Testing for mean reversion in heteroskedastic data II: Autoregression tests based on Gibbs-sampling-augmented randomization

A decade ago Fama and French [Fama, E.G., French, K.R., 1988. Permanent and temporary components of stock prices. J. Political Econ. 96 (2) 246–273] estimated that 40% of variation in stock returns was predictable over horizons of 3–5 yr, which they attributed to a mean reverting stationary component in prices. While it has been clear that the Depression and war years exert a strong influence on these estimates, it has not been clear whether the large returns of that period contribute to the information in the data or rather are a source of noise to be discounted in estimation. This paper uses the Gibbs-sampling-augmented randomization methodology to address the problem of heteroskedasticity in estimation of multi-period return autoregressions. Extending the sample period to 1995, we find little evidence of mean reversion. Examining subsamples, only 1926–1946 provides any evidence of mean reversion, while the post war period is characterized by mean aversion. A test of structural change suggests that this difference between pre and post war periods is significant.     

Testing for mean reversion in heteroskedastic data II: Autoregression tests based on Gibbs-sampling-augmented randomization

A decade ago Fama and French [Fama, E.G., French, K.R., 1988. Permanent and temporary components of stock prices. J. Political Econ. 96 (2) 246–273] estimated that 40% of variation in stock returns was predictable over horizons of 3–5 yr, which they attributed to a mean reverting stationary component in prices. While it has been clear that the Depression and war years exert a strong influence on these estimates, it has not been clear whether the large returns of that period contribute to the information in the data or rather are a source of noise to be discounted in estimation. This paper uses the Gibbs-sampling-augmented randomization methodology to address the problem of heteroskedasticity in estimation of multi-period return autoregressions. Extending the sample period to 1995, we find little evidence of mean reversion. Examining subsamples, only 1926–1946 provides any evidence of mean reversion, while the post war period is characterized by mean aversion. A test of structural change suggests that this difference between pre and post war periods is significant.     

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.     

Information based trade,the PIN variable,and portfolio style differences: Evidence from Tokyo stock exchange firms

We investigate whether the variables related to information based trade proposed by Easley et al. [Easley, D., Kiefer, N.M., O'Hara, M., Paperman, J.B., 1996. Liquidity, information, and infrequently traded stocks. Journal of Finance 51, 1405–1436.] help explain the daily price discovery process in an electronically order-driven market of the Tokyo Stock Exchange using the microstructure tick data. We find strong evidence that the value firms show higher probability of bad news occurrences than the growth firms. We also find that the PIN is higher for smaller firms as is the case in the U.S. With the portfolio ranking tests and the Fama and MacBeth test we find that the alpha variable, which represents the information event occurrence rate, is systematically related to required returns, while the evidence related to the PIN is weaker. In the final Fama and MacBeth test, in which the PIN or alpha variable is used as an additional explanatory variable to the benchmark Fama and French three factor model, we find that the sign of the alpha variable supports our hypothesis that the arrival of new information reduces the risk of the stock, though not significantly. We also find that the higher PIN value increases the risk of the stock, at the same time it can marginally improve the explanatory power of the multifactor model. We conclude that the PIN variable cannot be a substitutable proxy variable for the book-to-market factor unlike in the U.S., and that it is strongly related to the size variable.     

Asset Pricing and the Illiquidity Premium

In this paper, we examine the asset‐pricing role of liquidity (as proxied by share turnover) in the context of the Fama and French (1993) three‐factor model. Our analysis employs monthly Australian data, covering the sample period from 1990 to 1998. The key finding of our research is that the main test is unable to reject the test of over‐identifying restrictions, thus supporting the overall favorability of the liquidity‐augmented Fama–French model. In addition, we find that the asset‐pricing performance of the liquidity factor is generally very robust to a wide range of sensitivity checks.     

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.     

The “forward premium puzzle” and the sovereign default risk

Carry-trade strategies which consist of buying forward high-yield currencies tend to yield positive excess returns when global financial markets are booming, whereas they generate losses during crises. Firstly, we show that the sovereign default risk, which is taken on by investing in high-yield currencies, may increase the magnitude of the gains during the boom periods and the losses during crises. We empirically test for this hypothesis on a sample of 18 emerging currencies over the period from June 2005 to September 2010, the default risk being proxied by the sovereign credit default swap spread. Relying on smooth transition regression (STR) models, we show that default risk contributes to the carry-trade gains during booms, and worsens the losses during busts. Secondly, we turn to the “Fama regression” linking the exchange-rate depreciation to the interest-rate differential. We propose a nonlinear estimation of this equation, explaining the puzzling evolution of its coefficient by the change in the market volatility along the financial cycle. Then, we introduce the default risk into this equation and show that the “forward bias”, usually evidenced by a coefficient smaller than unity in this regression, is somewhat alleviated, as the default risk is significant to explain the exchange-rate change.     

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.     

Default risk and equity returns: Australian evidence

We test whether default risk is related to equity returns using the Fama and MacBeth [Fama, E.F., MacBeth, J., 1973. Risk, return, and equilibrium: empirical tests. Journal of Political Economy 81, 607–636.] regression framework. The proxy we use for default risk is the default probability obtained from option-based models. Our findings show that default probability is negatively related to returns. While we find that size and book-to-market are related to default risk, the ability of these variables to explain cross-sectional variation in returns is not because they are proxying default risk. Further, our evidence suggests that the negative relationship between default probability and returns is not due to a leverage, volatility or momentum effect.     

The Return Performance of Cubic Market Model: An Application to Emerging Markets

This article studies the performance of the high-order moment capital asset pricing model (CAPM) market models in emerging markets. We apply the cubic market model (4-moment CAPM) to 16 emerging market stock indices ranging from January 2010 to September 2015. Performance of the model is evaluated through the Fama and MacBeth’s two-step regression and through different corrections proposed in the literature, as well as generalized method of moments (GMM) estimation. According to Fama–MacBeth’s procedure, CAPM, the quadratic and cubic market models seem to be insignificant for the analyzed sample; however, the GMM estimation shows that quadratic model is valid for Indian, Polish, and Thai country indices, whereas cubic market model is accurate for Indian country index.     

Information asymmetry and the value of cash

This study investigates the market value of corporate cash holdings in connection with firm-specific and time-varying information asymmetry. Analyzing a large international sample, we test two opposing hypotheses. According to the pecking order theory, adverse selection problems make external financing costly and imply a higher market value of a marginal dollar of cash in states with higher information asymmetry. In contrast, the free cash flow theory predicts that excessive cash holdings bundled with higher information asymmetry generate moral hazard problems and lead to a lower market value of a marginal dollar of cash. We use the dispersion of analysts’ earnings per share forecasts as our main measure of firm-specific and time-varying information asymmetry. Extending the valuation regressions of Fama and French [Fama, E.F., French, K.R., 1998. Taxes, financing decisions, and firm value. Journal of Finance 53, 819–843], our results support the free cash flow theory and indicate that the value of corporate cash holdings is lower in states with a higher degree of information asymmetry.     

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.     

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.     

Nonparametric event study tests

This paper provides the first documentation of the power and specification of the generalized sign test, which is based on the percentage of positive abnormal returns in an estimation period. In simulations using daily stock return data, the generalized sign test is well specified with both exchange listed and NASDAQ stocks. A rank test is more powerful under ideal conditions. However, the rank test is more sensitive to increases in the length of the event window, to increases in return variance, and to thin trading. The generalized sign test is a viable alternative to the rank test under these conditions.     

Asset pricing models with errors-in-variables

This paper revisits Fama and French [Fama, Eugene F., French, Kenneth R., (1993) Common risk factors in the returns on stock and bonds. Journal of Financial Economics 33 (1), 3–56] and Carhart [Carhart, Mark M., 1997. On persistence in mutual fund performance. Journal of Finance 52 (1), 57–82] multifactor model taking into account the possibility of errors-in-variables. In their well known paper, Fama and French [Fama, Eugene F., French, Kenneth R., 1997. Industry costs of equity. Journal of Financial Economic 43 (2), 153–193] concluded that estimates of the cost of equity for the three-factor model of FF (1993) were imprecise. We argue that this imprecision is even more severe because of the pervasive effects of measurement errors. We propose Dagenais and Dagenais [Dagenais, Marcel G., Dagenais, Denyse L., 1997. Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics 76 (1–2), 193–221] higher moments estimator as a solution. Our results show that estimates of the cost of equity obtained with Dagenais and Dagenais estimator differ sharply from popular OLS estimates and shed a new light on performance attribution and abnormal performance (α). Adapting the Generalized Treynor Ratio, recently developed by Hübner [Hübner, Georges, 2005. The generalized treynor ratio. Review of Finance 9 (3), 415–435], we show that the performance of managed portfolios with multi-index models should be revisited in presence of errors-in-variables.     

The heterogeneous impact of macroeconomic information on firms' earnings forecasts

This paper re-examines the role of macroeconomic information in forecasting firm earnings. We adopt a Fama–MacBeth regression model with the important extension of including information from over 140 macroeconomic variables that enter into the model in a reduced dimension form as a consequence of common factor analysis. The resulting factor-augmented model is then used to evaluate the importance of macroeconomic information on earnings forecasts for U.S. firms from 1962 to 2009. The same model is also examined for each individual time window and industry subsample. The results reveal a clear and heterogeneous impact of macroeconomic information on firm-specific earnings forecasts, and that these effects differ markedly during certain periods and across industries. In addition, when compared to analyst forecasts, we show that our model is generally more accurate over longer forecast horizons. The results of the identified heterogeneous impacts are used to define the conditions under which macroeconomic information becomes important for the firm.     

Risk parity portfolio optimization under a Markov regime-switching framework

We formulate and solve a risk parity optimization problem under a Markov regime-switching framework to improve parameter estimation and to systematically mitigate the sensitivity of optimal portfolios to estimation error. A regime-switching factor model of returns is introduced to account for the abrupt changes in the behaviour of economic time series associated with financial cycles. This model incorporates market dynamics in an effort to improve parameter estimation. We proceed to use this model for risk parity optimization and also consider the construction of a robust version of the risk parity optimization by introducing uncertainty structures to the estimated market parameters. We test our model by constructing a regime-switching risk parity portfolio based on the Fama–French three-factor model. The out-of-sample computational results show that a regime-switching risk parity portfolio can consistently outperform its nominal counterpart, maintaining a similar ex post level of risk while delivering higher-than-nominal returns over a long-term investment horizon. Moreover, we present a dynamic portfolio rebalancing policy that further magnifies the benefits of a regime-switching portfolio.     

Beta,size, book-to-market equity and returns: A study based on UK data

This paper examines the role of beta, size and book-to-market equity as competing risk measurements in explaining the cross-sectional returns of UK securities for the period July 1980 through June 2000. The methodology of [Fama, E., French, K., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427–467] and [Pettengill, G., Sundaram, S., Mathur, I., 1995. The conditional relation between beta and returns. Journal of Financial and Quantitative Analysis 30, 101–116] is adopted. Results show that, when adopting the methodology of [Pettengill, G., Sundaram, S., Mathur, I., 1995. The conditional relation between beta and returns. Journal of Financial and Quantitative Analysis 30, 101–116], where data is segmented between up and down markets, a significant relationship is found between beta and returns even in the presence of size and book-to-market equity. Size is not found to be a significant risk variable, whereas book-to-market equity is found to be priced by the market and is thus a significant determinant of security returns. This is the case irrespective of the methodology adopted.     

Foreign exchange volatility and stock returns

This paper explores whether foreign exchange volatility is a priced factor in the US stock market. Our investigation is motivated by a number of empirical as well as theoretical considerations. Empirically, Menkhoff et al. (2012) find that foreign exchange volatility is a pervasive factor across a variety of test assets. Theoretically, Shapiro (1974), Dumas (1978), and Levi (1990) imply that foreign exchange volatility can influence firms’ cash flow volatility therefore the discount rate. In terms of empirical implementation, we employ the cross-sectional regression methodology of Fama and MacBeth (1973) as well as the time-series regression approach of Fama and French (1996). For robustness, we also use the mimicking portfolio approach of Fama and French (1993). We find that foreign exchange volatility has no power to explain either the time-series or the cross-section of stock returns, which calls for more research on foreign exchange risk. Bartov et al. (1996) and Adrian and Rosenberg (2008) suggest an alternative and maybe promising direction.     

SMB — Arousal,disproportionate reactions and the size-premium

This paper examines SMB (small minus big), the mimicking portfolio in Fama and French's [Fama, E., French, K., 1993. Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3–56] three-factor asset pricing model. We do not examine whether SMB is a factor in explaining the cross-section of returns. This paper's focus is why S is greater than B. After controlling for market-pervasive effects, we argue that the small-firm premium is driven by both investors' emotional arousal (proxied by the turnover ratio) and their disproportionate reactions to arousing stimuli.