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.     

Common risk factors in bank stocks

This paper provides evidence on the risk factors that are priced in bank equities. Alternative empirical models with precedent in the nonfinancial asset pricing literature are tested, including the single-factor CAPM, three-factor Fama–French model, and ICAPM. Our empirical results indicate that an unconditional two-factor ICAPM model that includes the stock market excess return and shocks to the slope of the yield curve is useful in explaining the cross-section of bank stock returns. However, we find no evidence that firm specific factors such as size and book-to-market ratios are priced in bank stock returns. These results have a number of important implications for the estimation of the banks’ cost of capital as well as regulatory initiatives to utilize market discipline to evaluate bank risk under Basel II.     

Using the credit spread as an option-risk factor: Size and value effects in CAPM

This paper takes an option-theoretic approach to explain why pricing anomalies are observed when traditional CAPM is used. By extending CAPM to incorporate the option-risk factor of stocks, we show that stockholders’ limited liability can explain Fama and French’s size and value effects. We use bonds’ excess credit spread as a proxy for stocks’ default risk to control for the changing non-diversifiable option-risk characteristic of stocks. Because sensitivity to the excess credit spread becomes smaller as size increases and as value decreases, excess credit spread explains the CAPM anomalies in a fashion similar to the Fama–French factors. While the excess credit spread is significant in explaining Fama and French’s size and value effects, adding the Fama–French factors does not improve the performance of our model. Our revised model resembles conditional CAPM, but it offers a more intuitive explanation for the size and value effects.     

What explains the investment growth anomaly?

We examine if an existing asset pricing model in an unconditional or conditional setting can explain the investment growth anomaly, as represented by higher returns on stocks of the firms with lower growth in capital expenditures. Our results indicate that the conditional Fama–French 3-factor model that allows factor loadings to be time-varying and further linked to firm-level characteristics and the business cycle can explain the anomaly.     

Explaining the Poor Performance of Consumption-based Asset Pricing Models

We show that the external habit-formation model economy of Campbell and Cochrane (1999) can explain why the Capital Asset Pricing Model (CAPM) and its extensions are betterapproximate asset pricing models than is the standard onsumption-based model. The model economy produces time-varying expected eturns, tracked by the dividend–price ratio. Portfolio-based models capture some of this variation in state variables, which a state-independent function of consumption cannot capture. Therefore, though the consumption-based model and CAPM are both perfect conditional asset pricing models, the portfolio-based models are better approximate unconditional asset pricing models.     

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.     

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.     

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.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.     

An examination of alternative CAPM-based models in UK stock returns

We evaluate the performance of unconditional and conditional versions of seven stochastic discount factor models in UK stock returns between January 1975 and December 2001. We find that the conditional four-moment capital asset pricing model (CAPM) has the best performance among the models we consider in terms of the lowest [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 591–607] distance measure and explaining the time-series predictability of industry portfolio excess returns. Conditional models also do a better job than unconditional models. However we find that the superior performance of the conditional four-moment CAPM, and conditional models in general, arises in part due to overfitting the data.     

The critical role of conditioning information in determining if value is really riskier than growth

Conditional asset pricing models have been used to determine whether the value premium and other CAPM anomalies are due to risk. We show that the conclusions on whether these anomalies are due to risk are very sensitive to the choice of the information variables used to define good and bad states of the world. We use a conditional CAPM framework allowing for alternative sets of plausible conditioning information and find that value appears to be riskier than growth in only about ten to twenty percent of specifications. We find even less evidence that size, issuance, momentum, and asset growth portfolio returns are due to risk. Overall, our results suggest that common CAPM anomalies are not due to risk.     

Stock price reaction following large one-day price changes: UK evidence

We examine the short-term price reaction of 424 UK stocks to large one-day price changes. Using the GJR-GARCH(1,1), we find no statistical difference amongst the cumulative abnormal returns (CARs) of the Single Index, the Fama–French and the Carhart–Fama–French models. Shocks ?5% are followed by a significant one-day CAR of 1% for all the models. Whilst shocks ?−5% are followed by a significant one-day CAR of −0.43% for the Single Index, the CARs are around −0.34% for the other two models. Positive shocks of all sizes and negative shocks ?−5% are followed by return continuations, whilst the market is efficient following larger negative shocks. The price reaction to shocks is unaffected when we estimate the CARs using the conditional covariances of the pricing variables.     

The conditional CAPM does not explain asset-pricing anomalies

Recent studies suggest that the conditional CAPM holds, period by period, and that time-variation in risk and expected returns can explain why the unconditional CAPM fails. In contrast, we argue that variation in betas and the equity premium would have to be implausibly large to explain important asset-pricing anomalies like momentum and the value premium. We also provide a simple new test of the conditional CAPM using direct estimates of conditional alphas and betas from short-window regressions, avoiding the need to specify conditioning information. The tests show that the conditional CAPM performs nearly as poorly as the unconditional CAPM, consistent with our analytical results.     

Macroeconomic risk and the cross-section of stock returns

We develop a conditional version of the consumption capital asset pricing model (CCAPM) using the conditioning variable from the cointegrating relation among macroeconomic variables (dividend yield, term spread, default spread, and short-term interest rate). Our conditioning variable has a strong power to predict market excess returns in the presence of competing predictive variables. In addition, our conditional CCAPM performs approximately as well as Fama and French’s (1993) three-factor model in explaining the cross-section of the Fama and French 25 size and book-to-market sorted portfolios. Our specification shows that value stocks are riskier than growth stocks in bad times, supporting the risk-based story.     

A semiparametric conditional capital asset pricing model

This paper proposes using a functional coefficient regression technique to estimate time-varying betas and alpha in the conditional capital asset pricing model (CAPM). Functional coefficient representation relaxes the strict assumptions regarding the structure of betas and alpha by combining the predictors into an index. Appropriate index variables are selected by applying the smoothly clipped absolute deviation penalty. In such a way, estimation and variable selection can be done simultaneously. Based on the empirical studies, the proposed model performs better than the alternatives in explaining asset returns and we find no strong evidence to reject the conditional CAPM.     

A liquidity-augmented capital asset pricing model

Using a new measure of liquidity, this paper documents a significant liquidity premium robust to the CAPM and the Fama–French three-factor model and shows that liquidity is an important source of priced risk. A two-factor (market and liquidity) model well explains the cross-section of stock returns, describing the liquidity premium, subsuming documented anomalies associated with size, long-term contrarian investment, and fundamental (cashflow, earnings, and dividend) to price ratios. In particular, the two-factor model accounts for the book-to-market effect, which the Fama–French three-factor model fails to explain.     

Market proxies as factors in linear asset pricing models: Still living with the roll critique

A new model misspecification measure for linear asset pricing models is proposed for the case where misspecification maps to latency of one of the pricing factors; in this case, the market return. This measure is suited both for testing models that include the market return as a pricing factor in a traditional sense (i.e., whether the chosen model does or does not price a collection of risky assets) and ranking those models (i.e., determining which model performs best). The proposed measure is used in pricing portfolios reflecting the size, value, and momentum premia. The conditional CAPM of Jagannathan and Wang (1996) is found to best the performance of both the simple CAPM and the ICAPM of Petkova (2006). Moreover, it is discovered that winner stocks in a momentum portfolio may have higher market betas than loser stocks.     

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.     

Accounting measures and international pricing models: Justifying accounting homogeneity

We study the importance of homogeneous accounting data when testing international versions of asset pricing models. Specifically, we focus on a pricing model commonly used by practitioners – the Fama–French three-factor model – which uses accounting information and has traditionally performed poorly at the cross-country level. We show that international versions of the model perform significantly better if the accounting information is homogeneous across firms. We apply the model to a set of firms that follow common accounting standards – the IAS/IFRS – and also to firms that have issued ADRs in the US – and therefore must report following both US GAAP and their own domestic standards. In both cases our results show that the accounting dimension is relevant: the use of homogeneous accounting measures allows for much higher goodness-of-fit of international versions of the three-factor model, at levels similar to those of domestic versions and superior to those of non-homogeneous versions. This suggests that further accounting homogeneity could lead to more accurate pricing and valuation of international assets and to an improvement of the efficiency of international fund allocation.