Fama and French and Hou, Xue, and Zhang Essay

Paper Type:  Essay
Pages:  6
Wordcount:  1575 Words
Date:  2022-05-17


The empirical shortcomings noted in financial theories used in market finance inspires huge effort by researchers to improve the accuracy of capital asset pricing model. Their efforts reveal a fact-finding mission to avoid the pitfalls linked with capital asset pricing model since initiated by William Sharpe in 1964. The research activities feature dominating attempts to understand and explain price disparity and volatilities that existing financial theories fail. Latest attempts to overcome the empirical bias in the capital pricing model results in extensions that bear similarities and differences in their comparison. Fama and French (2015) and Hou, Xue and Zhang (2015) bear similarities and differences in their derivation extended to their compared performances to explain equity returns.

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Similarities in Fama and French (2015) and Hou, Xue, and Zhang (2015) Models

Hou, Xue, and Zhang (2015) model support Fama and French (2015) argument that profitability and investment elements play a vital role in the pricing of equity assets. Improving from the three-factor model, Fama and French (2015) affirm the importance of size, investment, market value, profitability and investment patterns of the stock. It matches Hou, Xue and Zhang proposal in the q-factor model arguing on the sensitivity of asset returns beyond the risk-free rate depends on the size, investment and profitability factors. The q-factor model, E[Ri] - Rf = vi MKT E[MKT] + vi ME E[rME] + vi I/A E[rI/A] + vi ROE E[rROE] features investment and return on equity variables that Fama and French introduced to the three-factor model of valuation theory. As such, Fama and French emphasized size, investment and profitability variables influence expected returns on the assets. Hou, Xue, and Zhang (2016) found the resulting five-factor alphas in the investment and return on equity factors reveal a noisy version of q-factors within the robustness-minus-weak profitability and conservative-minus-aggressive investment. The retention of annual sorts in the CMA matched the q-factor construction on the investment factor.

Although extending the five-factor model to capture volatility, market beta, and accruals, Fama and French replicated the conceptual grounds using a triple 2x3x3 rationale comprising stock size, the ratio of investment to the assets and individual return on equity. The conceptual framework of five-factor pricing model in robust-minus-weak profitability and conservative-minus-aggressive investment elements use the double (2x3) sorts restricted to the assets size, operating profitability and investment (Hou, Xue, & Zhang, 2016). The q-factor emphasizes monthly sorts in the return on equity (ROE) similar to the annual sorts in RMW to the operating profitability within the five-factor model Rit-RFt = ai + bi (RMt-RFt) + siSMBt +hiHMLt + hiRMWt +ciCMAt +eit.

Differences in the derivation of Hous, Xue, and Zhang (2015) q-theory and Fama and French (2015) five-factor model

Hou, Xue, and Zhang (2015) benchmark the framework in the neoclassical q- investment theory that argues that forecasts on return on equity apply to the extent of future returns. The model uses the triple (2x3x3) construct comprising size, investment and equity return unlike Fama and French (2015) who utilize the double sorts (2x3) to accommodate the robust-minus-weak profitability and the conservative-minus-aggressive investment loading factors. Notably, Fama and French integrate size within the operating profitability and investment. The conceptual path for q-factor model uses monthly sorts for its return on equity factor, unlike the annual sorts the five-factor model uses on its robust-minus-weak (RMW) operating profitability (Maeda, 2017). Hou, Xue, and Zhang (2015) held the monthly construct important as derived from the q investment theory, thereby efficient to use the latest quarterly earnings data. That differed from Fama and French (2015) approach who used the annual RMW that considered earnings from the previous year-end.

The derivation of the five-factor model by Fama and French (2015) uses the valuation theory framework using book-to-market, profitability and investment factors. They use focused on the resulting interactions with the internal rate of return, often a long-term average in the expected returns. The approach differed greatly from the q-factor derivation to accommodate latest quarterly relations (Ball, Gerakos, Linnainmaa, & Nikolaev, 2015). Applying the accounting -based valuation approach to estimate the internal rate of return in CMA and RMW. The derivation of the q-factor model showed an internal rate of return estimates were inconsistent and often negative.

The inclusion of value loading factor by Fama and French (2015) showed a separate element consideration derived from the valuation theory. They differed with q-factor derivation where the value factor appeared overly redundant when interacting with investment factor. Hou, Xue, and Zhan (2015) applied the q-theory investment framework asserting marginal cost rises with the investment, thereby retaining the close relationship to the market-to-book equity. The q-model framework held investment and value factors as highly correlated with the economic link. Fama and French (2015) held the interaction of expected investment, market-to-book and expected profitability produced three separate elements in the valuation model. Q-factor held a tight economic link allowing the market-to-book exist in high correlation with investment factor (Hou, Xue, & Zhang, 2015). Q-theory insights oppose the valuation equation in the five-factor model derived from market-to-book, Pit/Bit by declaring one cannot motivate investment factor from expected book equity growth, E[Bit+t ]/Bit.

Fama and French formulated the Conservative-minus-aggressive (CMA) as a negative relation of the expected investment with the internal rate of return within the valuation theory. It contradicted the perspective in the q-factor model where Hou, Xue, and Zhang reformulated the valuation equation using the expected return of one-period-ahead to show the positive relationship with expected investment (Harvey, Liu, & Zhu, 2016). Consequently, the derivation of the q-factor model considered a restricted influence of market-to-book in the investment factor. The five-factor model applies previous investment as proxies to the expected investment evident when formulating CMA (Fama & French, 2015). The assumption differed in the q-factor model that regarded the strong proxy of past profitability to expected returns, past investment lacks such link to the expected investment.

Performance of q-Factor and Five-Factor Models in Explaining Equity Returns

The two models demonstrate comparable items in intangibles, trading and investment elements. However, the inclusion of the HML gives the five-factor model an edge over the q-factor model. A converse performance is noted with q-factor model betters with a lower magnitude of alphas indicating pricing errors as compared to the five-factor and Carhart models (Hou, Xue, & Zhang, 2016). A similar performance when testing for momentum categories where five-factor model showing non-significant high-minus-low alphas. The q-model triumphs the five-factor model in the investment and profitability categories (Hou, Xue, & Zhang, 2016). Testing the five-factor model on gross profits-to-assets indicates significant high-minus-low alphas indicating exclusion of organizational capital to asset effect. Hou, Xue and Zhang (2016) found the five-factor model perfectly fits to accommodate the research and development-to-market anomalies. Parity is noted in capturing systematic volatility in equity assets.

The q-factor model underperforms in research and development-to-market anomalies compared its dominant result in intangibles and trading frictions. In high-minus-low element, closer performance is noted in the two, though the inclusion of monthly sort gives the q-factor model an edge in high-minus-low of maximum daily returns and tracking of dispersions affecting analysts' earnings (Hou, Xue, & Zhang, 2015). The five-factor model demonstrates significant fit to address anomalies in the maximum daily return and earnings disparities. The q-factor model triumphs the five-factor model in alternative factor constructions. Empirically, it outperforms the Fama and French (2015) model to capture price momentum, earnings momentum, and anomalies in its profitability. Relative performance is noted in the Hou, Xue and Zhang (2015) model on return-weighting alongside breakpoints. However, the five-factor model shows better performance in value-growth categories.

Criticism of Fama and French (2015) Five-Factor Model

The five-factor model formulation fails to capture the disparity in average returns arising in small stocks that resemble bulk investment in low profitability items. Again, it features insensitivity to its formulation from the valuation theory framework. Notably, the formulation assumes negative correlation involving the internal rate of return and one-period-ahead expected return. The assumption of past investment ability to forecast future investment replicates is not possible undervaluation framework. Such indicates generalization of ability to use past profitability to forecast future profitability.

Evidence on the five-factor model shows inconsistency with the conceptual argument that market-to-book expected investment and profitability bear three separate factors. However, adding RMW and CMA shows redundant HML within the average returns description. The evidence disputes the formulation of the valuation theory and appears consistently supporting the investment construct where marginal costs increase with investment-to-assets.


The q-factor model has an edge over five-factor model save for value-growth category and on multiple occasions shows the better capture of significant anomalies. Although lacks the HML that gives the five-factor model an edge when applied in the value-minus-growth category, the q-factor model is viable for best asset pricing model. It outperforms the five-factor model when applied to capture anomalies in price and profitability factors. Besides capturing anomalies in earnings momentum, its produces robust performance in return-weighting and alternative factor constructions, placing it as a candidate for the best asset pricing model.


Ball, R., Gerakos, J., Linnainmaa, J., & Nikolaev, V. (2015). Accruals, cash flows, and operating profitability in the cross section of stock returns. Journal of Financial Economics, 117, 225-248.

Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116, 1-22.

Harvey, C. R., Liu, Y., & Zhu, H. (2016). The cross-section of expected returns. Review of Financial Studies, 29, 5-68.

Hou, K., Xue, C., & Zhang, L. (2015). Digesting Anomalies: An Investment. The Review of Financial Studies, 28(3), 650 - 705.

Hou, K., Xue, C., & Zhang, L. (2016, June). A Comparison of New Factor Models.

Maeda, B. A. (2017). Application of the q-factor Model to the Japanese Share Market. International Journal of Economics and Finance, 9(6), 15-23.

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Fama and French and Hou, Xue, and Zhang Essay. (2022, May 17). Retrieved from https://proessays.net/essays/fama-and-french-and-hou-xue-and-zhang-essay

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