation is based on more intiuitive and less restrictive underlying assumptions than the original CAPM . However, the CAPM and APT are not inconsistent and the original CAPM can be obtained as a special case of the more general APT under certain conditions. The model that APT posses has attracted on extensive literature including which Huberman (1982,1987),Dybvig and ross (1985), Ross (1984), Gültekin and Gültekin (1987),Burmeister et al.(1988), Chen (1983,1991). At the core of APT is the recognation that only a few systematic factors effect the long term average returns of financial assets. It focuses on the major forces that move aggregates of assets in large portfolios. The ultimate goal is acquire a better undestanding of portfolio structuring and evaluation and thereby to improve overall portfolio design and performance. The return on any individual stock will depend on a variate of anticipated and ununticipated events . Anticipated events will be incorparated by investors into their expectations os returns on individual stocks and thus will be incorporated into market prices. However , most of the return ultimately realized will be the result of unanticipated events. Since, through the process of diversification idiosyncratic returns on individual assets cancel out,returns on large portfolios are influenced mainly by the systematic factors alone. Systematic factors are the major sources of risk in portfolio returns. Actual portfolio returns depend upon the same set of common factors. However ,different portfolios heve different sensitives to these factors. A portfolio that is hedged to be insensitive to these factors and that is sufficiently large and well proportioned, i.e. idiosyncratic risk is diversified away is essetially riskless. As the systematic factors are the primary sources of risk , they are the principal determinants of the expected as well as the actual returns on portfolios. ARBITRAGE PRICING MODEL The APT assume that investors believe homogeneously that asset returns are randomly generated according to a k- factor model which be depicted as follows: (1) where is the (Random ) return on asset i ; E( Ri) is the expected return on asset i ; Fj is systematic (Common ) factor j ( j = 1,2,3... k ) ; is a measure of the sensitivity of asset i to factor j ; ei is the idiosyncratic component of return , unique to asset i . In the factor model of equation (1) it is assumed that there are k systematic factors that are mainly resposible for the movements in the prices of all assets. These factors are common to all assets ;the components of return due to unsystematic factors such as firm - specific or industry events represented by ei . The difference between the actual return realized on asset i , Ri and the expected return E(Ri ) is due to the influence of the k - factors F1 . . .Fk . Since E(Ri ) at the begining of a period already incorporates expectations, the k - factors are unanticipated events or surprises. If the factors are all zero, that is there are no surprises during a period than the actual return will be equal to the expected return . The k - factors are random ;therefore the expected value of each factor is zero. E(Fj ) = 0 , similarly the expected value of the idiosyncratic component of return is zero ; E(ei ) = 0 Also since the idiosyncratic component of return for each asset unique to that asset ei is independent of ej for all i and j ; E(ei ,ej ) = 0 , i nonequal j . Similarly the factors are assumed to be independent of each other E(Fi ,Fj ) = 0 and independent of ei , E(ei ,Fj ) = 0 for all i and j . The systematic factors would be expected to be related to fundamental economics factors such as economic activity, interest rates , and inflation which heve economy - wide effect on all assets or firm to varying degrees. However , the APT does not address the question of how many factors there are and what the factors are. In the derivation of the original APT other assumptions include the following : 1) Asset markets are perfectly compatative and frictonless. 2)All investors heve homogenous beliefs that returns are generated according to the model depicted in equation (1). 3)İnvestors heve monotonically increasing concave utility functions. The number of assets existing in the capital market from which portfolios are formed is much larger than the number of factors. Ross's derivations was based on the intiution that (1) In an efficient market and cosistent with market equlibrium no risless arbitrage profit opportunities (2) Only a few common factors are priced for large, well diversified portfolios. The resulting pricing relation expresses as follows ; (2) Where is the risk primium requred by investors per unit of the risk due to factor j as neasured by the . may denote the riskless rate of return if a riskless asset exists. Thus in the APT pricing relation (equation 2) the expected return on an asset is dependent on its sensitivities to each of the k risk factors ( the 's ) and the risk primuim associated with each of the factors. 's (factor coefficients or factor loadings ) are proportional to the covariance ofthe assets return with the factors. Much the same as the market beta is a measure of the covariance of an asset's return with the market portfolio in the CAPM. (2) can therefore be rewritten in term of expected return on the k pure factor portfolio as follows ; (3) which expresses the expected excess return on an asset i in terms of the expected excess returns on the pure factor portfolios and the respective WHAT ARE THE APT FACTORS ? The APT does not say anything anything the nature of the pervasive factors or how many there are. This issue has therefore been the subject of emprical tests. Emprical researchers heve used two major approaches in attempts to determine the nature and number of factors. 1. Factor Analysis and Principal Component Analysis are statistical prosedures used to extract factors from the historical returns of a group of securities. 2. A set of economic and financial factors judged to represent pervasive sources of risk are examined in relation asset returns using regression analysis to determine if they provide edidence consistent with the model METHODOLOGY Analysis proceeds in the following stages ; 1 ) The monthly returns are extracted from the daily prices file for all the securities. 2) The indivudial asset factor loading estimated. 3) Factor loading estimates are used to explain the cross- sectional variation of individual estimated monthly returns. 4) Estimates are used to measure risk premium associated with estimated factors. CONCLUSIONS There are two ways to study the problem of explaining the cross- section of expected returns . The first one deal with making assumption and production a theory that determines the variables of the pricing equation(2) and then test the theory. The other way examines asset realized returns and tries to specify the macro variables which effect the returns. By using data from the ISE, our findings encourage factor pricing models . This has very important implications on investment strategies and is probabily a valuable direction for future research.
Keywords: Ekonomi; Finansman ekonomisi; Fiyat Teorisi; Spekülasyon; Yatırım