Literature Review

APT in International Markets

Literature Review

In any field of research, models are accepted because they increase understanding of what is observed, and they are discard when newer models further increase understanding. CAPM has enhanced our understanding of expected returns on assets. APT, it is claimed, adds more to that understanding, explains why CAPM was a helpful step, and offers a systematic link between expected return and the return generating process.

Stephen Ross (1976) derived rigorously the Arbitrage Pricing Theory model (APT), whose starting premises are that markets are competitive and that individuals homogeneously believe that the return of all assets in the economy are driven by a linear structure of k risk factors.

The APT model represented an answer to criticizes suffered by the popular Capital Asset Pricing Model (CAPM), of Sharpe (1964), Lintner (1965) and Treynor (1961). CAPM establishes a linear relation between the excess assets’ return and a single risk factor – the excess return on the market portfolio. It assumes that all assets can be held by an individual investor. Although it can be considered a particular case of APT, the theoretical construction of CAPM requires normality of returns or quadratic utility function, what isn’t always easy to justify. Besides, it can be proved that any mean-variance portfolio satisfies exactly the CAPM equation. So, testing the CAPM is equivalent to testing the mean-variance efficiency of the market portfolio. However, the true set of all investment opportunities would include everything with worth. There are some assets, human capital for example, that are non-tradable. Nevertheless, transaction costs and market frictions can preclude individuals from owning the portfolio of all marketable assets. Those facts originated the famous Roll’s critique (1977), which states that CAPM isn’t empirically testable as the true market portfolio can’t be observed and is substituted by its proxy. The market portfolio proxy isn’t necessarily mean-variance efficient, even if the real market is and the contrary is also true.

In opposition to CAPM, APT allows for multiples risk factors, accounting for various sources of non diversifiable risks. The market portfolio doesn’t have any special importance and can be or not included as a risk factor. It′s not necessary to assume any hypothesis related to the returns’ distribution or the individuals’ utility function. The model proposed by Ross, however, doesn’t specify which the risk factors are. Several empirical works focused on the attempt to determine them

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through two different strands: using pre-specified observed macroeconomic factors or assuming that, a priori, the factors were unknown.

APT is developing. Its basis is the step, from an assumed multifactor return generating process to a linear relationship between an asset’s sensitivity to these factors and the asset’s expected return, that Ross took by attributing to investors rational behavior tht exhausts arbitrage opportunities in “The Arbitrage Theory of Capital Asset Pricing”. Additionally, much research have been done, such as “Asset Prices in a Well Diversified Economy,” by Gregory Connor in 1980, “Arbitrage Pricing Theory: A Simple Approach.” By Gur Huberman in 1979, “Some Results in the Theory of Arbitrage Pricing”, Jonathan E. Ingersoll, Jr. in 1982, “Real Assets, Technology and the Arbitrage Pricing Theory” by Robert Jarrow and Andrew Rudd in 1980. The work above has embellishes on and expands the basic analysis.

After that, Dorothy H. Bower, Richard S. Bower, and Dennis E. Logue. in “APT Project, July 20, 1982” in 1982 provides simplification and variations of its presentation and a similar work is also been done by H. Russell Fogler in “Common Sense on CAPM, APT, and Correlated Residuals” in 1982.

In addition, many researchers raise questions on how to test the model and whether it can be tested. For example, M. J. Brennan had a discussion of treasury bill factors and common stock returns in 1981, and Phoebus J. Dhrymes, Irwin Friend, and N. Bulent Gultekin had a research on the contribution of Arbitrage Pricing Theory to capital asset pricing in1982. Furthermore, there are also many thesis talking about the issue of how to test the model and whether it can be tested, such as “Some Results in the Theory of Arbitrage Pricing” by Jonathan E. Ingersoll, Jr. in 1982, and ”The Arbitrage Pricing Theory: Is It Testable?” by Jay Shanken in 1982.

None of the research challenges or changes the basic logic that the relationship between return and risk will be determined by self-interested investors who will exploit opportunities to build portfolios of short and long positions, while making zero investment but certain, positive returns.

The empirical tests of the APT model may not satisfy all the analytic objections, but they provide no reason for suspecting that the model will fail to add something more to understanding of the return/risk relationship than does CAPM. Evidence explicitly presented as a challenge to this conclusion is offered by Marc Reinganum who, with the size effect as the example, simply argues that APT may not explain everything about expected return which presented in “The Arbitrage Pricing Theory: Some Empirical Results” in 1981. Reinganum provides no indication that APT does not add to CAPM, however. He only finds that it does not tell a complete story.

Phoebus J. Dhrymes, Irwin Friend, and N. Bulent Gultekin, in “Contribution of Arbitrage Pricing Theory to Capital Asset Pricing”, question work by others but present findings that are not inconsistent with the model. Nai-fu Chen wrote the paper “Some Empirical Tests of the Theory of Arbitrage Pricing” in 1983 that looks at APT in an empirical study that avoids some statistical difficulties of factor analysis by drawing returns for estimating the cross-sectional return/risk relationship from

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days not used in developing factor sensitivities. He not only finds evidence consistent with a conclusion that APT adds to understanding but also tests for a Reinganum-like residual size effect and finds no evidence of it. That is, his approach suggests that size, if it is an important determinant of returns at all, is captured by the APT factors.

George S. Oldfield and Richard J. Rogalski demonstrate that factor score estimates from bond return data can add to the explanation of stock returns that is provided by a stock index in his thesis “Treasury Bill Factors and Common Stock Returns.”. Further, the find that the intercept and risk premiums estimated for the APT return/risk equation from stock returns and factor sensitivities are not significantly different from the values the theory predicts. Richard Roll and Stephen A. Ross in their “An Empirical Inestigation of the Arbitrage Pricing Theory” find significant risk premiums for multiple factors in more sets of stocks than chance would suggest. Many other studies such as P. Brennan’s “A Test of the Arbitrage Pricing Model.”, S. J. Brown and M, I, Weinstein’s “A New Test of the Arbitrage Pricing Model.”, John Kose, and James Tipton’s “Three Factors, Interest Rate Differentials and Stock Groups.”, Michael Gibbons’s “Empirical Examination of the Return Generating Process of the Arbitrage Pricing Theory”, N. Bulent Gultekin and Richard J. Rogalski’s “Government Bond Returns, Measuremnt of Interest Rate Risk, and the Arbitrage Pricing Theory”, Robert A. Pari and Son-Nan Chen’s “An Empirical Test of the Arbitrage Pricing Theory.”, Willia, F. Sharpe’s “Factors in New York Stock Exchange Returns, 1931-1979.”, Richard J. Sweeney and Arthur Warga’s “Affects on Estimating Beta of Changes in Expected Inflation: The Case of Electric Utilities”, provide nothing to suggest that the model will find support in empirical work. Even the work by Roll and Ross in “Regulation, the Capital Assets Pricing Model, and the Arbitrage Pricing Thoery.” urges its practical usefulness and significantce.

Dorothy, Richard anf Dennis in 1984 presents some new evidence that APT may lead to different and better estimates of expected return than CAPM and that it may be more helpful to policymakers as a result. They describe CAPM and APT, note work done by others, show hoe estimates of required returns for utilities developed by applying each model may differ. In their tests, however, APT does do better than CAPM in expaining and conditionally forecasting return variations through time and across assets. Others might make different choices of form and estimation methods for CAPM and APT, and their results might show APT in a less favorable light. Until conflicting results emerge, though,they believe policymakers should not adopt CAPM as a sole standard. Instaed they would be wise to give APT greater weight in decitions.

For equities from the United States economy, the empirical work of Roll and Ross (1980) adopted the second strand. The authors used a statistical technique denominated factor analysis to extract the risk factors and estimate the sensitivity’s coefficients. They conclude that at least three factors were important for pricing the

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assets. A clear interpretation for those risk factors isn’t available, though. Also, an investigation about the return′s individual variance revealed that, although expected returns are highly correlated with their respective variance, the variance itself doesn′t add any explanatory power to the factors previously estimated in the APT.

Chen, Roll and Ross (1986) used macroeconomic variables to estimate an APT applying the two-pass methodology from Fama and Macbeth (1973). Based on Financial theories they choose the following variables: the spread between long and short run interest rate, expected and unexpected inflation, industrial production, the spread between high and low grade bonds, market portfolio, aggregated consumption and oil price. However, only the first four variables were found to be significantly priced.

Still working with data from U.S. economy, McElroy and Burmeister (1988) employed a new methodology to estimate an APT with macroeconomic variables. The Iterated Nonlinear Seemingly Unrelated Regression (ITNLSUR) presents several advantages over factor analysis and the Fama and Macbeth two-pass procedure. ITNLSUR overcomes the econometric problems of previous methodologies such as loss of efficiency, non uniqueness of the second step and unrobustness of the estimate if the errors are not normally distributed. Estimators obtained from ITNLSUR are strongly consistent and asymptotically normal, despite the distribution of the errors. The five macroeconomic factors adopted by McElroy and Burmeister were the spread between 20 years government and corporate bonds portfolios, the excess return of 20 years government bond portfolios over the one month Treasury bill, an unexpected deflation series, an expected growth in sales and the S&P 500 index. Although significant risk prices were found to all of them, the authors warning that there isn’t justification for which or how many factors to use and nothing suggests the existence of just one set of variables with important role in asset pricing.

The APT model was also expanded to an international framework. Solnik (1983) provides an analysis of the model developed by Ross (1976) when investors from different countries are considered. The author argues that the models of international asset pricing used until that moment were controversial due to different hypothesis for the utility function and sources of uncertainty. International Arbitrage Pricing Theory (IAPT) is an alternative, since it isn’t based in any hypothesis about the utility function and only requires perfect capital market. The article shows that (1) every riskless portfolio will be riskless to any foreigner investor and (2) if the linear factor model is believed to hold in one given currency, it must also be valid in any arbitrarily currency chosen as numeraire.

Ikeda (1991) discuss the introduction of foreign exchange risk when adapting the

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