Revisiting the three factor model in light of circular behavioural simultaneities
Authors: Bekiros Stelios , Loukeris Nikolaos , Eleftheriadis Iordanis , Uddin Gazi 
Published: July 2018

Purpose
The authors construct asset portfolios comprising small-sized companies and value stocks that provide with higher returns for the UK market based on a three-factor model with incorporated behavioural features. The authors were able to demonstrate that value factor model is vulnerable to behavioural patterns, especially corporate fraud. In all of the above, the authors utilised a new proportional sorting methodology against the value ranking approach, commonly employed in empirical studies. Strong evidence is observed that portfolio performance based on various syntheses of allocated assets reveals counter-intuitive results related to the BE/ME, namely, that expected returns based on size and BE/ME produce significant errors and small firms retain consistently better returns. The reason might be the unusual accounting techniques many firms follow to receive extended capital after management decisions. The paper aims to discuss these issues.

Design/methodology/approach
The authors were able to demonstrate that value factor model is vulnerable to behavioural patterns, especially corporate fraud. In all of the above, authors utilised a new proportional sorting methodology against the value ranking approach, commonly employed in empirical studies. Strong evidence is observed that portfolio performance based on various syntheses of allocated assets reveals counter-intuitive results related to the BE/ME, namely, that expected returns based on size and BE/ME produce significant errors and small firms retain consistently better returns. The reason might be the unusual accounting techniques many firms follow to receive extended capital after management decisions.

Findings
Value factor model is vulnerable to behavioural patterns, especially corporate fraud. In all of the above, the authors utilised a new proportional sorting methodology against the value ranking approach, commonly employed in empirical studies. Strong evidence is observed that portfolio performance based on various syntheses of allocated assets reveals counter-intuitive results related to the BE/ME, namely, that expected returns based on size and BE/ME produce significant errors and small firms retain consistently better returns. The reason might be the unusual accounting techniques many firms follow to receive extended capital after management decisions. Overall, asset pricing models with embedded risk factors which entail either shares or dividends are logically circular behavioural simultaneities, thus invalid when tested and estimated by statistical methods as an outcome of the EMH.

Originality/value
In distinctive contrast to the recent literature, the authors show that the returns from a size factor model of small stocks tend to outperform big stocks especially in crisis periods. Moreover, the authors were able to demonstrate that value factor model is vulnerable to behavioural patterns, especially corporate fraud. In all of the above, the authors utilised a new proportional sorting methodology against the value ranking approach, commonly employed in empirical studies. Strong evidence is observed that portfolio performance based on various syntheses of allocated assets reveals counter-intuitive results related to the BE/ME, namely, that expected returns based on size and BE/ME produce significant errors and small firms retain consistently better returns. The reason might be the unusual accounting techniques many firms follow to receive extended capital after management decisions. Overall, asset pricing models with embedded risk factors which entail either shares or dividends are logically circular behavioural simultaneities, thus invalid when tested and estimated by statistical methods as an outcome of the EMH.