Estrategia creativa

Significant criticism of Fama and French three-factor model and new evidence on the impact of profitability and investment on expected returns (such as Novy-Marx, 2013 and Aharoni, Grundy and Zeng, 2013) leaded to a new Fama and French five-factor model (Fama and French, 2015). The new model included five risk factors, the market, size and book-to market factors (as for the three-factor model) and additional profitability and investment factors, which, according to Fama and French, were chosen as natural choices as both, profitability and investment add to the description of average returns provided by book-to market.

The model was written as:

𝑅𝑖,𝑡− 𝑅𝐹,𝑡= 𝛼𝑖+ 𝛽𝑀(𝑅𝑀,𝑡− 𝑅𝐹,𝑡) + 𝛽𝑆𝑀𝐵(𝑅𝑆𝑀𝐵,𝑡) + 𝛽𝐻𝑀𝐿(𝑅𝐻𝑀𝐿,𝑡) + 𝛽𝑅𝑀𝑊(𝑅𝑅𝑀𝑊,𝑡) + 𝛽𝐶𝑀𝐴(𝑅𝐶𝑀𝐴,𝑡) + 𝑒𝑖,𝑡 [5]

where R_i,t is the return on security or portfolio i in period t, RFt, is risk free rate (US 1 month Treasury bill), RMt is the return on the value-weigh market portfolio (the value-weighted return of all CRSP stocks incorporated in the US and listed on the NYSE, AMEX, or NASDAQ),

SMB and HML are Fama and French (1993) size (small minus big returns) and value (high minus low book-to-market returns) factors respectively, RMW and CMA are new profitability and investment factors calculated as the difference between the returns of stocks with robust and weak profitability (RMW) and the difference between the returns of low and high investment firms (conservative minus aggressive (CMA)), and 𝑒𝑖,𝑡 is error term. Intercept α_i should be equal to zero for all securities and portfolios if the factor exposures (betas) β_M, β_SMB, β_HML, β_RMW, β_CMA capture all variation in expected returns.

The size and value factors are constructed using independent sorts of stocks into two Size groups and three B/M groups (HML) (2x3 factors). NYSE median market cap was applied as the Size breakpoint. The 30th and 70th percentiles of B/M for NYSE stocks were used for the B/M breakpoints. The profitability and investment factors of the 2x3 sorts, are built in the same way as HML (two Size groups and three OP groups (RMW), or three Investment groups (CMA). Operating profitability, OP, in the sort for June of year t was calculated using accounting data for the fiscal year ending in year t-1 and was estimated as revenues minus cost of goods sold, minus selling, general, and administrative expenses, minus interest expense all divided by book equity. Investment was measured as the rate of growth of total assets from the fiscal year ending in year t-2 to the fiscal year ending in t-1.

The results revealed that the value factor becomes redundant for describing average returns when profitability and investment factors are added, as high average returns are fully captured by its exposures to RMRF, RSMB, and especially RRMW and RCMA. Authors suggested that four factor model (without RHML factor) can be used as well as five factor model for estimation of abnormal returns. As another alternative, RHML can be substituted by RHMLO (orthogonal HML) as the sum of the intercept and residual from the regression of RHML on RMRF, RSMB, RRMW, and RCMA.

Overall, Fama and French (2015) claim that the five-factor model is superior to the three-factor model (Fama and French 1993) although FF5 model fails the GRS test rejecting the null hypothesis that the market model pricing errors are jointly zero. According to the results, the new five-factor model explains between 71% and 94% of the cross-section variance of expected returns for the Size, B/M, OP, and Investment portfolios. However, it was noted that the model

is unable to describe average returns of the small stocks of firms that invest a lot despite low profitability.

The next study of Fama and French (FF, 2016) tested the five-factor model on the range of anomalies which cannot be captured by FF3 model and were previously discussed in the literature; such as accruals, net share issues, momentum and volatility. The results showed that in contrast to the three-factor model, five-factor model’s positive exposures to RMW and CMA (typical of profitable firms that invest conservatively) are able to explain the high average returns associated with low β, share repurchases, and low volatility. Contrariwise, negative FF5 exposures to RMW and CMA, (typical of less profitable firms that invest aggressively) capture the low average returns associated with high β, large share issues, and highly volatile returns.

However, it was explained that the portfolios that are in the smaller size quintiles (microcaps) and in the highest quintiles of share issues and volatility cause serious problems when tested in respect to net share issues and volatility anomalies. Moreover, similarly to the three-factor model, accruals are still the main problem which remains unexplained by the five-factor model.

The model also showed poor performance for portfolios formed on momentum. Authors emphasised that adding momentum factor is beneficial to the five-factor model and improves its explanatory power. Six-factor model (with momentum included, MOM-factor) performed best on the GRS test. Authors claim that models with MOM factor, including Carhart’s (1997) four-factor model, perform almost as well as the six-factor model. Nevertheless, the six-factor model leaves lots of momentum in microcap returns unexplained.

Fama and French (2017) conducted further FF5 tests using international data from four regions:

North America, Europe, Japan and Asia Pasific. The results showed that average stock returns for all regions excluding Japan increase with the book- to-market ratio and profitability and are negatively related to investment. Global FF3 and FF5 models were considered poor performing in tests on regional portfolios. For Japan, a strong positive relation between B/M and average returns is the only pattern captured by the local version of FF3 model. The factor spanning tests conducted for the period from 1990-2015 revealed that investment factor (CMA) is redundant for Europe and Japan as it adds little to the description of average returns. The study also confirmed the issues raised in FF (2015) that portfolios of small stocks whose returns behave like those of firms that invest a lot despite low profitability have low average returns and cause problems to FF5 in many different sorts.

Among other evidence on the Fama and French five-factor model performance we can mention Lin (2017) who tested the ability of the five factor model to describe average returns in the Chinese equity market over the period 1997-2015. Similarly to Fama and French (2017) they found FF5 investment factor to be redundant. In contrast to Fama and French (2015) both value and profitability factors were considered important, however, based on the results profitability has higher explanatory power than HML factor. Nichol and Dowling (2014) compared the performance of the Fama and French model with a three factor model proposed by Chen et al., (2011) consisting of the market factor, an investment factor, and a return-on-equity factor. The results suggest that investment factors appear not to be effective in the UK context, and that FF5 provides marginal improvements to the widely used FF3 model with its profitability factor offering the most potential. On the opposite side Chiah et al. (2016) compared the performance of the FF3 vis a vis FF5 model in pricing Australian equities and provided results that FF5 outperforms FF3 and is able to explain better asset pricing anomalies.

Similarly, the superiority of the FF5 in explaining the returns of anomaly portfolios was stated in Zaremba and Czapkiewicz (2017), who performed a comparative analysis of factor pricing models for Eastern European markets (Czech Republic, Hungary, Poland, Russia, and Turkey).

Huyhn (2017) tested the ability of FF3 and FF5 models to explain anomalies in Australia with focus on the spread return to long-short trading strategies. The results showed significant spread returns for 16 out of 19 anomalies examined. This study confirmed that the number of anomalies that remain decreased when FF5 applied; however, it stated that the findings provide cautious support that the new factors RMW and CMA have a role to play. The work emphasised that both FF3 and FF5 models failed GRS test and concluded that the search for the most accurate asset pricing model continues. Similai (2016) asserted that FF5 can provide a parsimonious description of average returns of accrual-sorted portfolios. Ball et al., (2016) posited that FF3 and FF5 does not explain accrual anomaly and suggested to use cash-based operating profitability (a measure that excludes accruals), which is better in explaining the cross section of expected returns than gross profitability, operating profitability, and net income, all of which include accruals. According to the results, cash-based operating profitability explains expected returns as far as ten years ahead.

2.3.4. Recent evidence criticising Fama-French-Carhart portfolio/factor