 The introduction of capital asset pricing model in the field of financial economics has been considered as a Significant contribution and the model has been found as an effective and efficient tool in pricing the risky assets but studies on its usefulness Have found certain deficiencies in it and And one such deficiency is its inability to develop a relationship between risk and return There are certain other deficiencies that are available in the empirical literature related to the CAPM It is said that CAPM tests indicate unstable betas for the Individual securities, but stable beta for the portfolios There is mixed sport for positive linear relationship between rate of return and the systematic risk of portfolios of stocks Recent evidence indicate they need to consider more or different risk variables or The proxies thereof There is a limitation of the model in the sense that the model is unable to Select a proxy for market portfolio as a benchmark In an efficient market return differential means the markets are not particularly efficient for extended period of times or The market prices are efficient, but there is something wrong with the way the single model Which is like CAPM may or is the risk The return differential occurs due to knowledge of certain firm or security characteristics market size or The value etc So in the presence of deficiencies with the CAPM what is the alternative? We have an alternative in the name of arbitrage pricing three are the APT Arbitrage pricing theory is an alternative asset pricing model Which is reasonably intuitive it requires Limited assumptions and it allows for multiple dimensions of investment risk factors The assumptions of APT says that the capital markets are perfectly competitive Investors prefer more wealth to less wealth with Certainity and the third is that the stochastic process to generate it asset returns can be expected expressed as a linear relationship between the as a linear relationship function of a set of key factors Unlike CAPM APT does not assume certain other things like a market portfolio that contains all risky Asserts and it is a main variance portfolio The APT also does not assume normally distributed returns It does not assume quadratic utility function So obviously a simple model with the ability to explain different differential security prices will be considered superior theory to the CAPM theory On the screen you can see the APT model in which we have certain factors like we have are We have the betas or the lambdas But these variables Say by are we mean the return on asset I during a specific time period By expected return we mean the expected return for asset I by beta We means the reaction in asset I return to the investments in a common factor by Delta we mean a common factor which has a zero mean and that influences the returns on all assets and that is the factor that is the essence of the APT theory and finally we have the E or the a return which is a unique effect on asset eyes return that by assumption is completely diversifiable in large portfolios and has a mean of zero and Whereby n means a number of assets Delta are the multiple factors or as these factors are Unidentified these are expected to have an impact on all assets these factors may include inflation GDP growth and many others Betas determine how each asset reacts to to this common factors This mean that beta relates the relationship with the factors and the return similar to the CAPM the unique factors are the errors random errors are independent and diversifiable in the larger portfolios APT assumes that in equilibrium the return on a zero investment Zero systematic risk portfolio is zero where the when the unique effects are diversified away This also implies that expected return on any asset I can be expressed in an other equation like E is equal to lambda naught plus lambda B plus lambda to B to plus lambda K and The BK so what these lambdas and betas say Lambda naught is the expected return on the asset with zero systematic risk This means that the lambda naught is equal to E naught or there is no return Lambda J is the risk premium related to the each common factor so this lambda basically is the risk premium of the factor that we are considering as a Factor that is affecting our expected return, which is on the left side of the equation Betas is the pricing Relationship between the risk premium and the asset I this means that this says that how responsive an asset I is to the common factor K There are certain similarities and dissimilarities between APT and the CAPM If we see the form of equation both have linear format If we see the number of risk factor in CAPM, there is only one risk factor. That is the beta But in case of APT, there are K number of risk factors means there are Greater than one risk factors so far as the factor risk premium is there in case of CAPM we have excess market return, but in case of APT we have the lambdas For a factors risk sensitivity in we have betas in the case of CAPM and we also have betas in the case of APT We have zero beta return in CAPM in the form of risk free rate and in the form of Lambda naught we have for the APT