GRS Test Research Articles

The Fama-French Three Factor Model Test on Excess Stock Return: Evidence From Hong Kong, Indonesia and Singapore Capital Market

The presence of the capital market has a very important role in the world economy because the capital market carries out economic and financial functions. One of the instruments in the capital market is stock. In stock investment, investors expect a return with a size that is in accordance with the level of risk they can afford. This study wants to test whether the Fama-French Three Factor Model variables, namely market excess returns, book-to-market equity and firm size, can be used to explain excess returns on the stock markets of Hong Kong and Indonesia with the observation period of 2018–2022. Based on the test results multiple linear regression, Gibbons, Ross, and Shanken test (GRS test) and spanning test, this study found that the variables in the Fama-French Three Factor Model can simultaneously be used to explain the excess return on all stock portfolios on the stock market in Hong Kong and Indonesia, and can only be used to explain the excess return on Big and S-H portfolios in Singapore. Based on the results of the GRS-test, in the Hong Kong market the most efficient portfolio is S-M, in the Indonesian market the most efficient portfolio is the Big portfolio, while in the Singapore market all portfolios are efficient and based on the spanning test, in the Hong Kong market the potential redundant factor is SMB, in in the Indonesian market, the potential redundant factor is HML, while in the Singapore market, there is no redundant potential factor.

A factor pricing model based on double moving average strategy

The heterogeneous market hypothesis states that there are different types of investors with different investment term-structures in the stock market. Based on the hypothesis, we analyze the trading strategies of moving averages with different term structures, and we find that the trading strategies formed by the 1-month short-term moving average with 3-, 6-, 9-, 12-, 18-, and 24-month long-term moving averages can gain significant excess returns in the Chinese market. Accordingly, this paper adopts the moving average factor formed by the method of Liu’s to expand the current four-factor pricing model of the Chinese market. The results of spanning regression show that the introduction of the short-term average with a period of 1-month and the long-term moving average with a period of 3- and 12-month can significantly improve the pricing power. The GRS test developed by Gibbons et al. (1989) also shows that the augmented six-factor model with moving average factors can pass the test at the significance level of 5%, and the average absolute value of intercept terms decreases by about 50% compared with the results of the four-factor model. At the same time, under different macro-state dependence, the overall performance of the augmented six-factor model with moving averages is still better than that of the four-factor pricing model proposed by Liu et al.’s. Our main contribution is to introduce double moving average factors to capture the behaviors of investors’ different term structures and add these factors to the most competitive asset pricing model for enhancing the pricing power. It is of great significance to supplement the pricing model in the Chinese market.

Financial Distress and Value Premium using Altman Revised Z-score Model

In the stock market, investors and value managers desire to be safe. Estimating equity returns and evaluating potential financial distress risk are essential for investment and trading decisions. The link between distress risk and stock return is controversial, and current literature yields contradicting results. A variety of models may be used to evaluate distress risk-return trade-offs. This paper employs a revised Altman Z-score to examine financial distress and value premiums. Using univariate and multivariate techniques, we examine firm- and industry-level portfolio returns, encompassing all Indian companies listed on the Bombay Stock Exchange (BSE). Results confirm the existence of the distress factor effect found in industry and firm-level portfolios. It shows that the distress risk factor significantly determines stock returns as an independent systematic risk factor. This result is consistently found in most industries. The study demonstrates the existence of a value premium in both distressed and safe zones. The study also used a multivariate GRS test and the Fama-Macbeth procedure to validate the reliability of the distress factor and pricing models. Results confirm that Altman model-based distress factor augmented models improve the performance of existing pricing models with higher reliability and accuracy.

Fama and French three and six-factor models: Evidence from Indian stock exchange

This study attempts to compare the performance of Fama–French three-factor model (FFTFM) and Fama and French six-factor model (FFSFM) in predicting the variations in expected returns of Nifty-100 listed stocks. Only 5/6 of the total listed companies are chosen, while the remaining 1/6 are ignored because they are not listed for the whole study period. The stocks are divided into two size groups and three groups based on B/M, OP, Inv and MOM using independent sorts to create 24 portfolios. The monthly average returns of the MC-MOM portfolios increase as momentum increases, in contrast to MC-B/M and MC-Inv portfolios. Almost all the portfolios with high returns are paired with significant risk, apart from the BM portfolio in size and profitability group. The findings prove that the FFSFM outperforms FFTFM on all the GRS test parameters. However, there is no significant improvement in explanatory power over the FFTFM.

The Empirical Explanatory Power of CAPM and the Fama and French Three-Five Factor Models in the Moroccan Stock Exchange

This study empirically tests and compares the performances of three famous financial asset valuation models in the Moroccan stock exchange: CAPM, the Fama and French three-factor model, and the Fama and French five-factor model. Our sample considers monthly data covering the sample period of July 2002 to June 2020. The main findings reveal that the GRS test typically rejects each of the examined model. On the basis of our analysis, we find that the value effect is more pronounced than the size effect. However, profitability and investment effects are almost absent. Regarding the factor spanning tests, the results show that the value factor was not redundant. Beyond this, the size and investment factors are the redundant factors. In Morocco, the market factor is the most powerful factor, perhaps assisted by value and profitability factors. Although the CAPM performs poorly in capturing the variation in Moroccan returns, the market factor continues to play an important role, even after adding other factors. Overall, all the tested models were improved slightly, but leave part of the variation in Moroccan stock returns unexplained.

A Revised Comparison between Fama and French Five-Factor Model and Three-Factor Model——Based on China's A-Share Market

In allusion to some contradicting results in existing research, this paper selects China's latest stock data from 2005 to 2020 for empirical analysis. In this paper, the redundant factors (HML, CMA) are orthogonalized, and the regression analysis of the 5*5 portfolio of Size-B/M and Size-Inv is carried out with these two orthogonalized factors. It found that the HML and the CMA are still significant in many portfolios, indicating that they have a strong explanatory ability, which is also consistent with the results of GRS test. All these show that the five-factor model has a better ability to explain the excess return rate. Then, we analyze the possible reasons for the strong explanatory ability of the HML, CMA, and RMW from the aspects of price-to-book ratio, turnover rate, and correlation coefficient. We also explain the results and analyze China's stock market policy changes and investors' investment style in recent years.

Is Industry-Specific Value Premium Declining? Evidence from India

This article examines whether the literature promised value effect exists and the changing nature of value premium at the industry level. It also determines the value premium’s strength by controlling the January effect within and across the regulated industry groups. This is done by utilizing the two most prominent pricing models: Fama–French three- and five-factor, considering all listed firms trading at BSE India between 1999 and 2020. The results show that a significant value effect exists in 15 of the 17 regulated industry groups over 21.5 years, while sub-period analysis revealed variation in the value effect at industry-based portfolio returns. We developed quintile and multivariate portfolios within and across the industries. Results show that the industry-specific value premium has been relatively low in the current decade due to decreasing industry portfolio returns and increasing P/B ratios within industry groups. The study also used the GRS test to explore the explanatory power of models. Results indicated that the explanatory power of models has declined in post-crisis periods. While controlling the January effect, the value premium has slightly diminished within and across the industry groups in the recent decade. We also observed that investors who seek to allocate assets within and across industries are likely to have potentially predictable and pretty stable returns. While other countries have found industry-specific value premiums, no such study has been conducted in India. As a first attempt, these findings are relevant for investors and academia.

Selectivity and Market-Timing Performance of Mutual Funds Using Human-Capital Augmented Various Asset-Pricing Models: Evidence from Pakistan

This study demonstrates the selectivity skills and market-timing ability performance of funds mangers through various sophisticated augmented asset pricing models. The results indicate better performance for selectivity and market-timing ability of fund managers but unexpectedly after adjusting size and value factors into the specifications, both demonstrate insignificant findings. It also investigates the nexus between various risk-adjusted factors including market, size, value, momentum and human-capital sixth-factor, with the excess portfolio mutual funds returns using sample of 120 open-ended mutual funds monthly data for the time span of 16 years 2005-2020. The simple and multivariate time-series OLS regression approaches are employed to investigate the nexus between various factors and mutual funds returns. The findings of the study evidenced statistically significant nexus of market, size and value factors with mutual funds returns while insignificant results for human-capital and momentum factors. Moreover, based on GRS test, the average absolute alpha of Income-Growth augmented CAPM is closer to zero therefore, assumed to be the best model among the risk-adjusted completing asset pricing models in mutual funds.

A better model? Testing of Fama and French six-factor model in Pakistan

This study examines the performance of the Fama and French six factor model and the alternative six-factor model in explaining anomalous return patterns using a broad sample of the Pakistani stock market from 2000 to 2017. This study is the first to test the applicability of these models in Pakistan and their performance in explaining anomalous returns. There are 11 anomalies taken, which proved to be significant in the Pakistani market. The GRS test is used with other time-series measures to check the power of the given models in explaining one-way sorted quintile portfolios. The results reveal that both models provide an incomplete description of anomalous returns. However, the six-factor model seems to be dominant with no major exception as it can explain 5 out of 11 anomalous portfolios returns, while the alternative model can explain four anomalies. The findings recommend that investors use the six-factor model because of its dominancy. It further recommends the investors about how they can maximize their returns by taking a long and short position in anomalous portfolios. Lastly, it is suggested to search for a better model to explain Pakistani stocks returns and capture anomalous patterns

Multifactor Market Indexes

This paper combines the CRSP market index with multiple factors to create a single multifactor market index. Empirical tests of different multifactor market indexes indicate that: (1) Sharpe ratios substantially increase and GRS test statistics decrease as multifactors are incrementally added to the CRSP index; and (2) the resultant multifactor market indexes are significantly priced in cross-sectional tests of associated beta loadings with t-values exceeding 3.0 in most cases.

The saving, human wealth and asset pricing nexus: Evidence from around the world

The present study examines the dynamics of the saving, human wealth and asset pricing nexus across developed and emerging economies. We introduce two equilibrium asset pricing models in an intertemporal capital asset pricing framework, including the priced factors human wealth and market portfolio in the first framework and the saving and market portfolio in the second framework. Both asset pricing frameworks consist of two-factor, four-factor and five-factor asset pricing models. We control for size and value factors in the four-factor model and size, value and momentum factors in the five-factor model. The IV-GMM estimation and GRS test results indicate that human wealth and market portfolio for the first framework and saving and market portfolio in the second framework are primary priced factors in explaining the average returns for developed economies and the aggregate level. On the contrary, both frameworks fail to yield significant results explaining the average returns for emerging economies.

Research & Development Premium in the Indian Equity Market: An Empirical Study

This article aims to investigate the research and development (R&D) premium and explore the three most prominent asset pricing models: capital asset pricing and the three-and five-factor models (Fama & French, 1993; 2015). The results show that India's annualized average R&D premium is significantly higher than the existing value, market, profitability, size and investment premiums, implying that the R&D premium is a more significant concern for Indian investors, particularly for high R&D firms. It was also observed that by applying the GRS test and the Fama and MacBeth (1973) two-pass procedure, the R&D risk factor augmented the CAPM, FF3F and FF5F models outperforming the existing CAPM, FF3F and FF5F models, respectively. We can also report that R&D is, unquestionably, a priced ingredient and a critical factor in developing pricing models for developing markets such as India. The paper's conclusions add to the current literature in R&D and asset pricing and assist investment professionals in developing better investment and trading strategies.

Does Five-Factor Model Perform Better Than Three Factor Model? Evidence from Developed Countries of The Asia Pacific Region

This study evaluates whether the “Fama-French five-factor model” can explain the variations in expected returns better than the “three-factor model.” Using the stock returns and accounting variable data from DataStream for 1,300 plus listed firms across six developed countries of the Asia Pacific region, including; Australia, Hong Kong, Japan, Israel, New Zealand, and Singapore for the period of Jun-2006 to February-2020. The paper is the first to examine the “five-factor model” performance across the developed countries of the Asia Pacific region. The empirical findings reveal that the Asia Pacific region for the sample period earns an equity premium. In addition, results report the redundancy of size factor (SMB) and value factor (HML), while the profitability (RMW) and investment premium (CMA) are positive and significant. Moreover, the study used Gibbons, Ross, and Shanken (GRS) test to the asset pricing model. The GRS test results on the “five-factor model” compared with the “three-factor model” demonstrate that profitability and investment factors add significant explanatory power to the analysis in the Asia Pacific region.

Models for Expected Returns with Statistical Factors

In this paper, we propose multifactor models for the pan-European Equity Market using a block-bootstrap method and compare the results with those of traditional inferential techniques. The new factors are built from statistical measurements on stock prices—in particular, coefficient of variation, skewness, and kurtosis. Data come from Reuters, correspond to nearly 2000 EU companies, and span from January 2008 to February 2018. Regarding methodology, we propose a non-parametric resampling procedure that accounts for time dependency in order to test the validity of the model and the significance of the parameters involved. We compare our bootstrap-based inferential results with classical proposals (based on F-statistics). Methods under assessment are time-series regression, cross-sectional regression, and the Fama–MacBeth procedure. The main findings indicate that the two factors that better improve the Capital Asset Pricing Model with regard to the adjusted R2 in the time-series regressions are the skewness and the coefficient of variation. For this reason, a model including those two factors together with the market is thoroughly studied. We also observe that our block-bootstrap methodology seems to be more conservative with the null of the GRS test than classical procedures.

Is idiosyncratic risk ignored in asset pricing: Sri Lankan evidence?

The present study focused on one of the important South Asian nations—Sri Lanka—to examine the role of idiosyncratic volatility in asset prices. A four-factor model with idiosyncratic volatility was designed for capturing the market, size, value and idiosyncratic risk yields better than Fama and French’s (J Financ Econ 33:3–56, 1993) three-factor model and performance of the model. Fama–MacBeth’s cross-sectional regression, residual graphs and GRS test all confirm the superiority of four-factor model over 2 three-factor models. For all MC- and IVOL-based portfolios, idiosyncratic volatility is negatively related to the expected returns and positively related for all PB-based portfolios. Finally, study findings confirm that there is a high importance for idiosyncratic volatility risk factor while considering investment decision in Colombo stock exchange. Hence, investor should compensate for holding such risk factors in the portfolio.

Asset pricing factors in Islamic equity returns

AbstractPrevious studies have compared risk–return characteristics of Islamic equity indices with their conventional counterparts, which may produce spurious results because a conventional equity index includes both Islamic and non‐Islamic constituents. Hence, this study compares Islamic equity portfolios with their non‐Islamic counterparts. We find that aggregate Islamic equity portfolios generally outperform non‐Islamic equity portfolios after controlling for the five asset pricing factors—market, size, value, profitability, and investment (Fama and French, 2015). The average cost of equity is 2.77 percentage points lower for Islamic firms compared to non‐Islamic firms. The findings hold for the various segments of the global equity market, and remain robust when the interest rate‐augmented and the liquidity factor‐augmented versions of the Fama–French five‐factor model are employed. The GRS test results suggest these asset pricing models may not be adequate for pricing both Islamic and non‐Islamic equities.

The role of the volatility index in asset pricing: The case of the Indian stock market

This study examines whether the volatility index, a proxy for aggregate volatility risk, can be used as an additional factor in the standard asset pricing model for the Indian stock market after controlling for well-documented risk factors. This study first examines the empirical performance of the capital asset pricing model, the Fama-French three-factor model and the Carhart four-factor model. On the basis of a GRS test, the Fama-French three-factor model is used as the baseline model to explore the role of the volatility index as an additional factor considered in the asset pricing model. The factor mimicking portfolio returns for the volatility index innovations is constructed and is included as an additional factor in the Fama-French three-factor model. The study provides strong evidence of size effects but relatively weak value-growth and momentum effect. Further, stock’s sensitivity to volatility index innovation is a priced risk factor during high volatility period, but not during low volatility period. Nevertheless, the addition of volatility risk factor leads to marginal improvements in the capacity for the model to explain the variation in stock returns. The results of this study will help financial analysts and corporate financial managers to evaluate the performance of professionally managed portfolios.

Is human capital the sixth factor?

PurposeThe purpose of this paper is to focus on one of the major emerging Asian economies – India – to examine the role of human capital in asset prices.Design/methodology/approachThe analysis uses various statistical techniques (e.g. multifactor regression model, 3D graphs, GRS test and residual graphs) to test the role of human capital in asset prices.FindingsA six-factor model designed for capturing the size, value, profitability, investment and human capital patterns in average portfolio returns performs better than both Fama–French’s (1993) three- and Fama–French’s (2015) five-factor model. The main problem of six-factor model is its failure in capturing the average returns on “microcap with low-value stocks that are highly profitable invests aggressively for asset growth but invests much lesser for human growth” and “microcap with unprofitable stocks whose returns behave like those of low-value firms with conservative investment”. The study finds the investment factor (CMA) of Fama–French’s (2015) five-factor model as the redundant factor for describing the portfolio average returns in the study sample.Research limitations/implicationsThe paper argues that human capital also plays a role in predicting returns. This has significant public policy content.Originality/valueThe present study is novel for several reasons: first, it includes six-factor model descriptions; second, no comprehensive asset pricing study is done with human capital in Asian emerging markets, especially in India. Perhaps, this is the first study to examine whether portfolio returns are affected by the human capital in the Indian context. Third, the study period and methodology used are completely different from the previous studies.

Asset Pricing Models and Anomalies: An Empirical Analysis

In this paper, we find noticeable relationships between traditional factors, with evidence in favor of the B/M effect and little for the size effect. Using the Fama-Macbeth procedure, we find that the market risk premium is significantly positive, whereas the size factor is significantly negative. There is no evidence of a low volatility effect, the momentum effect is persistent and low dividend yield firms outperform firms with high dividend yields. Using the Chi-squared and GRS test, we find that the inclusion of various risk factors does lead to a fairly high proportion of variability of stock returns being explained. It also shows that the models suffer from significant pricing errors. Furthermore, the rank restriction test shows that there are several irrelevant risk factors, and most of the models used in this paper don't pass the HJ-distance test nor the LM test, except for the CAPM specification. Lastly, low volatility is priced, whereas momentum and dividend yield are not.

An Exact Test of the Improvement of the Minimum Variance Portfolio

AbstractI propose an exact finite sample test of the risk reduction of the global minimum variance (GMV) portfolio. The GMV test statistic is proportional to the reduction in the variance of the GMV portfolio and has a straightforward geometric and portfolio interpretation and complements the celebrated GRS test in Gibbons et al. (1989). In practical applications, the GMV test leads to a rejection of the null hypothesis of no improvement in the GMV portfolio more often than the GRS test rejects the null hypothesis of no improvement in the risk‐return profile of the tangent portfolio. The power of the GMV test increases with the variance reduction of the GMV portfolio. Using test asset returns scaled by predetermined predictive variables is equivalent to increasing the overall number of test assets and leads to substantial power gains.