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The Basic Theory Of The Arbitrage Pricing Theory Finance Essay


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The Arbitrage Pricing Theory is an asset pricing theory that is derived from a factor model, using diversification and arbitrage arguments. The theory describes the relationship between expected returns on securities, given that there are no opportunities to create wealth through risk-free arbitrage investments.

APT is one of the most influential theories in the stock pricing which is initiated by the economist Stephen Ross in 1976. It predicts there is a linear relationship between expected return and risk which can be linked by SML. APT suggests that the asset''s return to investors could be influenced by many independent macro-economic variables. It does not require the existence of true market portfolio and demand less restrictive assumptions compare the other asset pricing model such as the CAPM. Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit.

APT relies on three propositions: (i) the security returns can be described by a factor model (ii) idiosyncratic risk can be diversified away (iii) arbitrage opportunities are eventually diversified away.

Since no investment is required, investors can create large position to secure large level of profit. However, profitable arbitrage opportunities disappear in efficient markets. The APT formula is as following:

E(Ri) = Rf + b1*(E(R1) - Rf) + b2*(E(R2) - Rf) + 'K+ bn*(E(Rn) - Rf)

Rf = Risk free interest rate

bi = Sensitivity of the asset to factor i

E(Ri) - Rf) = Risk premium associated with factor i where i = 1, 2,...n

Multi-factor model and many relevant researches to basic financial factor has developed since Ross (1976) raised the arbitrage pricing theory, such as the three factor model of Fama and French (1993). Fama and French (1993) continues the research method of Fama and Macbeth (1993)'Aand conclude that the APT has explain better the return of the stock than the CAPM . Fama and French (1996) argue that the CAPM does not explain the patterns such as size, book-to-market equity, earnings/price etc. in average return on common stock. And these anomalies are captured by the three factor model of Fama and French (1993). The three factor model is as following which indicates that the three factors, (Rm ? Rf), SMB and HML are used to explain the returns of stocks :

SMB = Small Minus Big; returns on small stocks in excess of returns on large stocks

HML = High Minus Low; returns of stocks with high BTM ratio in excess of returns on low book-to-market ratio

According to the equation above, Fama and French (1993) states that the pattern in the HML slopes does not predict the continuation but the reversal for future returns. Therefore, the continuation of short-term returns documented by Jegadeesh and Titman (1993) is left unexplained by the three 'Vfactor model (Fama and French). The three-factor model in the above equation captures much of the cross-sectional variation in average stock

with the reversal of long term returns documented by DeBondt and Thaler.

The results of the empirical tests were taken by Fama & French']1996'^are consistent with APT asset pricing. Fama and French argue that it is an equilibrium pricing model, a three-factor version of APT (Ross 1976) due to the empirical successes. Fama and French (1996) conclude that the three-factor model is a good model although it does not explain the expected return on all securities and portfolios. But it captures the anomalies on the portfolios formed on size and book 'Vto market equity, earnings/price etc.

On the other hand, Roll and Ross (1995) conclude that ''The APT approach to the portfolio strategy decision involves choosing the desirable degree exposure to the fundamental economic risks that influence both asset returns and organizations.'' Roll and Ross (1995) states that APT can be adapted to special situation comparing to many traditional approaches because of its flexibility and it will be well-suited to the management of huge amount of funds. Later on, Chen, Roll and Ross (1986) examined the validity of the APT in the US stock markets. The test is based on the APT and suggests the multi-factor model .Chen, Roll and Ross (1986) found that the set of macroeconomic variables including: industrial production, changes in the risk premium, twists in the yield curve etc. are found to be significant in explaining the expected stock returns. The result of their research is consistent with the APT (Ross 1976) which implies that APT is valid. They believe that the multi-factor of APT captures more risk factors and explains better of the asset returns, therefore, it is more useful than the CAPM.

In conclusion, Arbitrage pricing theory (APT) is a valuation model as it does not required the existence of true market portfolio and fewer assumption is used which is more rational comparing to the CAPM. APT relates the individual asset price to the variety of unanticipated events driving it rather than rely on the measuring of the market performance. Beenstock and Chan (1986) found that the multi-factor APT has a better explanation than the single factor CAPM in the UK stock market through the Non-Nested Test. Also, Fama and French (1996), Chen, Roll and Ross (1986) have consistent results with the APT and therefore support APT over CAPM.

However, there still many ambiguities hide in the model. Shanken (1982) challenge to testability of the APT as theory has been silent about which economic state variables are likely to influence all assets and there is a complete ignorance to the identity of the relevant factors that explains different returns. Also, the economic variables are not yet determined that which are responsible to the asset prices. Reinganum (1981) found that his results are inconsistent with the APT and according to the Roll and Ross''s study, they conclude that although the evidence generally support the APT, acknowledged that their empirical tests were inconclusive. Therefore, due to the complexity of and dubiosities of the APT, companies choose to apply the CAPM instead. In view of this, more researches and improvements should be made to the APT in order to increase the usefulness of it.


Beenstock, M. and Chan, K. 1986, Testing the Arbitrage Pricing Theory in the United Kingdom, Oxford Bulletin of Economics and Statistics, Vol. 48, No 2, pp.121-141.

Eugene F. Fama and Macbeth, J, 1973, Risk Return and Equilibrium: Some Empirical Tests, The Journal of Political Economy, Vol.8, pp.607- 636

Eugene F. Fama and Kenneth R. French, 1992, The cross-section of expected stock returns, The Journal of Finance Vol.47, pp.427-465

Eugene F. Fama, and Kenneth R. French, 1993, Common Risk Factors in the Returns on Stocks and Bonds, The Journal of Financial Economics, Vol.33, pp.3-56

Eugene F. Fama, and Kenneth R. French, 1996, Multifactor Explanations of Asset Pricing Anomalies, The Journal of Finance, Vol. 51, (Mar.,1996), pp.55-84

Nai-Fu Chen; Richard Roll; Stephen A. Ross, 1986, Economic Forces and the Stock Market, The Journal of Business, Vol. 59, No 3 (Jul., 1986), pp.383-403.

Reinganum, Marc, 1981, The Arbitrage Pricing Theory: Some Empirical Results, The Journal of Finance, Vol.36, No.2, (May,1981), pp.313-321.

Richard Roll and Stephen A. Ross, 1995, The Arbitrage Pricing Theory Approach to Strategic Portfolio Planning, The Financial Analysts Journal, January-February 1995.

Shanken, Jay, 1982, The Arbitrage Pricing Theory: Is It Testable, The Journal of Finance, Vol.37, pp.1129'V1140.

Stephen A. Ross, 1976, The arbitrage theory of capital asset pricing, The Journal of Economic Theory, Vol.13, pp341-360.

Zvi Bodie, Alex Kane, Alan J.Marcus, 2009, Chapter 10, Arbitriage pricing theory and multifactor models of risk and return, Investment

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