It takes a model to beat a model: Volatility bounds

Models like the CAPM and Fama–French three-factor models are commonly used as benchmarks for calculating cost of capital and evaluating portfolio performance, despite the empirical evidence to reject them. For many practical purposes, “it takes a model to beat a model.” In this paper we derive restrictions on models that could “beat” a bench-mark model but might still be misspecified. In these “takes-a-model-to-beat-a-model” (TMBM) bounds, model A beats model B if model A's quadratic form of pricing errors is smaller. The bounds generalize the Hansen–Jagannathan bound and distance measure. We use the TMBM bounds to evaluate various linear factor models and consumption-based models. The failure of the power utility model is much less extreme when it is compared with the CAPM and Fama–French model. For reasonable utility curvature, the Ferson–Constantinides model and Epstein–Zin model perform best among the consumption-based models, beating the model of Campbell and Cochrane, in which model the value of the persistence parameter that matches the time-series properties of aggregate stock market returns seems too low for cross-sectional asset pricing.     

The Conditional Relationship Between Beta and Returns: A Reassessment

Abstract:  Several recent empirical tests of the Capital Asset Pricing Model have been based on the conditional relationship between betas and market returns. This paper shows that this method needs reconsideration. An adjusted version of this test is presented. It is then demonstrated that the adjusted technique has similar, or lower, power to the more easily implemented CAPM test of Fama and MacBeth (1973) if returns are normally distributed.     

Time-varying betas and the cross-sectional return–risk relation: evidence from the UK

The seminal study by Fama and MacBeth in 1973 initiated a stream of papers testing for the cross-sectional relation between return and risk. The debate as to whether beta is a valid measure of risk was reanimated by Fama and French and subsequent studies. Rather than focusing on exogenous variables that have a larger explanatory power than an asset's beta in cross-sectional tests, the matrix of variances-covariances is assumed to follow a time varying ARCH process. Using monthly data from the UK market from February 1975 to December 1996, the cross-sectional return–risk relations obtained with an unconditional specification for assets’ betas are compared to those obtained when the estimated betas are based on an ARCH model. The approach taken by Pettengill, Sundaram and Mathur, which allows a negative cross sectional return–risk relation in periods in which the market portfolio yields a negative return relative to the risk free rate, was also investigated. These tests are also carried out on samples pertaining to a specific month and on samples from which a particular month is removed. Results suggest that the CAPM holds better in downward moving markets than in upward moving markets hence beta is a more appropriate measure of risk in bear markets.     

Does Money Explain Asset Returns? Theory and Empirical Analysis

A cash-in-advance model of a monetary economy is used to derive a money-based CAPM (M-CAPM), which allows us to implement tests of asset pricing restrictions without consumption data. A test as in Fama and MacBeth of the model suggests that the money betas have some explanatory power for the cross-sectional variation of expected returns; however, the model is rejected using conditional information. Consistent with our predictions, estimates of the curvature parameter are lower than those of the consumption CAPM (C-CAPM) and pricing errors of the M-CAPM tend to be smaller than those of the C-CAPM.     

Evaluating asset pricing models in the Korean stock market

This paper evaluates and compares asset pricing models in the Korean stock market. The asset pricing models considered are the CAPM, APT-motivated models, the Consumption-based CAPM, Intertemporal CAPM-motivated models, and the Jagannathan and Wang conditional CAPM model. By using various test portfolios as well as individual stocks, we conduct time-series tests and cross-sectional regression tests based on individual t-tests, the joint F-tests, the Hansen and Jagannathan (1997) distance, and R-squares. Overall, the Fama and French (1993) five-factor model performs most satisfactorily among the asset pricing models considered in explaining the intertemporal and cross-sectional behavior of stock returns in Korea. The Fama and French (1993) three-factor model, the Chen et al. (2010) three-factor model, and the Campbell (1996) model are the next. The results indicate that the two bond portfolios, term spread and default spread, play an important role in explaining stock returns in Korea.     

Testing multi-beta asset pricing models

This paper presents a complete solution to the estimation and testing of multi-beta models by providing a small sample likelihood ratio test when the usual normality assumption is imposed and an almost analytical GMM test when the normality assumption is relaxed. Using 10 size portfolios from January 1926 to December 1994, we reject the joint efficiency of the CRSP value-weighted and equal-weighted indices. We also apply the tests to analyze a new version of Fama and French's [Fama, E.F., French, K.R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics. 33, 3–56.] three-factor model in addition to two standard ones, and find that the new version performs the best.     

The Robustness of the APT to Alternative Estimators

We test the robustness of the APT to two alternative estimation procedures: the Fama and MacBeth (1973) two-step methodology; and the one-step procedure due to Burmeister and McElroy (1988). We find that the APT is indeed sensitive to the chosen estimator and assumptions about the factor structure of stock returns. We believe that our findings have implications for the estimation of asset pricing models in general.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

中国股票市场流动性风险溢价研究

本文在对Fama三因素模型和LACAPM模型进行改进的基础上,实证研究了中国股票市场的流动性风险溢价、规模效应以及价值效应。实证结果发现,改进的FAMA三因素模型能够比CAPM更好地解释价值效应,但却不能解释规模效应和流动性风险溢价现象;而改进的LACAPM在解释市场异象上的有效性则明显优于其他定价模型。     

Estimation of expected return: CAPM vs. Fama and French

Most practitioners favour a one-factor model (CAPM) when estimating expected return for an individual stock. For estimation of portfolio returns, academics recommend the Fama and French three-factor model. The main objective of this paper is to compare the performance of these two models for individual stocks. First, estimates for individual stock returns based on CAPM are obtained using different time frames, data frequencies, and indexes. It is found that 5 years of monthly data and an equal-weighted index, as opposed to the commonly recommended value-weighted index, provide the best estimate. However, performance of the model is very poor; it explains on average 3% of differences in returns. Then, estimates for individual stock returns are obtained based on the Fama and French model using 5 years of monthly data. This model, however, does not do much better; independent of the index used, it explains on average 5% of differences in returns. These results therefore bring into question the use of either model for estimation of individual expected stock returns.     

Testing Conditional Asset Pricing Models Using a Markov Chain Monte Carlo Approach

We use Markov Chain Monte Carlo (MCMC) methods for the parameter estimation and the testing of conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors‐in‐variables. Using S&P 500 panel data, we analyse the empirical performance of the CAPM and the Fama and French (1993) three‐factor model. We find that time‐variation of betas in the CAPM and the time variation of the coefficients for the size factor (SMB) and the distress factor (HML) in the three‐factor model improve the empirical performance. Therefore, our findings are consistent with time variation of firm‐specific exposure to market risk, systematic credit risk and systematic size effects. However, a Bayesian model comparison trading off goodness of fit and model complexity indicates that the conditional CAPM performs best, followed by the conditional three‐factor model, the unconditional CAPM, and the unconditional three‐factor model.     

Return Distributions and Improved Tests of Asset Pricing Models

We compare and contrast some existing ordinary least squares(OLS)- and generalized method of moments (GMM)-based tests ofasset pricing models with a new more general test. This newtest is valid under the assumption that returns are ellipticallydistributed, a necessary and sufficient assumption of the linearcapital asset pricing model (CAPM). This new test fails to rejectthe CAPM on a dataset of stocks sorted by market valuations,whereas similar tests constructed from OLS and GMM estimationmethods reject the linear CAPM. We also find that outliers reducethe OLS-estimated mispricing of the linear CAPM on monthly returnssorted by previous performance, that is, momentum. Monte Carloevidence supports superior size and power properties of thenew test relative to OLS- and GMM-based tests.     

Quality of PIN estimates and the PIN-return relationship

This paper provides new evidence concerning the probability of informed trading (PIN) and the PIN-return relationship. We take measures to overcome known estimation biases and improve the quality of quarterly PIN estimates. We use the average of a firm’s PIN estimates in four consecutive quarters to smooth out the effect of seasonal variation in trading activities. We find that when high-quality PIN estimates are used, the Fama–MacBeth cross-sectional regressions show stronger evidence for the positive PIN-return relationship than documented in the prior literature. This finding is robust to controls for the January, liquidity, and momentum effects.     

Pricing innovations in consumption growth: A re-evaluation of the recursive utility model

We re-evaluate the cross-sectional asset pricing implications of the recursive utility function of  and , using innovations in future consumption growth in our tests. Our empirical specification helps explain the size, value and momentum effects. Specifically, we find that (?) the beta associated with news about consumption growth has a systematic pattern: beta decreases along the size dimension and increases along the book-to-market and momentum dimensions, (??) innovation in consumption growth is significantly priced in asset returns using both the Fama and MacBeth (1973) and the stochastic discount factor approaches, and (???) the model performs better than both the CAPM and Fama–French model.     

Can An 'Estimation Factor' Help Explain Cross-Sectional Returns?

Abstract:  We show in a theoretical model that the expected excess return on any asset depends on its covariance not only with the market portfolio, but also with changes in the representative agent's estimate. We test our model using GMM and compare it to the CAPM. The results suggest that adding an 'estimation factor' to the CAPM helps explain cross-sectional returns and that, unconditionally, this estimation factor carries a negative risk premium.     

Financial Sector Risk and the Stock Returns: Evidence from Tokyo Stock Exchange Firms

We investigate whether the activity of financial firms creates value and/or risk to the economy within the asset pricing framework. We use stock return data from nonfinancial firms listed in the first section of the Tokyo Stock Exchange. The value-weighted index that is solely composed of nonfinancial firms is augmented with the index of the firms from the financial sector, and we estimate multivariate asset pricing model with these two indices. We note that our procedure can simultaneously take into account the cross-holding phenomena among Japanese firms, especially between the financial sector and the nonfinancial sector. Our augmented index model performs well both with cross-sectional Fama and MacBeth regression test and GMM test. Our two index model with additional Fama and French's HML factor can capture cross-sectional variations of the returns of sample portfolios better than the original Fama and French model can, when measured by Hansen and Jagannathan distance measure. We find that this additional new sector variable can be a substitute for Fama and French's size factor, but not related to the bond index return. This variable has similar factor characteristic as money supply growth or the term structure, but the latter variables contain more information than the former. Morever, our financial sector model helps explain the return and risk structure of Japanese firms during the so-called bubble period.     

Asset Pricing with Conditioning Information: A New Test

This paper presents a new test of conditional versions of the Sharpe-Lintner CAPM, the Jagannathan and Wang (1996) extension of the CAPM, and the Fama and French (1993) three-factor model. The test is based on a general nonparametric methodology that avoids functional form misspecification of betas, risk premia, and the stochastic discount factor. Our results provide a novel view of empirical performance of these models. In particular, we find that a nonparametric version of the Fama and French model performs well, even when challenged by momentum portfolios.     

Conditional coskewness and asset pricing

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.     

Reports of beta's death are premature: Evidence from the UK

A number of authors have found that firm size and book-to-market-value capture the cross-sectional variation in average stock returns. More importantly, these variables have been shown to out-perform the CAPM's β coefficient in explaining the cross-section of US stock returns. However, these studies all employ variants of the two-step estimator due to Fama and MacBeth (Fama, E.F., MacBeth, J.D., 1973. Risk, return and equilibrium: Empirical tests. Journal of Political Economy 71, 607–636), which impose implicitly the restriction that idiosyncratic returns are uncorrelated. In this paper we use a one-step estimator due to McElroy et al. (McElroy, M.B., Burmeister, E., Wall, K.D., 1985. Two estimators for the APT model when factors are measured. Economics Letters 19, 271–275) and find a highly significant role for β risk in the UK stock market when we allow for correlation amongst idiosyncratic returns.     

Alternative beta risk estimators and asset pricing tests in emerging markets: The case of Pakistan

This paper tests and compares the applicability of two asset pricing models specifically, the CAPM and the Fama–French three factor models for an emerging stock market namely, Pakistan. The paper analyses a number of beta risk estimators, including OLS, the Dimson thin trading estimator, a trade-to-trade estimator and a sample selectivity estimator. To uncover any possible influence of the return interval and the type of the market index, the analysis is carried out on three data frequencies namely daily, weekly and monthly as well as for a value and an equally weighted market index. The alternative beta estimators appear to correct thin trading bias but their effects on asset pricing tests are not visible. Moreover contrary to the expectations the test results for monthly and weekly frequencies are not promising. Instead for daily data the cross-section of returns are explained by a number of risk factors and trading volume.