Three Propositions of the Arbitrage Pricing Theory Finance Essay

Arbitrage opportunity arises if an investor can construct a zero investment portfolio with a zero profit, in other words, ability to make profit without any risk. Arbitrage Pricing Theory based on three main propositions. First, Security returns can be described by a factor model. Second, idiosyncratic risk can be diversified away. Third, Arbitrage opportunities are eventually diversified away. A “This theory predicts a relationship between the returns of aA portfolio and the returns of a single asset through a linear combination of many independent macro-economic variables.”1 In order to define how good the APT is, we need to look at how it work and how useful can it be. Roll and Ross (1995) stated that the actual return of a stock must follow the APT formula: R=E + AZA²f + e where E is equal to the expected return on the asset, AZA² is equal to the asset’s sensitivity to a change in the systematic factor, f is the actual return on the systematic factor, and e is the return on the unsystematic, idiosyncratic factors.2 The expected return = rf + AZA²1*f1 + AZA²2*f2 +AZA²n*fn which rf is the risk free rate, AZA² is the sensitivity of the stock and f is the risk premium associated with each factor. AZA² is the measure of the relationship between the sensitivity of returns and the unanticipated movements in the factors. The unanticipated returns are what determine the AZA²s and their measurement is one of the important components of the APT approach. There are four main economic factors that are related to unanticipated returns on large portfolios, which are unanticipated changes in inflation, industrial production, risk premiums and the slope of the term structure of interest rate. Capital Asset Pricing Model is a model that describes the relationship between risk and expected returnA andA which has been used in the pricing of risky securities.3 The risk premium on individual securities is E(ri) = rf + AZA²i[ E(rm)-rf] which rf is the risk free rate, AZA²i is the coefficient of the security relative to the market portfolio and rm is the market return. The APT and the CAPM are two of the most important theories on stock and asset pricing. CAPM is a dominant pricing model compare to APT. The APT and CAPM are similar as both of them gives us a standard criterion for rate of return that can be used in capital budgeting, security valuation, or investment performance evaluation. However, they are different in some point as APT is less restrictive in the assumptions. It allows the investor to develop their model of expected return for an asset. In the CAPM theory, “the expected return on a stock is described by the movement of that stock relative to the stock market”4 and the only factor that should be considered is the risk of the stock relative to the entire stock market. Test of the single-index model that account for human capital and cyclical variations in asset betas are far more consistent with the single-index APT. These tests suggest that macroeconomic variables are not necessary to explain expected returns. Moreover, anomalies such as effects of size and book-to-market ratios disappear once these variables are accounted for. According to Fama and French 1996, “the multifactor APT is refined theories of how exposure to systematic risk factors would have influence expected returns, but it provide little guidance regarding which factors such as sources of risk, ought to result in risk premiums.”5 According to the APT, only a few systematic factors will affect the long term average returns of financial assets and it focuses on the main forces that move aggregates of assets in large portfolio. In Chen, Roll and Ross (1986), the paper is about economic forces and the stock market which has explored a set of systematic economic state variables “that has influences on stock market returns and has examined their influence on asset pricing.”6 Asset prices that describe the economy should depend on how visible they are to the state variables. Stock returns are visible to regular economic news in which they are priced according to their visibility, and that the news can be measured as innovations in state variables which the proofing can be done through simple financial theory. The APT highlights the crucial distinction between non-diversifiable risk also as known as factor risk, that requires a reward in the form of a risk premium and diversifiable risk that does not. It is an extremely appealing model as it depends on the assumption that a rational equilibrium in capital markets precludes arbitrage opportunities. A violation of the APT’s pricing relationships will cause extremely strong pressure to restore them even if only a limited number of investors become aware of the disequilibrium. Moreover, the “APT yields an expected return-beta relationship using a well-diversified portfolio, in other words, it choose an appropriate degree of exposure to the major economic risks that influence both asset returns and organizations which practically can be constructed from a large number of securities.”5 For these stated reasons, APT can somehow be defined as a good asset pricing model. However, the APT implies that the expected return-beta relationship holds for all but perhaps a small number of securities. Because it focuses on the no-arbitrage condition, without the further assumptions of the market or index model, the APT cannot rule out a violation of the expected return-beta relationship for any particular asset. For this reason, CAPM has a dominant role in today’s financial market rather than the APT, which shows APT, is a good model but not a perfect model for asset pricing as it is not as good as the CAPM.

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