Carhart Four-factor Model Research Articles

Expected Investment Growth and the Cross Section of Stock Returns

Expected investment growth (EIG) is a strong predictor for cross-sectional stock returns. Between July 1953 and December 2015 in the US, an investment strategy that takes a long position in firms with high EIG and a short position in firms with low EIG generates an average annual return of more than 20%, with a Sharpe ratio of 1.01. This return predictability holds both in subperiods and in different subsamples of firms, as well as in all other G7 countries. Leading empirical factor models including CAPM, Fama-French three-factor model, Carhart four-factor model, and the recent Hou, Xue, and Zhang four-factor model and Fama and French five-factor model all fail to fully capture the profitability of this investment strategy. Further analyses suggest that EIG is closely related to financial distress risk, especially at a short horizon up to one year, and is a better predictor of stock returns than failure probability from Campbell, Hilscher, and Szilagyi (2008). We provide supporting evidence for both risk-based explanation and behavioral explanation for this large EIG premium.

Fixed Income Asset Pricing: Extending the Elton et al. (1995) Four-Factor Model

This paper is enhancing the four-factor fixed income asset pricing model initially developed by Elton et al. (1995). The aim is to increase the explanatory power of the model in time series analysis. Vast progress has been made on equity asset pricing models since the introduction of the Capital Asset Pricing Model in the 1960s with the introduction of the Fama and French (1993) three-factor model and the Carhart (1997) four-factor model. Progress into fixed income asset pricing has been slow, and there is still no consensus of which combinations of bond indexes are most suitable for explaining the returns of fixed income securities and bonds. This paper shows that by introducing a duration factor, a global bond factor, and three exchange rate factors, the resulting ninefactor model can explain up to 95.42% of return variations in fixed income fund portfolios and up to 99.97% of the return variations of individual fixed income funds. The model is shown to be robust when using a global and regional benchmark specifications, and when used in the analysis of a wide range of fund strategies, fund types, and fund objectives.

An Analysis of the Expense Ratio Pricing of SMB,HML, and UMD Exposure in U.S. Equity Mutual Funds

The expense ratio price of U.S. equity market exposure is close to zero with funds such as the Vanguard Total Stock Market Index (ticker: VTSAX), which charges an expense ratio of just 5 bps. An interesting, and more difficult, question to answer is, How much are mutual fund companies charging investors to gain exposure to small-capitalization, value, and positive momentum stocks? The authors answer this question using monthly returns data for low-cost mutual funds and ETFs in tandem with Fama–French three- and Carhart four-factor equity pricing models and current fund expense ratio levels. They indeed find strong evidence that fund companies charge for exposure to individual factor premiums. Additionally, they find significant variation in how aggressively factor exposure is priced, both across fund companies and across portfolios offering identical levels of factor premium exposure.

The Impact of the Financial Sector on Asset Pricing Tests: Evidence from the Colombo Stock Exchange

<p>This paper aims to identify how the inclusion of financial sector affects the ability of asset pricing models to explain the average stock returns in the CSE. Most of the asset pricing researches, the firms in the financial sector are excluded on the basis that their characteristics and the leverage are notably different than firms in other industries. Therefore the objective of this study is to identify the impact of the inclusion of financial sector on the ability of the Carhart four-factor model to explain the average stock returns in the CSE and to compare its performance with the Capital Asset Pricing Model (CAPM) and the Fama and French three-factor model. The study finds that the four-factor model; incorporating the market premium, size premium, value premium and momentum premium provides a satisfactory explanation of the variation in the cross-section of average stock returns in the CSE, even when the financial sector is included. It is found that the Carhart four-factor model performs better than the CAPM in all scenarios; and that it performs notably better than the Fama and French three-factor model.However, there is no notable difference in the findings either the financial sector is included or not. </p>

The long-term performance of new product introductions

This study investigates the long-term stock market performance of firms following announcements of new product introductions (NPIs). We find that firms announcing NPIs experience significantly positive abnormal stock returns in the three- and five-year post-announcement periods. Further, firms’ marketing capabilities and industry background, firm size, and the timing new products are introduced significantly affect shareholder gains from NPIs. The Carhart four-factor model, the zero-investment portfolio method, and the buy-and-hold return procedure yield consistent results. Our findings show that investors on average do not fully capture the valuation impact of new products nor incorporate the information contained in the initial announcements.

Asset liquidity and stock returns

We document the significant predictive power of firms' asset liquidity in the cross section of subsequent stock returns. The annual return spread between portfolios featuring the highest and lowest levels of asset liquidity is significantly positive. Our proposed measure of asset liquidity outperforms those measures developed by Gopalan et al. (2012) in predicting returns. The asset liquidity anomaly also provides significantly positive alphas when controlling for the asset pricing factors in the Fama and French (1993) three-factor model and the Carhart (1997) four-factor model. Asset liquidity exhibits strong return forecasting power even after controlling for acknowledged cross-sectional determinants of return. The positive relation between asset liquidity and future returns tends to be stronger for firms with greater asset productivity, higher quality cash flow and lower capital investment.

Faith Based Investing (FBI) Fund Performance: Luck or Skill?

This study uses monthly net return data on 27 actively managed faith based mutual funds and the latest Fama-French bootstrap methodology to distinguish between luck and skill of fund managers. The main benchmark of this study is the Carhart (1997) four-factor model. The evidence suggests that majority of fund managers do not have enough skill to produce expected benchmark-adjusted net returns that cover costs. By ranking funds on performance after costs, we find that the performance of the majority of funds can be attributed to "bad skill". The evidence is strongest in the top 95th percentile and above, and from the bottom 10th percentile and below.

Sin Is In: An Alternative to Socially Responsible Investing?

This article examines the return characteristics of a portfolio of U.S. “vice stocks”—firms that manufacture and sell socially irresponsible products such as alcohol, tobacco, gaming services, and national defense. The author constructs a portfolio comprising the daily returns of 41 vice stocks from May 1995–May 2015 and computes the riskadjusted returns by using the Carhart four-factor model and Sortino ratio. Full-period results show a positive and significant alpha for the entire portfolio and positive, yet insignificant, alphas for each vice industry. Down market results show a negative, yet insignificant, alpha for the entire portfolio. Bull market results show a significant alpha for the entire portfolio, as well for the alcohol and defenseindustry securities.

Performance persistence in institutional investment management: The case of Chinese equity funds

This paper investigates the performance and persistence in performance of equity funds in China. We apply the capital asset pricing model (CAPM) and the Carhart four-factor model to examine 520 equity funds for an eleven-year period with 39,449 observations. To investigate persistence, the entire sample is divided into ten portfolios (deciles) on the basis of lagged one-year performance and then observed over the next 12 months. We find that equity funds in China outperform their benchmark market but do not find any evidence of persistence in the performance of equity funds. Top-performing (worst-performing) funds do not continue to perform well (worse) in the following year. Top-performing funds are younger and have lower expense ratios than the worst-performing funds. However, the size of the top-performing funds and the worst-performing funds show no significant difference. Our results suggest that past performance of equity funds is not predictive of future fund performance.

An investor’s perspective on risk-models and characteristic-models

Purpose In capital markets, research risk factor loadings and characteristics are considered as opposing explanations for the cross-sectional dispersion in average stock returns. However, there is little known about the performance an investor would obtain who believes either in the characteristics explanation (CB-investor) or in the risk factor loadings explanation (RB-investor). The purpose of this paper is to compare the performance of CB- and RB-investors. Design/methodology/approach To compare the competing strategies, the authors propose a simple new approach to equity portfolio optimization in the style of Brandt et al. (2009) by modeling the portfolio weight in each asset as a function of the asset's risk factor loadings or characteristics. The authors perform an empirical analysis on the German stock market, exploiting the risk factor loadings from the Carhart (1997) four-factor model and the respective characteristics size, book-to-market equity ratio and momentum. Findings The results show that investment strategies relying on characteristics (particularly on momentum) outperform risk-based investment strategies in horse races. These findings hold in- and out-of-sample. Furthermore, the characteristics-based investment strategies outperform a value-weighted market portfolio strategy in- and out-of-sample. Originality/value The authors introduce a portfolio optimization approach that enables investors to directly link portfolio decisions to the firm’s characteristics or risk factor loadings.

A new perspective on the size, value, and momentum effects

Purpose This paper aims to provide a comprehensive analysis of whether stock returns in Europe are best characterized by country-specific or Europe-wide versions of widely used factor models. Design/methodology/approach To estimate the cost of equity in Europe, both region-wide and nationally, the Fama and French (2012) three-factor and Carhart (1997) four-factor models are used. Findings The results show that although the value and momentum premiums are present on a Europe-wide basis, the size premium is country-specific. Originality/value The paper offers an explanation to the puzzle of why Fama and French (2012) detect value and momentum premiums but no size premium in Europe. Furthermore, the results shed new light on these premiums and present a challenge to existing applications of widely used factor models.

Size, value and momentum in stock returns: evidence from India

This paper examines the effects of size, value and momentum on the cross-sectional relation between expected returns and risk in the Indian stock market. We find that the conditional Carhart four-factor model empirically describes the variation of cross-section of return better than the unconditional model. When size, book-to-market and momentum effects are controlled in the conditional model, the positive relation of market beta, book-to-market and momentum with expected returns remains economically and statistically significant. However, this evidence is found to be subject to characteristics of test portfolios. The expected returns are sensitive to changes in predictive macroeconomic variables.

Size, Value, and Momentum Effects in Stock Returns: Evidence from India

We examine in this article if stock returns show a pattern which indicates certain anomalies predominantly size, value, and momentum effects. We also examine whether asset pricing models capture mean excess returns on portfolios constructed based on size–value and size–momentum factors. We find that average stock returns exhibit patterns that have size, value, and momentum effects. We also show evidence that the empirical results do not fully support asset-pricing models. Capital asset-pricing model (CAPM) does not capture average returns on portfolios. Fama–French three-factor model partly explains average returns on size–value sorted portfolios while Carhart four-factor model captures returns on size–momentum sorted portfolios mainly small size-winner portfolio. Hence, size, value and momentum factors continue to exist in Indian stock market and they are found to be profitable investment strategies which would maximize invested wealth of the investors.

An Analysis of the Expense Ratio Pricing of SMB, HML and UMD Exposure in U.S. Equity Mutual Funds

The expense ratio price of U.S. equity market exposure is close to zero with funds such as the Vanguard Total Stock Market Index (ticker: VTSAX), which charges an expense ratio of just 5 bps. An interesting, and more difficult, question to answer is, How much are mutual fund companies charging investors to gain exposure to small-capitalization, value, and positive momentum stocks? The authors answer this question using monthly returns data for low-cost mutual funds and ETFs in tandem with Fama-French three- and Carhart four-factor equity pricing models and current fund expense ratio levels. They indeed find strong evidence that fund companies charge for exposure to individual factor premiums. Additionally, they find significant variation in how aggressively factor exposure is priced, both across fund companies and across portfolios offering identical levels of factor premium exposure.

Market Sentiment as a Factor in Asset Pricing

This paper explores whether market sentiment should be used as an additional factor in the asset-pricing model. We use a unique dataset from Investor Intelligence as a direct measure of market sentiment. We form ten portfolios based on their correlations with the new market sentiment measure. Following Fama and French (1993) we build a market sentiment factor (SENT) and add this factor to the Carhart four-factor model. We find that SENT is significant for all portfolios in the sentiment augmented four-factor model and increases explanatory power of the model measured by adjusted R2s. We also find that the addition of SENT factor reduces the explanatory power of all other risk factors in the four-factor model.

Does it pay to be good? An analysis of vice and virtue stock performance in the Eurozone

This paper provides a performance analysis of vice and virtue stocks in the Eurozone for the period between January 2005 and December 2014. In order to do so, a vice index consisting of listed Eurozone companies operating in selected vice industries is created and subsequently matched with a corresponding virtue index, which for the purpose of this analysis is represented by the DJSI Eurozone. The tools used to conduct the performance evaluation are the Sharpe ratio, the capital asset pricing model and the Carhart four-factor model. The analysis indicates no consistent outperformance or underperformance of one or the other index, yet the realised performance over the whole period favours the vice index. Consequently, it can be concluded that from a statistical point of view, there is no substantial advantage or disadvantage in being “good” when investing into stocks, as such it is a matter of investor preference, with the note that historical returns do favour vice stocks.

Investment styles and the multifactor analysis of market timing skill

PurposeThe purpose of this paper is to present and demonstrate how the use of a multifactor model in the analysis of market timing skill can be misleading because the use of a multifactor model does not suit all investment styles equally well. If the factors of the analysis model do not span the portfolio holdings of a fund with less conventional investment strategy, the use of a multifactor model may even deteriorate the overall inference in measuring the market timing skill of a large sample of funds.Design/methodology/approachThis study investigates the limitations of multifactor models in the analysis of market timing skill by applying the traditional Treynor-Mazuy and Henriksson-Merton analysis models of market timing skill using a set of “placebo” funds which are “natural” passive market timers.FindingsThe results of the study show that the incorporation of the Carhart four-factor model into the analysis of market timing skill considerably reduces the percentage of significant market timing results. But, as expected, the reduction of bias is not equal for different investment styles, and it works best when the factors of the analysis model are related to the investment style of the placebo portfolio.Practical implicationsThis style-related limitation of multifactor models in the analysis of market timing skill may result in detecting funds with less conventional investment strategies as market timers since the factors used in the analysis are not likely to span their investment styles.Originality/valueThis study shows that the use of a multifactor model may lead to inferring passive market timers with less conventional investment styles as market timers. In addition, the findings of the study leave option replication approaches as more preferable bias corrections than multifactor extensions.

Market anomalies, asset pricing models, and stock returns: evidence from the Indian stock market

Purpose– This paper aims to investigate whether the use of conditional and unconditional Fama and French (1993) three-factor and Carhart (1997) four-factor asset pricing models (APMs) captures the role of asset pricing anomalies in the context of emerging stock market like India.Design/methodology/approach– The first step time series regression approach has been used to drive the risk-adjusted returns of individual securities. For examining the predictability of firm characteristics or asset pricing anomalies on the risk-adjusted returns of individual securities, the panel data estimation technique has been used.Findings– Fama and French (1993) three-factor and Carhart (1997) four-factor model in their unconditional specifications capture the impact of book-to-market price and liquidity effects completely. When alternative APMs in their conditional specifications are tested, the importance of medium- and long-term momentum effects has been captured to a greater extent. The size, market leverage and short-term momentum effects still persist even in the case of alternative unconditional and conditional APMs.Research limitations/implications– The empirical analysis does not extend for different market scenarios like high and low volatile market or good and bad macroeconomic environment. Because of the constraint of data availability, the authors could not include certain important anomalies like net operating assets, change in gross profit margin, external equity and debt financing and idiosyncratic risk.Practical implications– Although the active investment approach in stock market shares a common ground of semi-strong form of market efficiency hypothesis which also supports the presence of asset pricing anomalies, less empirical evidence has been explored in this regard to support or repute such belief of practitioners. Our empirical findings make an attempt in this regard to suggest certain anomaly-based trading strategy that can be followed for active portfolio management.Originality/value– From an emerging market perspective, this paper provides out-of-sample empirical evidence toward the use of conditional Fama and French three-factor and Carhart four-factor APMs for the complete explanation of market anomalies. This approach retains its importance with respect to the comprehensiveness of analysis considering alternative APMs for capturing unique effects of market anomalies.

Multifactor Asset Pricing Model Incorporating Coskewness and Cokurtosis: The Evidence from Asian Mutual Funds

This research adds cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model to be six-factor model to evaluate the equity mutual fund performance of three selected countries in Asia — China, Singapore, and Thailand as representatives of fast growing Asian countries. To my knowledge, this is the first research to incorporate both coskewness and cokurtosis risk factors into Carhart (1997) four-factor model, to become a six-factor model, to explain the equity mutual fund returns. The result shows that coskewness and cokurtosis risk factors show some significance in some countries in Asia. Adding coskewness and cokurtosis risk factors in both CAPM and four-factor model, show some increment in the explanatory power of the models.

Reward-risk momentum strategies using classical tempered stable distribution

Abstract We implement momentum strategies using reward-risk measures as ranking criteria based on classical tempered stable distribution. Performances and risk characteristics for the alternative portfolios are obtained in various asset classes and markets. The reward-risk momentum strategies with lower volatility levels outperform the traditional momentum strategy regardless of asset class and market. Additionally, the alternative portfolios are not only less riskier in risk measures such as VaR, CVaR and maximum drawdown but also characterized by thinner downside tails. Similar patterns in performance and risk profile are also found at the level of each ranking basket in the reward-risk portfolios. Higher factor-neutral returns achieved by the reward-risk momentum strategies are statistically significant and large portions of the performances are not explained by the Carhart four-factor model.