Tests Of Asset Pricing Models Research Articles

Why Does an Equal-Weighted Portfolio Outperform Value- and Price-Weighted Portfolios?

Does the choice of weighting scheme used to form test portfolios influence inferences drawn from empirical tests of asset pricing? To answer this question we first show that, with monthly rebalancing, an equal-weighted portfolio outperforms a value-weighted portfolio in terms of total mean return, four-factor alpha, and Sharpe ratio. We then explain that this outperformance is partly because the equal-weighted portfolio has higher exposure to systematic risk factors; but, a considerable part (42%) of the outperformance comes from the difference in alphas, which is a consequence of the rebalancing to maintain constant weights in the equal-weighted portfolio. Finally, we demonstrate that the inferences drawn from tests of asset-pricing models are substantially different depending on whether one uses equal- or value-weighted test portfolios. We illustrate this by considering four applications: (1) a test of the CAPM, using the methodology of Gibbons, Ross, and Shanken (1989); (2) a test of the spanning properties of the stochastic discount factor, using the approach of Hansen and Jagannathan (1991); (3) a test of the relation between characteristics and returns, using the multivariate weighted two-stage procedure of Fama and MacBeth (1973); and (4) a test of whether expected idiosyncratic volatility is priced or not, using the non-parametric methodology of Patton and Timmermann (2010). For all four tests, we explain how the weighting scheme influences our inferences.

Evaluating alternative methods for testing asset pricing models with historical data

We follow the correct Jagannathan and Wang (2002) framework for comparing the estimates and specification tests of the classical Beta and Stochastic Discount Factor/Generalized Method of Moments (SDF/GMM) methods. We extend previous studies by considering not only single but also multifactor models, and by taking into account some of the prescriptions for improving empirical tests suggested by Lewellen, Nagel and Shanken (2009). Our results reveal that SDF/GMM first-stage estimators lead to lower pricing errors than OLS, while SDF/GMM second-stage estimators display higher pricing errors than the classical Beta GLS method. While Jagannathan and Wang (2002), and Cochrane (2005) conclude that there are no differences when estimating and testing by the Beta and SDF/GMM methods for the CAPM, we show that their conclusion can not be extensible for multifactor models. Moreover, the Beta method (OLS and GLS) seem to dominate the SDF/GMM (first and second-stage) procedure in terms of estimators’ properties. These results are consistent across benchmark portfolios and sample periods.

Multivariate tests of asset pricing: simulation evidence from an emerging market

The finite sample performance of the Wald, GMM and Likelihood Ratio (LR) tests of multivariate asset pricing tests have been investigated in several studies on the US financial markets. This paper extends this analysis in two important ways. Firstly, considering the fact that the Wald test is not invariant to alternative non-linear formulation of the null hypothesis the paper investigates whether alternative forms of the Wald and GMM tests result in considerable difference in size and power. Secondly, the paper extends the analysis to the emerging market data. Emerging markets provide an interesting practical laboratory to test asset pricing models. The characteristics of emerging markets are different from the well developed markets of US, Japan and Europe. It is found that the asymptotic Wald and GMM tests based on Chi-Square critical values result in considerable size distortions. The bootstrap tests yield the correct sizes. Multiplicative from of bootstrap GMM test appears to outperform the LR test when the returns deviate from normality and when the deviations from the asset pricing model are smaller. Application of the bootstrap tests to the data from the Karachi Stock Exchange strongly supports the zero-beta CAPM. However the low power of the multivariate tests warrants a careful interpretation of the results.

Benchmark Concentration: Capitalization Weights Versus Equal Weights in the FTSE 100 Index

Identifying a suitable benchmark is essential when testing asset pricing models, measuring the performance of active investors, or providing market proxy portfolios for passive investors. Concern that increased domination of capitalization weighted stock indices by a few large firms will lead to inefficient portfolio diversification is leading some investors and researchers to argue that index providers should adjust their weighting methods to limit concentration. This study tests and rejects the hypothesis that concentration arising as a result of capitalization weights in the FTSE 100 Index increases risk, either during normal market conditions or during negative tail events in the return distribution. On the contrary, during the left tail of the return distribution, the equally weighted portfolio of FTSE 100 Index constituents exhibits higher risk and lower returns than the capitalization weighted FTSE 100 Index portfolio, a finding consistent with variations of the CAPM that allow for time varying risk premia.(JEL: G11, G12, G14)

Pricing Currency Risk in the Stock Market: Evidence from Finland and Sweden 1970-2009

We investigate the role of currency risk on stock markets in two interlinked Nordic countries exhibiting a gradual move from fixed to floating exchange rates. We apply the Ding and Engle (2001) covariance stationary specification in a multivariate GARCH-M setup to test a conditional international asset pricing model. Using a sample period from 1970 to 2009, we find that the currency risk is priced in both stock markets, and that the price and the risk premium are lower after the floatation of the currencies, especially for Finland. We also find the cross-country exchange rate shock from Finland to affect the price of currency risk in Sweden, but not vice versa. Finally, we discuss some of the potential issues in applying multivariate GARCH-M specifications in tests of asset pricing models.

A net beta test of asset pricing models

While many recent empirical studies of the CAPM have used conditional beta tests, this technique has recently been shown to have several weaknesses. Here we introduce a new, more robust, net beta test which shares a number of characteristics with conditional beta tests. The method is extended to the multi-factor case when there are mimicking portfolios of assets for the underlying factors, including the Fama–French three-factor model. We demonstrate theoretically, by simulation and using market data that the net beta estimators have lower standard errors than those generated by the standard Fama–MacBeth test.

The Impact of Large Changes in Asset Prices on Intra‐Market Correlations in the Domestic and International Markets

AbstractWe consider the impact of “large” changes in asset prices on intra‐market correlations in domestic and international markets. Assuming normally distributed asset returns, we show that the absolute magnitude of the correlation, conditional on a change is greater than or equal to a given absolute size of one of the variables, is monotonically increasing in the magnitude of that absolute change. Empirical tests using domestic and international‐market data support this theoretical result. These results have significant implications for portfolio management, hedging interest rate risk, tests of asset pricing models, Roll's concern with asset pricing models' explanatory power, and implementation of Value‐at‐Risk.

Time varying consumption covariance and dynamics of the equity premium: Evidence from the G7 countries

Abstract We examine implications of time-varying correlation and covariance between excess equity returns and consumption growth for the equity premium of the G7 countries. We find that the correlation and covariance are higher when there is a negative shock to labor income and a positive shock to returns. The combined effect is that the correlation and covariance are countercyclical and so is the equity premium. We test asset pricing models with time-varying consumption risk and find that the conditional price of risk is generally positive. These results survive several robustness checks. Our results highlight the importance of labor income for understanding dynamics of the equity premium.

A robustness test of asset-pricing models using individual security returns

Tests of asset-pricing models typically form portfolios of stocks (based on criteria such as market capitalization and book-to-market values). The validity of this approach has been debated (see, for example, Berk, 2000). We consider a simple method of testing asset-pricing models using the returns of individual securities and illustrate the approach in a test of the robustness of analyses reported by Durand et al. (2006) and Limkriangkrai et al. (2008).

Improvement in finite sample properties of the Hansen–Jagannathan distance test

Jagannathan and Wang [Jagannthan, R., and Wang, Z., “The conditional CAPM and the cross-section of expected returns.” Journal of Finance, 51 (1996), 3–53] derive the asymptotic distribution of the Hansen–Jagannathan distance (HJ-distance) proposed by Hansen and Jagannathan [Hansen, L.P., and Jagannathan, R., Assessing specific errors in stochastic discount factor models." Journal of Finance, 52 (1997), 557–590], and develop a specification test of asset pricing models based on the HJ-distance. While the HJ-distance has several desirable properties, Ahn and Gadarowski [Ahn, S.C., and Gadarowski, C., “Small sample properties of the GMM specification test based on the Hansen–Jagannathan distance.” Journal of Empirical Finance, 11 (2004), 109–132] find that the specification test based on the HJ-distance overrejects correct models too severely in commonly used sample size to provide a valid test. This paper proposes to improve the finite sample properties of the HJ-distance test by applying the shrinkage method [Ledoit, O., and Wolf, M., “Improved estimation of the covariance matrix of stock returns with an application to portfolio selection.” Journal of Empirical Finance, 10 (2003), 603–621] to compute its weighting matrix. The proposed method improves the finite sample performance of the HJ-distance test significantly.

The Link between Fama-French Time-Series Tests and Fama-Macbeth Cross-Sectional Tests

Many papers in the empirical finance literature implement tests of asset pricing models either via Fama-French time-series regressions or via Fama-Macbeth cross-sectional regressions. This short paper explains their conceptual relationships. There is a time-series equivalent method to implementing Fama-Macbeth regressions (in a stable world). This correspondence also helps to clarify the interpretation of the estimates from the two methods: The Fama-Macbeth test is better suited for APT tests, while the plain Fama-French test is better suited for equilibrium tests. (Of course, all equilibrium model must be arbitrage-free, but not vice-versa.) It is possible to test not only whether factors can price portfolios in an equilibrium framework, but also the less restrictive requirement that the factors should not allow for arbitrage. For example, this short paper shows that the Fama-French 3-factor model fails the weaker arbitrage pricing restriction for the the 2x3 Fama-French portfolios, and not just the stronger equilibrium pricing restriction.

Finite sample multivariate tests of asset pricing models with coskewness

Exact inference methods are proposed for asset pricing models with unobservable risk-free rates and coskewness; specifically, the Quadratic Market Model (QMM) which incorporates the effect of asymmetry of return distribution on asset valuation. In this context, exact tests are appealing given (i) the increasing popularity of such models in finance, (ii) the fact that traditional market models (which assume that asset returns move proportionally to the market) have not fared well in empirical tests, (iii) finite sample QMM tests are unavailable even with Gaussian errors. Empirical models are considered where the procedure to assess the significance of coskewness preference is LR-based, and relates to the statistical and econometric literature on dimensionality tests which are interesting in their own right. Exact versions of these tests are obtained, allowing for non-normality of fundamentals. A simulation study documents the size and power properties of asymptotic and finite sample tests. Empirical results with well-known data sets reveal temporal instabilities over the full sampling period, namely 1961–2000, though tests fail to reject the QMM restrictions over 5-year sub-periods.

Specification tests of asset pricing models using excess returns

In this paper, we discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. We point out that the popular way of specifying the stochastic discount factor (SDF) as a linear function of the factors is problematic because (1) the specification test statistic is not invariant to an affine transformation of the factors, and (2) the SDFs of competing models can have very different means. In contrast, an alternative specification that defines the SDF as a linear function of the de-meaned factors is free from these two problems and is more appropriate for model comparison. In addition, we suggest that a modification of the traditional Hansen–Jagannathan distance (HJ-distance) is needed when we use the de-meaned factors. The modified HJ-distance uses the inverse of the covariance matrix (instead of the second moment matrix) of excess returns as the weighting matrix to aggregate pricing errors. Asymptotic distributions of the modified HJ-distance and of the traditional HJ-distance based on the de-meaned SDF under correctly specified and misspecified models are provided. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification. We show that failure to take model misspecification into account is likely to understate the standard errors of the estimates of the SDF parameters and lead us to erroneously conclude that certain factors are priced.

Empirical Likelihood Estimators for Stochastic Discount Factors

Hansen and Jagannathan (HJ, 1991) provided bounds on the volatility of Stochastic Discount Factors (SDF) that proved extremely useful to diagnose and test asset pricing models. This nonparametric bound reects a duality between the meanstandard deviation frontier for SDFs and the mean-variance frontier for portfolios of asset returns. We extend this fundamental contribution by proposing information bounds that minimize general convex functions of SDFs directly taking into account higher moments of returns. These Minimum Discrepancy bounds reect a duality with nding the optimal portfolio of asset returns with a general HARA utility function. The maximum utility portfolio implies SDF estimators that are based on implied probabilities associated with the class of Generalized Empirical Likelihood estimators. We analyze the implications of these information bounds for the pricing of size portfolios and the performance evaluation of hedge funds.

A Bayesian Panel Data Approach to Explaining Market Beta Dynamics

We characterize the process that drives the market betas of individual stocks by setting up a hierarchical Bayesian panel data model that allows a flexible specification for beta. We show that combining the parametric relationship between betas and conditioning variables specified by economic theory with the robustness of an autoregressive specification delivers superior estimates of firm-specific betas. Our model also improves the accuracy of beta forecasts, which we use to construct optimal portfolios subject to target beta constraints. We further provide empirical support for the prediction of conditional asset pricing theory that individual stocks exhibit different risk dynamics. Finally, we document strong cross-sectional heterogeneity in firm-specific betas within the 25 size-B/M portfolios that are commonly used to test asset pricing models.

On the Calculation of the Risk Free Rate for Tests of Asset Pricing Models

The risk free rate is one of the most often used data series in empirical tests of financial theories. This paper discusses issues in calculating risk free rates from the money market instruments, especially for tests of asset pricing models and event studies. Special attention is given to situations where the maturity of the money market instruments does not match that of the other assets under investigation. This situation typically arises when one has to calculate risk free rates of return for periods shorter (e.g., a day or a week) than the shortest available market rates (e.g., one month) or when the available instruments are issued periodically (e.g., once a week) with fixed maturity.

Prices and Portfolio Choices in Financial Markets: Theory, Econometrics, Experiments

Many tests of asset pricing models address only the pricing predictions - but these pricing predictions rest on portfolio choice predictions which seem obviously wrong. This paper suggests a new approach to asset pricing and portfolio choices, based on unobserved heterogeneity. This approach yields the standard pricing conclusions of classical models but is consistent with very different portfolio choices. Novel econometric tests link the price and portfolio predictions and take account of the general equilibrium effects of sample-size bias. The paper works through the approach in detail for the case of the classical CAPM, producing a model called CAPM+. When these econometric tests are applied to data generated by large-scale laboratory asset markets which reveal both prices and portfolio choices, CAPM+ is not rejected.

Portfolio efficiency and discount factor bounds with conditioning information: An empirical study

Stochastic discount factor bounds provide a useful diagnostic tool for testing asset pricing models by specifying a lower bound on the variance of any admissible discount factor. In this paper, we provide a unified derivation of such bounds in the presence of conditioning information, which allows us to compare their theoretical and empirical properties. We find that, while the location of the ‘unconditionally efficient (UE)’ bounds of [Ferson, W., Siegel, A., 2001. The efficient use of conditioning information in portfolios. Journal of Finance 56 (3), 967–982] is statistically indistinguishable from the (theoretically) optimal bounds of [Gallant, R., Hansen, L., Tauchen, G., 1990. Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution. Journal of Econometrics 45 (1), 141–179] (GHT), the former exhibit better sampling properties. We demonstrate that the difference in sampling variability of the UE and GHT bounds is due to the different behavior of the efficient return weights underlying their construction.

Biases in Decomposing Holding-Period Portfolio Returns

A growing number of studies in finance decompose multiperiod portfolio returns into a series of single-period returns, using these to test asset pricing models or market efficiency or to evaluate the returns to investment strategies such as those based on momentum, size, and value–growth. We provide a formal analysis of the decomposition method. Crucially, we argue and present empirical evidence that some methods researchers use involve portfolios that nobody would seriously consider ex ante, that transactions costs associated with such portfolios make them poor investment vehicles, and that they can lead to spurious statistical inferences.

Specification Tests of Asset Pricing Models Using Excess Returns

In this paper, we discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. We point out that the popular way of specifying the stochastic discount factor (SDF) as a linear function of the factors is problematic because (1) the specification test statistic is not invariant to an affine transformation of the factors, and (2) the SDFs of competing models can have very different means. In contrast, an alternative specification that defines the SDF as a linear function of the de-meaned factors is free from these two problems and is more appropriate for model comparison. In addition, we suggest that a modification of the traditional Hansen-Jagannathan distance (HJ-distance) is needed when we use the de-meaned factors. The modified HJ-distance uses the inverse of the covariance matrix (instead of the second moment matrix) of excess returns as the weighting matrix to aggregate pricing errors. Asymptotic distributions of the modified HJ-distance and of the traditional HJ-distance based on the de-meaned SDF under the correctly specified model and the misspecified models are provided. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification. We show that failure to take model misspecification into account is likely to understate the standard errors of the estimates of the SDF parameters and lead us to erroneously conclude that certain factors are priced.