Some Empirical Tests of the Theory of Arbitrage Pricing

We estimate the parameters of Ross's Arbitrage Pricing Theory (APT). Using daily return data during the 1963–78 period, we compare the evidence on the APT and the Capital Asset Pricing Model (CAPM) as implemented by market indices and find that the APT performs well. The theory is further supported in that estimated expected returns depend on estimated factor loadings, and variables such as own variance and firm size do not contribute additional explanatory power to that of the factor loadings.     

Alternative Models for Estimating the Cost of Equity Capital for Property/Casualty Insurers

This paper estimates the cost of equity capital for Property/Casualty insurers by applying three alternative asset pricing models: the Capital Asset Pricing Model (CAPM), the Arbitrage Pricing Theory (APT), and a unified CAPM/APT model (Wei (1988). The in-sample forecast ability of the models is evaluated by applying the mean squared error method, the Theil U2 (1966) statistic, and the Granger and Newbold (1978) conditional efficiency evaluation. Based on forecast evaluation procedures, the APT and Wei's unified CAPM/APT models perform better than the CAPM in estimating the cost of equity capital for the PC insurers and a combined forecast may outperform the individual forecasts.     

The attributes,behavior, and performance of U.S. mutual funds

This article examines the risk and return characteristics of U.S. mutual funds. We employ an equilibrium version of the Arbitrage Pricing Theory (APT) and a principal-components-based statistical technique to identify performance benchmarks. We also consider the Capital Asset Pricing Model (CAPM) as an alternative. We implement a procedure for overcoming the rotational indeterminacy of factor models. This procedure is a hybrid of statistical factor estimation and prespecification of factors. We estimate measures of timing ability for the CAPM and extend it to the APT. We find that this timing test is misspecified due to noninformation-based changes in mutual fund betas. We develop a modification of the timing measure that, under certain conditions, distinguishes true timing ability from noninformation-based beta changes.     

Multifactor Asset Pricing Models

Since the early 1960s, the mean-variance Capital Asset Pricing Model (CAPM) has been a dominant paradigm in modern finance. Recently, the accumulation of anomalous evidence, and a realisation that empirical tests of the model are tautologically related to the efficiency of the market index, have pushed that paradigm to a point of crisis. This paper reviews alternative asset pricing models which coexisted with the CAPM and may provide plausible substitutes. The major distinguishing feature of these models is that they predict multiple risk factors and, with the exception of the Arbitrage Pricing Theory (APT), are extensions of the CAPM.     

The Arbitrage Pricing Theory: Is it Testable?

This paper challenges the view that the Arbitrage Pricing Theory (APT) is inherently more susceptible to empirical verification than the Capital Asset Pricing Model (CAPM). The usual formulation of the testable implications of the APT is shown to be inadequate, as it precludes the very expected return differentials which the theory attempts to explain. A recent competitive-equilibrium extension of the APT may be testable in principle. In order to implement such a test, however, observation of the return on the true market portfolio appears to be necessary.     

Temporal Aggregation and the Continuous-Time Capital Asset Pricing Model

We examine how the empirical implications of the Capital Asset Pricing Model (CAPM) are affected by the length of the period over which returns are measured. We show that the continuous-time CAPM becomes a multifactor model when the asset pricing relation is aggregated temporally. We use Hansen's Generalized Method of Moments (GMM) approach to test the continuous-time CAPM at an unconditional level using size portfolio returns. The results indicate that the continuous-time CAPM cannot be rejected. In contrast, the discrete-time CAPM is easily rejected by the tests. These results have a number of important implications for the interpretation of tests of the CAPM which have appeared in the literature.     

An Empirical Test of the Arbitrage Pricing Theory on Australian Stock Returns 1974-85

This paper examines empirically, issues concerning the Arbitrage Pricing Theory (APT). Firstly, in the spirit of Chamberlain and Rothschild [1983], the existence of an approximate factor structure is explored. Secondly, following Beggs [1986] and employing a principal components approach, a test of arbitrage pricing and the importance of the error of approximation, is conducted. Finally, using a non nested framework, the APT and CAPM are tested against each other. The results show mixed support for the APT having up to 3 priced factors.     

Arbitrage Pricing Theory and Utility Stock Returns

This paper presents some new evidence that Arbitrage Pricing Theory may lead to different and better estimates of expected return than the Capital Asset Pricing Model, particularly in the case of utility stock returns. Results for monthly portfolio returns for 1971–1979 lead to the conclusion that regulators should not adopt the single-factor risk approach of the CAPM as the principal measure of risk, but give greater weight to APT, whose multiple factors provide a better indication of asset risk and a better estimate of expected return.     

Simulating and Forecasting Utility Stock Returns: Arbitrage Pricing Theory vs. Capital Asset Pricing Model

Just when the capital asset pricing model (CAPM) has become accepted by public utility regulators as a method for estimating a utility's screening rate, academic criticism of the model's theoretical and empirical shortcomings has led to empirical testing of the alternative arbitrage pricing theory (APT). This paper expands on recent APT-CAPM performance comparisons by simulating returns of public utility stocks using versions of both models, as was done by Bower, Bower, and Logue in a 1984 paper. In addition, the models are used for ex-post forecasting of returns in a subsequent time period. The Litzenberger-Ramaswamy method is used to correct for errors-in-variables in the CAPM cross-sectional equation. This allows for estimating the security market line using firm betas. The same methodology is used in the APT stages. Three different criteria—the Theil inequality, the sources of mean square error, and Chen's estimated weights of expected return-are used to compare CAPM and APT simulation and forecasting of the equity screening rates. Tested on a sample of 128 public utility companies, results show that neither model is clearly dominant. There is a tendency for reversal of performance. The model that is superior for simulating returns tends to be inferior for forecasting them, and vice-versa.     

Reference Variables,Factor Structure,and the Approximate Multibeta Representation

The Arbitrage Pricing Theory (APT) implies that if asset returns have a factor structure, then an approximate multibeta representation holds with respect to the factors as reference variables. This paper assumes that asset returns satisfy a factor structure and derives a condition under which the approximate multibeta representation holds with respect to a set of reference variables which may not be the factors. This condition is that the regression matrix of the reference variables on the factors is nonsingular. Implications for the testability of the APT are also discussed.     

A conditional regime switching CAPM

The standard Capital Asset Pricing Model (CAPM) is simple, intuitive, and grounded in sound economic theory. Yet, almost half a century's worth of empirical testing has so far failed to demonstrate its relevance. One major reason given for the CAPM's empirical failure is that beta is not the sole measure of systematic risk. In other words, the standard CAPM does not hold. Another important explanation is that the CAPM may hold conditionally rather than unconditionally. The standard CAPM fails to explain the cross-section of returns because it ignores the fact that both the risk and the price of risk are time-varying. The search for conditional models has led researchers to either disregard the theory behind the CAPM or to use statistical procedures that are too complex to be replicated by other researchers and practitioners. In this paper we propose a conditional model that is compatible with the standard CAPM while remaining simple and accessible to both researchers and practitioners. Beta and the risk premium are assumed to be time-varying, with the latter being associated with bull and bear states. We find strong support for the conditional CAPM with beta explaining both bull and bear markets. While the bear market ex-post risk premium is negative, the weighted average risk premium is positive and highly significant.     

Resilience to the financial crisis in customer-supplier networks

Inspired by the Capital Asset Pricing Model (CAPM) beta, we construct customer and supplier betas to separately investigate potentially different properties of downstream and upstream linkages. With the adjacency matrix acting as a ‘filter’ to extract each company's return covariances with its trading partners, the cross-sectional dependence contained in the customer-supplier network is summarized by our betas. We explore how these two betas are related to a company's resilience to the financial crisis of 2008–2009. We observe that a higher customer beta is generally associated with more resilience during the crisis. Therefore, investors could construct the customer beta to gain insights into the relative negative impact of a potential crisis on a stock's performance.     

What Cost of Capital Should You Use? The Market Has an Answer

The most widely used means of estimating a company's cost of equity capital is the Capital Asset Pricing Model (CAPM). But as a growing number of academics and practitioners have suggested, use of the CAPM produces estimates that often fail to reflect the risks of the companies as perceived by current and potential investors. The authors' work, together with other research, also suggests that the cost of equity produced by the CAPM is often too high. To the extent this is so, companies are discounting investment projects at rates of return that may be leading them to pass up value‐adding opportunities. The authors advocate the use of a simple and practical alternative to the CAPM that does not use either an assumed market risk premium or a beta. It uses instead an equity premium that is implied by the current market price of a company's stock and, as such, is implicitly derived from investors' assessments of the firm's risk that are reflected in that price. More specifically, the alternative approach solves for the internal rate of return that equates the present value of expected future cash flows to the current market price. In support of this approach, studies have shown that such market‐implied measures are better predictors than CAPM‐based estimates of future stock returns, both at the individual‐firm and aggregate market levels.     

Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?

Abstract Markowitz and Sharpe won the Nobel Prize in Economics for the development of Mean‐Variance (M‐V) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximisation in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximise the expectation of an S‐shaped value function, which contains a risk‐seeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPM's underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.     

New estimates of the cost of capital for pharmaceutical firms

Academic researchers, as well as pharmaceutical firms themselves, often use the Capital Asset Pricing Model (CAPM) to estimate a firm's cost of capital. But the CAPM implicitly assumes that cash flows follow a random walk. This assumption is inconsistent with our finding that large U.S.-based pharmaceutical firms' cash flow growth rates display either momentum or mean-reversion. We show that growth rate momentum implies: (1) the systematic risk of a project increases monotonically with time to maturity of the cash flows; and (2) longer duration projects require a higher cost of capital. One of the practical implications of our results is that the traditional CAPM underestimates the cost of capital for some pharmaceutical firms by as much as 2.8%. These findings are quite relevant for the policy debate about the high rates of return earned by pharmaceutical companies, which some claim are pure rents and are not necessary to attract investors. Our theoretical and empirical analysis shows that high returns are often required to compensate for the higher systematic risk of long-duration pharmaceutical cash flows.     

The Discount Rate of IAS 36 – A Comment

Discussing the guidance in IAS 36 on how to determine the discount rate for present value measurements of impairment reviews, Husmann and Schmidt (Accounting in Europe, 5, pp. 49–62, 2008) conclude that the standard's option to use ‘the entity's incremental borrowing rate’ should be removed. I argue that their conclusion is based on a misconception about what is meant by incremental borrowing, and that the incremental borrowing rate may be a useful approximation to the cost of capital within a Capital Asset Pricing Model (CAPM) framework. The reference to it is even more useful if CAPM is deemed not to hold. An important objection to the IAS 36 rules on the discount rate is that they are so different from the US GAAP rules: the former are detailed and adhere closely to the CAPM ideal, whereas the latter are general in nature, superficial and lack theoretical underpinnings. Any modification of the accounting standards' rules on the discount rate should first seek to remove that gap.     

An Asset-Pricing Theory Unifying the CAPM and APT

This study shows that the competitive-equilibrium version of the APT may be extended to develop an exact model if idiosyncratic risks obey the Ross separating distribution. The results indicate that one only need add the market portfolio as an extra factor to the factor model in order to obtain an exact asset-pricing relation. Thus, this study presents an extension and integration of the CAPM and APT. The “empirical” APT is also generalized to allow for some factors to be omitted from the econometric model employed to test the theory. The developed model is extremely robust and may be reduced to the CAPM or expanded to approximate Ross's APT depending upon the number of omitted factors. Further, the importance of the market portfolio is shown to be a monotonic increasing function of the number of omitted factors. Finally, the study demonstrates that, in a finite economy, the pricing-error bound of the Ross APT in a correlated-residuals factor structure is an increasing function of the absolute value of market-residual beta, rather than the weight of the asset in the market portfolio as is the case of uncorrelated factor residuals. However, under the normality assumption, the pricing error becomes an extra component related to the market-portfolio factor, and the exact asset-pricing relation is once again obtained.     

An explicit bound on individual assets' deviations from APT pricing in a finite economy

Ross's Arbitrage Pricing Theory (APT) is a tractible and reasonable alternative to the mean-variance model. Nonetheless, understanding of the theory has been obscured by the complexity of the sequence economy models used for motivation. By contrast, we give a simple and direct derivation of the APT in a finite economy. Using an explicit bound on the deviations from APT prices across assets, a coarse calculation shows that theoretical deviations from APT pricing are negligible in our economy.     

Share Prices and Macroeconomic Factors

The APT with macroeconomic factors put forward by Chen, Roll and Ross (1986) was tested using monthly Australian sectoral share-price indexes for 1980–1994. The inflation rate was found to be consistently priced. The significance of other factors was found to depend on the choice of sample period and estimation method. The model was compared to both an APT with artificial factors and the CAPM. Both versions of the APT were found to clearly out-perform the CAPM but neither version of the APT was clearly superior to the other in terms of both within- and out-of-sample explanatory power.     

Possible explanations of no-synergy mergers and small firm effect by the Generalized Capital Asset Pricing Model

The Sharpe-Lintner Capital Asset Pricing Model (CAPM) and the General Capital Asset Pricing Model (GCAPM) suggested by Levy (1978), Merton (1987), and Markowitz (1989) are compared and analyzed. Under the GCAPM we obtain the following main results: 1) the value additivity principle breaks down, which explains mergers and acquisitions; 2) beyond a certain limit, the profit from additional merger is negative; and 3) in a GCAPM equilibrium, small firms earn an abnormal profit in comparison to what is predicted by the CAPM. These results, which are indeed observed in the market, are fully consistent with the GCAPM, but are in contradiction to the CAPM.