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The q-factor model and the redundancy of the value factor: An application to hedge funds

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Abstract

We test the new Fama and French five-factor model on a sample of hedge fund strategies. This model embeds the q-factor asset pricing model which lies on the CMA and RMW factors. We find that the HML factor is not redundant for many strategies, as conjectured by Fama and French in their setting. HML seems to embed risk dimensions which are not included in the Fama and French new factors. In contrast to Fama and French, the α puzzle is robust to the addition of CMA and RMW. Furthermore, hedge funds seem to prefer, on the one hand, firms which invest a lot to firms which invest less, and, on the other hand, weak firms over robust ones. Finally, our results are not sensitive to the addition of the Fung and Hsieh seven-factor model. However, the explanatory power of the eleven-factor model is much higher for some hedge fund strategies involved in arbitrage.

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Notes

  1. CMA is the abbreviation for ‘conservative minus aggressive’ – that is, a portfolio which is long in stocks of firms with a low ratio of investment to assets and short in stocks of firms with a high ratio of investment to assets.

  2. RMW is the abbreviation for ‘robust minus weak’ – that is, a portfolio which is long in stocks of robust firms in terms of profitability and short in stocks of weak firms in terms of profitability.

  3. HML is the abbreviation for ‘high minus low’ – that is, a portfolio which is long in stocks of firms having a high book-to-market ratio and short in stocks of firms having a low book-to-market ratio.

  4. SMB is the abbreviation for ‘small minus big’ – that is, a portfolio which is long in stocks of small firms and long in stocks of big firms.

  5. More precisely, firms overinvest when they are in financial distress and expect that projects with positive VAN may rescue them. By doing so, they expropiate their debt stakeholders.

  6. Even if they consider that the factors of their model – including market risk premium, SMB and HML – are measured with errors, Hou et al (2015) and Fama and French (2015) do not ‘instrument’ factors to tackle the problem related to measurement errors. Their objective, as ours, is to study the interaction between factors. Replacing factors with instruments is inconsistent with this objective since it creates interactions per se which are not related to our goal. Moreover, introducing more factors – that is, CMA and RMW – in the original Fama and French three-factor model is a way to reduce the co-movement of the original three factors with the innovation of the empirical model, which creates the problem related to errors-in-variables. This interaction will be partly taken into account by CMA and RMW. It is precisely the object of our paper to study the interaction between old and new factors.

  7. Note that Fama and French (2015) do not introduce the momentum factor (UMD) proposed by Carhart (1997) and the liquidity factor proposed by Pástor and Stambaugh (2003) in their new asset pricing model. They justify this omission by the fact that these two factors have regression slopes close to zero in their experiments so they decided to discard them. According to Fama and French (2015), these factors produce trivial changes in model performance.

  8. Note that investment represents a decrease in the book value of equity (B t) – that is, an expense or a negative cash-flow. Instead of putting ΔB in equation (4), Miller and Modigliani (1961) put I in their original equation – that is, equation (9) in their 1961 article.

  9. The address of French’s website is: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

  10. The address of Hsieh database is: https://faculty.fuqua.duke.edu/~dah7/HFData.htm.

  11. Note that there are more sophisticated ways to account for return smoothing. See Getmansky et al (2004) and Brown et al (2012).

  12. Excepting the futures strategy.

  13. Note that we list only the strategies which have a significant exposure to HML in the Fama and French three-factor model.

  14. That is, the model including the market risk premium, SMB, CMA and RMW.

  15. When excluding HML.

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Acknowledgements

The authors would like to thank the seminar participants at the SFA Annual Meeting held in November 2015.

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Authors and Affiliations

  1. Telfer School of Management, University of Ottawa, 55 Laurier Avenue East, Ottawa, K1N 6N5, Ontario, Canada

    François-Éric Racicot & Raymond Théoret

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  1. François-Éric Racicot
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Correspondence to François-Éric Racicot.

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1is a professor of finance and econometrics at the Telfer School of Management, University of Ottawa. His research interests focus on the problems of measurement errors, specification errors and endogeneity in financial models of returns. He is also interested in developing new methods used for forecasting financial time series – especially hedge fund measures of risk. He has published several books and articles in quantitative finance and financial econometrics. He is an advisory board member of Aestimatio, the IEB International Journal of Finance and an editorial board member of the Journal of Asset Management (JAM) and Journal of Derivatives & Hedge Funds (merged with JAM). He is an associate member of the Groupe de Recherche en Finance Appliquée (GReFA), University of Sherbrooke; the CGA-Canada Accounting and Governance Research Center (CGA-AGRC) and the Corporate Reporting Chair (ESG-UQAM).

2holds a PhD in Economics (financial economics) issued by the University of Montreal. He is full Professor of Finance at the Business School (ESG) of the University of Quebec, Montreal (UQAM). His articles appeared in the following journals: The Journal of Derivatives & Hedge Funds; The Journal of Banking and Finance; The Journal of International Financial Markets, Institutions and Money; Applied Economics; Managerial Finance; Review of Economics & Finance; Applied Financial Economics; The Journal of Asset Management; The Journal of Wealth Management; International Advances in Economic Research; L’Actualité Économique; Journal of Theoretical Accounting Research; Luxembourg Economic Papers and Journal of Risk and Insurance. He is member of the Corporate Reporting Chair (ESG-UQAM).

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Racicot, FÉ., Théoret, R. The q-factor model and the redundancy of the value factor: An application to hedge funds. J Asset Manag 17, 526–539 (2016). https://doi.org/10.1057/jam.2016.22

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