Sensitivity of Multivariate Tests of the Capital Asset-Pricing Model to the Return Measurement Interval

The capital asset-pricing model's (CAPM) primary empirical implication is a positively sloped linear relation between a security's expected rate of return and its relative risk (beta). Recent research indicates that inferences about the risk-return relation are sensitive to the choice of the return measurement interval. We perform multivariate tests of the Sharpe-Lintner CAPM using monthly and annual returns on market-value-ranked portfolios. The CAPM is rejected using monthly returns, a result consistent with previous research. In contrast, we fail to reject the CAPM when annual holding period returns are used.     

CAPM for estimating the cost of equity capital: Interpreting the empirical evidence

We argue that the empirical evidence against the capital asset pricing model (CAPM) based on stock returns does not invalidate its use for estimating the cost of capital for projects in making capital budgeting decisions. Because stocks are backed not only by projects in place, but also by the options to modify current projects and undertake new ones, the expected returns on stocks need not satisfy the CAPM even when expected returns of projects do. We provide empirical support for our arguments by developing a method for estimating firms' project CAPM betas and project returns. Our findings justify the continued use of the CAPM by firms in spite of the mounting evidence against it based on the cross section of stock returns.     

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.     

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.     

Monotonicity in asset returns: New tests with applications to the term structure,the CAPM,and portfolio sorts

Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model (CAPM) implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.     

Risk Interpretation of the CAPM's Beta: Evidence from a New Research Method

This study tests the validity of using the CAPM beta as a risk control in cross‐sectional accounting and finance research. We recognize that high‐risk stocks should experience either very good or very bad returns more frequently compared to low‐risk stocks, that is, high‐risk stocks should cluster in the tails of the cross‐sectional return distribution. Building on this intuition, we test the risk interpretation of the CAPM's beta by examining if high‐beta stocks are more likely than low‐beta stocks to experience either very high or very low returns. Our empirical results indicate that beta is a strong predictor of large positive and large negative returns, which confirms that beta is a valid empirical risk measure and that researchers should use beta as a risk control in empirical tests. Further, we show that because the relation between beta and returns is U‐shaped, that is, high betas predict both very high and very low returns, linear cross‐sectional regression models, for example, Fama–MacBeth regressions, will fail on average to reject the null hypothesis that beta does not capture risk. This result explains why previous studies find no significant cross‐sectional relation between beta and returns.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

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.     

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.     

行为模型新解及其实证检验

在以信息逐步扩散和投资者有限理性为主要假设的行为模型中,特定信息交易者和市场信息交易者的比例对股价行为有着重要影响：当特定信息交易者占多数时,个股收益更容易呈现正自相关;当市场信息交易者占多数时,个股收益更容易呈现负自相关。该模型可以解释成熟股市中存在基于总收益的动量效应,而中国股市中不存在基于总收益的动量效应,仅存在基于公司特定收益的动量效应;并解释了市场平均收益呈现负自相关等。另外,实证分析支持了传统的CAPM和APT定价模型中的带越小,动量效应越显著的结论。     

Some Tests of the Risk-Return Relationship Using Alternative Asset Pricing Models and Observed Expected Returns

This study examines the performance of three asset pricing models: the CAPM, the APT and the UAPT using observed expected returns from a three-phase dividend discount model with Value Line analyst estimates of future company-level earnings, dividends and growth rates. Our study is the first we know of to test the three major asset pricing models using observed expected returns. Our results are similar to prior research using ex post (realized) returns in that we find that the UAPT using macroeconomic factors is the best performing model, followed by the APT and the CAPM. However, our results also suggest that the importance of macroeconomic factors is much greater to expected returns than to realized returns, and the corresponding R2 values for models using expected returns are much higher than for models using realized returns. Combining our results for the UAPT with those of Marston and Harris (1993) for the CAPM suggests that these models are more successful in tests using observed expected returns than in tests using realized returns as proxies for expected returns. Unit root tests suggest that monthly observed expected returns follow the classic random walk without drift model while monthly realized returns do not.     

Betting against sentiment? Seemingly unrelated anomalies and the low-risk effect

The negative CAPM alphas of high-beta and high-variance stocks are attributable to an unaccounted factor in the CAPM. We use eight seemingly unrelated anomalies to construct a composite factor in the spirit of the optimal orthogonal portfolio (FOP). Accounting for FOP re-establishes a positive relation between beta and average returns in time series regressions as well as cross-sectional and explains the negative alphas of high-beta and high-variance stocks. To analyze economic drivers behind FOP, we perform a horse race between leverage constraints, investor sentiment, and disagreement. Our results highlight investor sentiment as the most promising explanation for the low-risk effect.     

Accounting for the Accuracy of Beta Estimates in CAPM Tests on Assets with Time-varying Risks

This paper advocates two ways to make more efficient use of available information in reducing the bias of the risk premium estimate in two-pass tests of the CAPM. First, explicit modelling of the time-variability of betas can improve the accuracy of the beta forecasts. Second, the cross-sectional information available can be exploited more efficiently using individual stocks instead of portfolios provided that noisy beta predictions are given a smaller weight than more accurate ones. This paper proposes an adjustment of the cross-sectional regressions of excess returns against betas to give larger weights to more reliable beta forecasts. A significant positive relationship between returns and the beta forecast is obtained when the proposed approach is applied to data from the Helsinki Stock Exchange, while the traditional Fama–MacBeth approach as such finds no relationship at all.     

Time-varying risk in the German stock market

This paper compares two specifications of the Capital Asset Pricing Model for a sample of German stocks. The specifications generate time-varying first and second moments by conditioning on past information. This explicit modelling of the time series behaviour of risk allows us to characterize the driving factors of variances and covariances of returns. In addition to a variety of diagnostic tests we evaluate the validity of the one-factor restriction in the CAPM. The main findings are that risk is time dependent and very variable and also that more than one factor is needed to fit the data set.     

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.     

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.     

Testing the CAPM with Time-Varying Risks and Returns

This paper draws on Engle's autoregressive conditionally heteroskedastic modeling strategy to formulate a conditional CAPM with time-varying risk and expected returns. The model is estimated by generalized method of moments. A CAPM that allows mean excess returns to shift in January survives generalized method of moments specification tests for a number of omitted variables. However, a residual dividend yield component is found to remain in the excess returns of smaller firms. We find significant monthly and quarterly components in the risk premia and beta estimates.     

On the power of cross-sectional and multivariate tests of the CAPM

This paper examines the power of the cross-sectional and multivariate tests of the CAPM under ideal conditions. When the CAPM is true the positively weighted market portfolio is MV-efficient and securities plot on the security market line. When the CAPM is false an alternative asset pricing model determines prices. An examination of the population intercepts, slopes and R² from cross-sectional regressions of expected returns on betas indicates that all three are unreliable indicators of whether the CAPM holds. Simulation analysis of the power of the cross-sectional tests expands on and reinforces the analysis based on the population values. The Gibbons et al. (1989) multivariate test fares much better.     

The Value Premium and the CAPM

We examine (1) how value premiums vary with firm size, (2) whether the CAPM explains value premiums, and (3) whether, in general, average returns compensate β in the way predicted by the CAPM. Loughran's (1997) evidence for a weak value premium among large firms is special to 1963 to 1995, U.S. stocks, and the book‐to‐market value‐growth indicator. Ang and Chen's (2005) evidence that the CAPM can explain U.S. value premiums is special to 1926 to 1963. The CAPM's more general problem is that variation in β unrelated to size and the value‐growth characteristic goes unrewarded throughout 1926 to 2004.