Arbitrage Pricing Theory
Arbitrage Pricing Theory (APT) is a financial model used to estimate an asset's expected return based on its risk factors. It suggests that an asset's return is influenced by multiple factors, such as interest rates, inflation, and market risk. APT helps investors understand the relationship between an asset's risk and its potential return, aiding in investment decision-making.
5 Key excerpts on "Arbitrage Pricing Theory"
- M. Ishaq Bhatti, Hatem Al-Shanfari(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
...Chapter 7 Arbitrage Pricing Model 7.1 Introduction In the rest of the book (Chapters 7 to 9), we will apply hypothesis testing and model selection procedures to models. Arbitrage Pricing Theory (APT) assumes that share prices are efficient in adjusting to new information in stock markets. Due to the price efficiency assumption, which implies that the current share prices are equal to their true value, the no arbitrage condition of the APT is realized. The efficient market hypothesis (EMH) and the APT share the same root as neoclassical economics and are built on some common assumptions, such as having perfect market competition in stock markets. Because of this very important inter-relationship between the APT and the EMH, we will include a section on the EMH at the start of this chapter. Bodie, Kane and Marcus (1996) define arbitrage as, ‘the exploitation of security mispricing in such a way that risk-free economic profits may be earned’ (p. 288). The theory presents a testable framework for estimating prices of risk for holding financial assets in relation to a set of factors that are perceived to be important in determining these assets’ returns. Elton and Gruber (1995) describe the APT in the following statement: ‘it remains the newest and most promising explanation of relative returns. The theory promises to supply us with a more complete description of returns than the Capital Asset Pricing Model’ (p. 388). Both the APT and the capital asset pricing model (CAPM) are equilibrium models which describe the expected returns of risky assets in terms of their risks. In an equilibrium state, the current prices of financial assets are equal to their true values. While the CAPM considers only one source of risk, the market portfolio, the APT considers the possibility of having more than one source of risk. In fact, listed shares have two types of risk: systematic risk and idiosyncratic risk...
eBook - ePub- Jean-Pierre Danthine, John B. Donaldson(Authors)
- 2014(Publication Date)
- Academic Press(Publisher)
...Ross SA. The Arbitrage Pricing Theory. J Econ Theory. 1976;1:341–360. 29. Rouwenhorst G. International momentum strategies. J Finan. 1998;53:267–284. 30. Santos T, Veronesi P. Labor income and predictable stock returns. Rev Finan Stud. 2006;19(1):1–44. 31. Santos, T. Veronesi, P. Labor income and predictable stock returns. Rev. Financ. Stud.. 19, 1–44. 32. Sloan R. Do stock prices fully reflect information in accruals and cash flows about future earnings? Account Rev. 1996;71(3):289–315. 33. Vassalou M. News related to future GDP growth as a risk factor in equity returns. J Finan Econ. 2003;68:47–73. 34. Zhang L. The value premium. J Finan. 2005;60(1):67–103. Appendix A.14.1: A Graphical Interpretation of the APT For illustrative purposes, we assume one common factor. As noted in Connor (1984), the APT requires existence of a rich market structure with a large number of assets with different characteristics and a minimum number of trading restrictions. Such a market structure, in particular, makes it possible to form a portfolio P with the following three properties: Property 1 P has zero cost; in other words, it requires no investment. This is the first requirement of an arbitrage portfolio. Let us denote w i as the value of the position in the i th asset in portfolio P. Portfolio P is then fully described by the vector w T =(w 1, w 2,…, w N), and the zero cost condition becomes ∑ i = 1 N w i = 0 = w T ⋅ 1 with 1 the (column) vector of 1’s. (Positive positions in some assets must be financed by short sales of others.) Property 2 P has zero sensitivity (zero beta) to the common factor: 16 ∑ i N w i β i = 0 = w T ⋅ β Property 3 P is a well-diversified portfolio...
eBook - ePubThe Efficient Market Hypothesists
Bachelier, Samuelson, Fama, Ross, Tobin and Shiller
- Colin Read(Author)
- 2015(Publication Date)
- Palgrave Macmillan(Publisher)
...The perfect competition requirement allows us to appeal to the arbitrage equilibrium and the Arrow-Debreu existence property. An Arrow-Debreu economy allows for both long purchases and short sales. In this case, an arbitrage opportunity would allow an investor to earn a positive profit by offsetting long purchases of an undervalued asset with short sales of an overpriced asset, without risk. The resulting inequality-generating profit opportunity would occur if any assets were mispriced according to the model. We shall use the property that there is no arbitrage in a competitive equilibrium to generate results in the APT model. Let us assume there is a mispriced asset that is a function of the same factors that span the market. To create an arbitrage portfolio, the arbitrageur will assemble a bundle of n+1 properly priced assets with weightings such that the weighting for the bundle has the same sensitivity, or beta, for each factor as does the mispriced asset. Then, by selling the portfolio short and using the proceeds to buy an underpriced asset, or buying the portfolio long funded by shorting the overpriced asset, it is possible to earn a certain profit with no risk once the mispriced asset reaches its equilibrium value. Assuming that each asset, including the mispriced asset, represents only on a small part of the overall market, this arbitrage has a negligible effect on other asset prices, and the mispriced asset is brought into alignment through arbitrage. Much like the assumption of the CAPM pricing that past covariances are used to generate the expectation of today’s security pricing, the APT assumes that a linear regression of past asset returns on the span of factors generates the factor loadings for the expectation of present security prices. However, these factor loadings are not the constant and easily interpreted risk premiums relating one asset to another, as occurs in the CAPM model...
eBook - ePub- Steven Peterson(Author)
- 2012(Publication Date)
- Wiley(Publisher)
...The multifactor model takes the general form: whereupon substituting the no-arbitrage constraint implications for α yields: In practice, analysts are interested in estimating the parameters of this model to help them form an expectation of the asset's return. For estimation purposes, the APT is written as the linear multiple regression model, with error term ε, which captures the asset's idiosyncratic (or specific) risk, that is, the variance in return not explained by the systematic sources of risk represented in the factors. Specific risk is unsystematic and can therefore be diversified away. To see why, let's construct a portfolio of N assets with weights indicating that the portfolio is fully invested, that is, and write the return to the portfolio as follows: In general, we diversify by adding assets to the portfolio. If we assume that the weights are all approximately the same (note that we are not assuming naïve investing as discussed in the chapter on anomalies), that is, w i is approximately equal to 1/ N, then if the idiosyncratic risks are bounded (they aren't infinite), then clearly, as N increases, must go to zero in the limit. In practice, factor selection can be designed to maximize the explanatory power of the model so that is minimized as well. I made the claim earlier that CAPM is a single-factor model with the market rate of return as the factor. Let's establish now the link between APT and CAPM. Suppose we have an asset whose returns are determined by two factors: In the CAPM, we would be interested in the covariance between r i and r m, that is, in estimating the asset's beta. If we divide both sides by, we get the asset's beta as follows: The connection to APT is that the CAPM beta is a weighted average of the underlying factor returns. The weights are a function of the covariances between the factors and the market return. We can generalize this to show that the CAPM beta is a weighted average of factors in any factor model...
eBook - ePub- Frank J. Fabozzi, Frank J. Fabozzi(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
...General Principles of Asset Pricing GUOFU ZHOU, PhD Frederick Bierman and James E. Spears Professor of Finance, Olin Business School, Washington University in St. Louis FRANK J. FABOZZI, PhD, CFA, CPA Professor of Finance, EDHEC Business School Abstract: Asset pricing is mainly about transforming asset payoffs into prices. The most important principles of valuation are no-arbitrage, law of one price, and linear positive state pricing. These principles imply asset prices are linearly related to their discounted payoffs in which the stochastic discount factor is a function of investors’ risk tolerance and economy-wide risks. The Arbitrage Pricing Theory, the capital asset pricing model, and the consumption asset pricing model, among others, are special cases of the discount factor models. In this entry, we discuss the general principles of asset pricing. Our focus here is to analyze asset pricing in a more general setup. Due to its generality, this entry is inevitably more abstract and challenging, but important for understanding the foundations of modern asset pricing theory. First, by extending the state-dependent contingent claims with two possible states allowing for an arbitrary number of states, we introduce the economic notions of complete market, the law of one price, and arbitrage. Then, we provide the fundamental theorem of asset pricing that ties these concepts to asset pricing relations. Subsequently, we discuss stochastic discount factor models, which is the unified framework of various asset pricing theories that include the capital asset pricing model (CAPM) (see Sharpe, 1964; Lintner, 1965; Mossin, 1966) and Arbitrage Pricing Theory (APT) (see Ross, 1976) as special cases. ONE-PERIOD FINITE STATE ECONOMY If a security has payoffs, denoted by x, it means that the economy will have two states next period, up or down, and the security will have a value of $1 or 0 in the up and down states, respectively...
