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Modern Portfolio Theory and Investment Analysis, 9th Edition by William N. Goetzmann, Stephen J. Brown, Martin J. Gruber, Edwin J. Elton

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16

The Arbitrage Pricing Model APT—A Multifactor Approach to Explaining Asset Prices

All of the equilibrium models discussed in Chapters 13, 14, and 15 have their basis in mean–variance analysis. All require that it is optimal for the investor to choose investments on the basis of expected return and variance. However, definitions of returns for which means and variances are calculated differ between models. For example, in the version of the capital asset pricing model (CAPM) involving taxes, investors examine means and variances of after-tax returns. As a second example, Elton and Gruber (1982) have shown that the alternative version of CAPM under conditions of uncertain inflation can be derived by assuming that investors maximize a utility function defined in terms of the mean and variance of real as compared to nominal returns. As noted in the previous chapter, there are major obstacles to testing any of these equilibrium theories.

Ross (1976, 1977) has proposed a multifactor approach to explaining the pricing of assets. Ross had developed a mechanism that, given the process that generates security returns, derives asset prices from arbitrage arguments analogous to (but more complex than) those used in the beginning of Chapter 13 to derive CAPMs. In this chapter we first present the mechanism of arbitrage pricing theory (APT). This is the derivation of equilibrium conditions given any prespecified return-generating process.

Following this, we discuss implementation of the APT. ...

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