Stock Return Anomalies and the Tests of the APT

This paper shows that the empirical tests of the Arbitrage Pricing Theory (APT) model are very sensitive to the anomalies observed in January in the stock returns data. There is a strong seasonal pattern in the estimates of the risk premia from the APT model. The most important implication of the findings in this paper is that the APT model can explain the risk-return relation mostly for January. Once the January returns are excluded from the data, there is no significant relation between the expected stock returns and the risk measures predicted by the APT model.     

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.     

Do Assumptions About Factor Structure Matter in Empirical Tests of the APT?

The effect of assumptions about factor structure on empirical tests of multifactor models such as the Arbitrage Pricing Policy Theory has received little attention in the literature. Using data on securities traded on the London Stock Exchange, we examine whether returns are best described by an approximate factor structure and whether assumptions about correlations across idiosyncratic returns have a significant impact on estimated prices of risk and their significance. Our findings suggest that returns are best described by an approximate factor structure and, if this is taken into account when empirically testing the APT, six factors carry significant prices of risk. However, if a strict factor structure is imposed, no factors carry significant prices of risk. These findings suggest that assumptions about factor structure matter in empirically testing the APT.     

Arbitrage pricing with information

The Arbitrage Pricing Theory is extended to a setting where investors possess information about future asset returns. A no-arbitrage pricing restriction is obtained with arbitrage conditioned on an investor's information. The pricing restriction contains unconditional factor loadings and either conditional or unconditional expected returns. Thus, tests of the theory can be based solely on time-series estimates of unconditional moments. Additional tests based on conditional expected returns are also appropriate.     

Pricing effects in Fannie Mae agency bonds

As a government-sponsored enterprise, Fannie Mae enjoys certain advantages over other firms. The extent of these advantages, while widely discussed, have not yet been fully quantified. This paper empirically examines the returns to Fannie Mae general obligation bonds under the assumptions of the Arbitrage Pricing Theory. The model provides an explicit method for estimating the risk premium on Fannie Mae bonds. The results indicate that liquidity and tax effects are important in explaining the returns to Fannie Mae bonds. The results also indicate that the market does not incorporate changes in the riskiness of the mortgage market into the returns on Fannie Mae bonds. The results provide support for the contention that Fannie Mae, as a government sponsored enterprise, enjoys a significant advantage over other firms in the capital market.     

Intermarket efficiency: An application of interbattery APT to mortgage-backed securities

Increasing popularity of investments in mortgage-backed securities has led to closer integration of the mortgage market into traditional capital markets. Using monthly returns during 1982–1988 for common stocks, Treasury bonds and GNMA and FHLMC mortgage-backed securities, the interbattery factor analytic Arbitrage Pricing Theory of (Cho, 1984) is used to test five hypotheses for intramarket and intermarket integration. Results indicate that three to five common factors are found within the same security market, while only one to three factors are found common between different markets.The APT could not be rejected within the same security market, but was rejected in most intermarket comparisons. While risk-free rates are found to differ between markets, the risk premium tests are conclusive indicators of integration. Our results support claims that the stock, bond, and the mortgage-backed securities markets are integrated.     

Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis

We present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied.     

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.     

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.     

Real‐Time Risk Pricing Over the Business Cycle: Some Evidence for the UK

Abstract:   The fully‐revised data typically utilized in empirical research do not reflect the true information available to financial market participants at the time of their decision‐making. This paper uses a new real‐time macroeconomic dataset to appraise the relative importance of different vintages of data on economic variables as determinants of UK stock returns using the framework of Arbitrage Pricing Theory. We find that two factors influence expected stock returns, namely unanticipated inflation and economic uncertainty, but only when measured in real‐time. Moreover, their pricing influence is only present during phases of the business cycle when their associated risks are at their most prevalent.     

On Testing the Arbitrage Pricing Theory: Inter-Battery Factor Analysis

This paper tests the Arbitrage Pricing Theory (APT) by estimating the factor loadings that are consistent between two industry groups of securities. One of the pitfalls in the study by Roll and Ross is that the factors estimated in one group may not be the same with the factors estimated in another group. This raises some concerns on the acceptability of their conclusions. For our study, we employ inter-battery factor analysis which enables us to estimate factor loadings by constraining the factors to be the same between two different groups. Our results show that there seem to be five or six inter-group common factors that generate daily returns for two industry groups of securities, and these inter-group common factors do not seem to depend on the size of groups. Also, based on our cross-sectional tests on the risk premia, we conclude that the APT should not be rejected.     

w-MPS risk aversion and the shadow CAPM: theory and empirical evidence

This paper presents the shadow capital asset pricing model (CAPM) of Ma [2011a. Advanced Asset Pricing Theory. London: Imperial College Press] as an intertemporal equilibrium asset pricing model, and tests it empirically. In contrast to the classical CAPM – a single-factor model based on a strong behavioral or distributional assumption – the shadow CAPM can be represented as a two-factor model, and only requires a modest behavioral assumption of weak form mean-preserving spread risk aversion. The empirical tests provide support in favor of the shadow CAPM over the classical CAPM, the consumption CAPM, or the Epstein and Zin [1991. “Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis”. Journal of Political Economy 99, 263–286] model. Moreover, the shadow CAPM provides a consistent explanation for the cross-sectional variations of expected returns on the stocks and for the time-varying equity premium.     

Alpha or beta in the eye of the beholder: What drives hedge fund flows?

Capital Asset Pricing Model (CAPM) alpha explains hedge fund flows better than alphas from more sophisticated models. This suggests that investors pool together sophisticated model alpha with returns from exposures to traditional (except for the market) and exotic risks. We decompose performance into traditional and exotic risk components and find that while investors chase both components, they place greater relative emphasis on returns associated with exotic risk exposures that can only be obtained through hedge funds. However, we find little evidence of persistence in performance from traditional or exotic risks, which cautions against investors’ practice of seeking out risk exposures following periods of recent success.     

Approximate Factor Structures: Interpretations and Implications for Empirical Tests

This paper provides some new insights about approximate factor structures, as defined by Chamberlain and Rothschild [2], and their implications for empirical tests. First, we show that any economy that satisfies an approximate factor structure can be transformed, in a manner that does not alter the characteristics of investor portfolios, into an economy that satisfies an exact factor structure, as defined by Ross [9]. Second, we show that principal components analysis represents just one of many methods of forming groups of well-diversified portfolios with no idiosyncratic risk in large samples. Correct factor loadings will be obtained by regressing security returns on any group of these portfolios. Our interpretations of the Chamberlain and Rothschild results also provide additional insights into the testability of the Arbitrage Pricing Theory. We show that securities cannot be repackaged to hide factors in the manner suggested by Shanken [10] without the variance of some of the repackaged securities approaching infinity in large economies.     

A MULTIVARIATE TEST OF THE GENERALISED MEAN-LOWER PARTIAL MOMENT ASSET PRICING MODEL: AUSTRALIAN EVIDENCE

This paper tests the Mean-Lower Partial Moment (MLPM) model of asset pricing, using the Gibbons (1982) multivariate methodology, as developed by Hariow and Rao (1989). The MLPM model specifies risk to be a measure of the downside deviations of return relative to a prespecified and exogenous target rate of return. The MLPM model of Hariow and Rao is a new model which has only been tested once, using US data. Therefore, further tests using independent data will help to assess whether the model deserves more serious consideration as a possible alternative to the Capital Asset Pricing Model (CAPM). In general, tests in this paper using Australian data confirm the results of Hariow and Rao (1989). The MLPM model cannot be rejected against an unspecified alternative, nor can it be rejected against the zero-beta CAPM. Conditional on the MLPM model's validity, the optimal target rate appears to be more closely related to mean market returns than either to a risk-free return or to a zero return. In addition, there is some evidence to support an intertemporally constant target rate of around 3 percent per month, over the 30 year period examined.     

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.     

Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.     

An Examination of UK Unit Trust Performance within the Arbitrage Pricing Theory Framework

This paper examines the performance of a sample of 101 United Kingdom unit trusts within an Arbitrage Pricing Theory framework and considers the relationship between performance and the investment objective, size and expenses of the trusts. Also, portfolio strategies using past trust performances to rank the trusts fails to generate significant abnormal returns relative to two different benchmark portfolios.     

A Cross-Sectional Empirical Test of a Dual-State Multi-Factor Pricing Model

During empirical testing of the Capital Asset Pricing Model an assumption is typically made that risk is intertemporally constant. However, prior research finds that risk changes over time. We empirically test a conditional dual-state cross-sectional model allowing risk to change through prior identification of different market and economic states. We examine relationships between returns and conditional market and economic-factor betas, size, book-to-market equity, and earnings-price ratios. We find that relationships shift across regimes, suggesting the importance of a conditional, as opposed to unconditional, model. Relationships also change in January.     

Factor pricing in a finite economy

Prior theoretical derivations of the Arbitrage Pricing Theory (APT) bound an aggregate measure of the deviation of mean asset returns from that predicted by a linear pricing equation. It is conceivable, given this bound, that some assets might be badly mispriced by the model. In this paper, a more intuitive derivation of the factor pricing equation is presented which describes the deviation on an asset by asset basis. The deviation is shown to be small for assets in a realistic finite economy and is arbitrarily close to zero for those assets with arbitrarily small size relative to aggregate wealth. It follows that the linear pricing equation provides a good approximation for the mean returns of all traded assets.