The gross profitability anomaly: UK evidence
∗
Tim van den Pol
†MSc thesis Finance
University of Groningen
February 12, 2016
Abstract
The scope of this paper is directed at profitability premium, as evidenced by Fama and French (2015) and Novy-Marx (2013). Literature regarding this specific profitability anomaly will be discussed and practically presented through the empirical research of British stocks during the period 1990-2015. The results prove that more profitable companies do yield higher average returns than those that are unprofitable. These results are convincing for the period post 2000 particularly during and right after times of financial distress, across the size spectrum and are not explained by transaction costs.
JEL classification: G12.
Keywords: Asset pricing, factor models, profitability.
Supervisor : prof. dr. R.M. Salomons.
1.
Introduction
“It’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price.” (Buffett, 1989)
Finance has not done away with Buffet’s focus on buying wonderful companies at a fair price. Greenblatt (2006) quantifies Buffet’s quote as earnings before interest and tax (EBIT) deflated by capital employed. Greenblatt’s ratio, the return on capital employed (ROCE), aims to select quality and wonderful companies at a fair price, in contrast to, the Fama and French (1993) Three-Factor Model which does take into account the quality of companies. Nonetheless, Fama and French (2006) argue on the basis of the Dividend Discount Model that profitable companies should generate higher returns than unprofitable companies. Additionally, Novy-Marx (2013) finds that quality, defined by gross profitability, predicts the cross-section of average returns just as well as the value anomaly. He argues that profitable companies outperform unprofitable companies despite having higher valuations, in that, he challenges Fama and French (1993) who associate the high average returns of value stocks to their low-profitability.
Novy-Marx (2013) makes a case for quality as a hedge for value since value strategies focus on obtaining inexpensive assets and selling off expensive assets, whereas strategies based on profitability are addressing the acquisition of productive assets and liquidation of unproductive assets. To put it another way, quality matters because value stocks consist of stocks with sustainable income and unsustainable income. Quality distinguishes between high yield companies and those for which the high yield is temporary and is on the verge of disappearing. Moreover, quality examines the extent to which the high yield of a company may be an representation of distress, future decline in profitability or negative future price returns. That same reasoning is what underpins Buffet’s “wonderful company at a fair price” philosophy. Nowadays, Fama and French (2015) incorporate the profitability measure as a new factor, extending their Three-Factor Model. They define the profitability premium as operating profits deflated by the book value of equity.
Sovereign wealth fund which lost more than 17 percent of its value within only the first eight months of 2008. This leads to Ang, Goetzmann, and Schaefer (2011) advising the Norwegian government to focus more on market anomalies and factor investing. While there is nothing inherently novel about the idea of factors, the so-called ‘factor-investing’ phenomenon, wielded equity market anomalies in far more stark ways than expected, which in turn, manifested new and improved definitions of market anomalies. Cochrane (2011) argues that: “we now have a zoo of new factors”. According to him, the quest now is to put this zoo of factors to order. Fama and French (2015); Novy-Marx (2013) present evidence for a profitability factor that is able to digest a portion of this new anomalies in American equity markets, which have become the primary sources for observation within this field. How does that relate to other countries? Fama and French (2012) show that anomalies do not always translate well between equity markets in the Unites states and those in other countries. So far, as I am aware of, there is no research for equity markets in the United Kingdom that focuses on explaining anomalies by a profitability factor, nor is there profound evidence for a profitability risk premium. This paper focuses on the latter as its endeavour is to amplify and extend the current literature by assaying profitability anomaly for the British equity markets from January 1990 through July 2015.
I find that profitability measures produce a spread that is not explained by either the size or value factor and the effect is not just present among small companies. However, the anomaly has only been observed in era post 2000 and has a tendency to perform well during and just after periods of market distress. Self-financing profitability portfolios gather most of their return due to relative under performance of low-profitable stocks in comparison to the market.
This paper begins with a comprehensive background on how the profitability premium has emerged and forms a hypothesis that more profitable companies should earn higher average returns. Following this, the data and methodology are described,whereby, the method is to sort through different measures of the profitability anomaly. The methodology is then applied to the data with consequent discussion and concluding sentiment.
2.
Literature
2.1.
The Fama and French Three-Factor Model
As mentioned in the introduction, the relationship between risk and return is still relevant today and the emergence of market anomalies and factors have fuelled this discussion. This subsection takes the three-factor1 asset pricing model (Fama and French, 2015), equation (1), and describes on the basis of that model how factor investing has evolved over the years.
Rit− RF t = ai+ bi(Rit− RF t) + siSM Bt+ hiHM Lt+ eit (1)
The Capital Asset Pricing Model (CAPM) describes a positive linear relationship between risk and return, in that, it exploits the interaction of assets with each other, as a loss on one asset is compensated by a gain on another (Sharpe, 1964; Lintner, 1965). It states that investors are only compensated for bearing systematic risk since this cannot be reduced through diversification. Thus, according to the CAPM, the only way to outperform the market is to take on more systematic risk. This explains the positive relation between returns and market betas, which measure the systematic risk of an asset in its relation to the market. In equation (1) this corresponds to Rit− RF t, where bi is the beta. Factor investing
is now questioning the relationship between risk and return as described by the CAPM. Jensen, Black, and Scholes (1972) pioneered these inquiries and found that the relationship between risk and return is not linear, low risk stocks produced a higher return than expected on the basis of the CAPM.
Fama and French (1993) explain asset returns with two additional factors compared to the conventional market factor of the CAPM, however, they did not discover these anomalies. The first factor is that of size and was discovered by Banz (1981). He finds that, despite adjusting for market betas, smaller companies still have higher returns than larger companies. However, nowadays the existence of the size premium has been questioned as Fama and French (2012) find international proof that argues against this notion. Nonetheless, Gregory, Tharyan, and Christidis (2013) contend that a small size premium within the UK market exists. In addition to that, the effects of other factors, such as value, differ between small and large stocks (Loughran, 1997).
A further anomaly under scrutiny is that of value, as evidenced by Basu (1977). This became widely known within the context of the Three-Factor Model by Fama and French (1993). The value factor is formed by subtracting the returns of a portfolio of companies with high book-to-market ratio from a portfolio of companies with low-book-to-market ratios. To
relate this to the CAPM, where companies with higher systematic risk earn higher returns, Fama and French (1993) point out that the two additional factors are estimates for systematic risk and why they are priced for that reason. Moreover, they state that small companies and those with a high book-to-market ratio are more likely than others to default. This risk, known distress risk, is estimated by the aforementioned factors. Beyond a rational angle, the value premium could be explained from a behavioral finance perspective. A proper illustration of this perspective is given by Lakonishok, Shleifer, and Vishny (1994), when they state that “value strategies yield higher returns because these strategies exploit suboptimal behavior of the typical investor and not because these strategies are fundamentally riskier”.
2.2.
Quality, defined by profitability
The focal factor for this paper is that of quality and points at capturing excess returns of high quality companies relative to the market. Benjamin Graham, known as “the father of value investing”, was one of the first to have advocated for the use of a set of criteria when buying stocks to ensure a minimum quality in their past performance and ensure a threshold levels of earnings (Graham, Dodd, and Cottle, 1934). His strategy towards value stock selection was isolating 30 companies with a price-to-earnings ratio lower than 10 and a debt-to-equity ratio of below 50 percent. Although Graham is perceived as a value investor, the principles he established clearly rely on selecting companies with a certain quality in their past performance.
Modern finance has not done away with the principles of Graham. When Ball and Brown (1968) research the relation between earnings and share prices, they find that earnings, defined by bottom line net income, predicted average returns. Sloan (1996) has put this principle in a modern asset pricing context and finds evidence for a quality premium. His definition lays within accruals, which is the difference between net operating cash flows and income. Moreover, earnings are then divided into operating cash flows and accruals. Sloan states that cash flows are more closely related to future earnings and share prices than accruals. The accrual anomaly challenged the efficient market hypothesis since publicly available accounting information was not entirely exposed.
He developed the F-score, nine measures that indicate the quality of a stock. These nine measures are divided into three categories: profitability, financial leverage and operating efficiency. Within profitability there are further four measures which can be defined as return on assets, the change in return on assets, accruals and operating cash flows. He finds that despite the strong overall performance of value portfolios more than half of the stocks underperformed in comparison to the market, over one and two year horizons. Conclusively, fundamental analysis appears to be robust over time since Graham et al. (1934) employed an approach quite similar to Piotroski (2000).
2.3.
Explaining profitability
The previous subsection described how profitability premium has evolved but did not clarify how it is related to average stock returns. In light of the significant mispricing of profitable and unprofitable companies as evidenced by Fama and French (2015) and Novy-Marx (2013), I will explore a number of behavioural finance theories that offer an explanation (Wang and Yu, 2013). Daniel, Hirshleifer, and Subrahmanyam (1998) show that investors underreact to public news and are overconfident about the quality of the private signals they receive. Hence, the effects of the profitability mispricing is expected to be stronger among companies with more overconfident investors. Barberis, Shleifer, and Vishny (1998) state that investors gradually presume that a trend they observe in stocks prices is representative of trends that they have seen in other data. Due to the conservatism bias, investors do not rapidly revise their views and therefore need some time to fully incorporate new informa-tion. The representativeness heuristic shows that people tend to make decisions in uncertain contexts based on comparisons to similar situation they have previously experienced and assume that future events will resemble past (Tversky and Kahneman, 1974). The con-servatism bias coupled with the representativeness heuristic leads Barberis et al. (1998) to the conclusion that investors underreact to sporadic news and overreact to consistent news trends. With this in mind, one expects the profitability anomaly to be less present among companies exposed to frequent news regarding their profitability.
combined make a case for the existence of the profitability anomaly, especially among the companies which are covered less by public news and do not have attentive investors; the smaller stocks.
Another explanation for the anomaly is grounded in investment-based asset pricing (To-bin, 1969; Cochrane, 1996). Q-theory states that a company’s return is based on its relative cost of investment, which means that returns are dependent on a company’s marginal ben-efits or investments in the future, relative to its marginal costs of investments today. Since profitability is positively related to marginal benefits of investments, more profitable compa-nies should earn higher returns. A further explanation is based on the real options approach where the value of projects by less profitable companies are by definition lower than those of highly profitable companies(Wang and Yu, 2013). Thus, the opportunity cost for abandon-ing a project and reducabandon-ing risk are less for an unprofitable company. The more unprofitable the company is, the more valuable this option becomes and consequently low-profitable companies are less risky and therefore have lower expected returns.
Yet, Fama and French (2006) have another compelling argument. They illustrate how both book-to-market and profitability are positively associated to expected returns utilising the Dividend Discount Model in combination with clean surplus accounting. The return of a company under clean surplus accounting is computed by excluding transactions with shareholders. Thus, retained earnings correspond to the change in book value which leads combinationly to equation the definition of a company’s market value as described by Miller and Modigliani (1961). Mt = ∞ X τ =0 Et(Yt+τ − dBt+τ) (1 + r)τ (2)
In equation (2), Yt+τ is the earnings in period t + τ , dBt+τ = Bt+τ − Bt+τ −1 is the change in
that the expected earnings in (2) reflect the economic profitability of a company. He states that earnings defined by a company’s income statement equal the economic profitability of a company minus investments that are treated as expenses, for example research & devel-opment costs. Consequently, he argues that gross profitability scaled by total assets is the cleanest accounting measure for expected earnings. Further, he points out that gross profits-to-total assets have the same predictive power in explaining returns as the book-to-market ratio. This paper applies the proxies described by Fama and French (2015) and Novy-Marx (2013) to the UK equity markets.
2.4.
Research gap and hypothesis development
In respect to the literature above, the core hypothesis for this paper argues that compa-nies which are more profitable should yield higher average returns. Furthermore, both the existence of the size anomaly and the behavioural arguments suggest that the profitability anomaly is starkly more present among small stocks than within large companies. There-fore, incorporating transaction costs may help to validate if the anomaly is at least partly explained by limits to arbitrage. Additionally, the paper examines the negative correlation between the profitability factor and the value factor as evidenced by Novy-Marx (2013). Most of these hypotheses are tested for equity markets in the Unites States and lead Fama and French (2015) to preliminary evidence for a five-factor model in explanation of asset re-turns. British equity markets, are according to Gregory et al. (2013), still best explained by the four-factor model of Carhart (1997). Hence, evidencing a profitability premium could be a first step to further the explanation of asset returns. The introduction discussed how the profitability metrics of Buffet and Greenblatt could be decomposed in two separate measures. The first measure is a proxy for profitability, the second is a measure of price and determines how efficient the company is using its capital to generate the amount of profitability.
gross profits total assets = gross profits revenue × revenue total assets (3) operating profits book value of equity =
operating profits
revenue ×
revenue
book equity (4)
I use the DuPont model to break down both the Profitable minus Unprofitable metric, equation (3), from Novy-Marx (2013) and the Robust minus Weak factor, equation (4), by Fama and French (2015). The hypothesis is that profitable and robust companies do not only have high margins but are also using their capital efficiently.2
3.
Data and methodology
The methodology employed in this paper to survey my outlined hypothesis is constructed through one-and-two-way sorts. This is akin to the structure of that used by Novy-Marx (2013) and Fama and French (2015), in addition, I also take into account the transaction costs. The data will be initially discussed followed by the methodology.
3.1.
Data gathering and selection
The data is accessed through Datastream and belongs to the United Kingdom (UK) Wordscope database. My sample is collected from data starting in 1989 and utilises ac-counting data for each given fiscal year at the end of June of the following calendar year. Consequently the asset pricing tests run from July 1990 to July 2015. The Woldscope database includes so-called “dead” stocks, which are stocks that have been delisted over the course of the sample, to minimize the impact of survivor-ship bias. The sample consists of companies with valid data on their market and book value of equity, book value of total as-sets, operating and gross profits and current monthly returns. As figure 1 shows, the sample starts with 433 companies in 1990, steadily increases to a peak of 667 companies in 1997 and then falls to 566 by the end of the sample. Although the UK Worldscope database provides data from 1985 onwards, I feel that this representation is incomplete and as figure 1 presents would result in a very small sample size for those years before 1990. I thus choose, to exclude these years.
On the data gathering and selection process, I closely follow Novy-Marx (2013) and Gre-gory et al. (2013), in that, I exclude financial and foreign companies and also, winsorise the control and independent variables at the first and last percentiles. In this regard, following Fama and French (2006), companies with book equity less than £12.5 million or with total assets less than £25 million are also excluded to preclude undue impact of mirco-caps. All this results in a data-set approximately comparable to the data-set constructed by Gregory et al. (2013) who provide the data on the SMB, HML and UMD factors for the UK equity markets in the period October 1980 to December. The reason for their longer sample period is that they, unlike Datastream, also have access to the London Business Share Price Database which thoroughly covers years before 1990. Note that appendix A.1 and A.2 expound on this matter.
as the equity multiplier. Both equation (3) and (4) can be further specified since book equityrevenue = total assetsrevenue × total assets
book equity and
revenue total assets =
revenue book equity×
book equity
Fig. 1: Sample size
This figure show the number of companies in the data-set as of the first of July for each year. The left, white filled bars, are the years that are not included in the data-set due to data limitations. The number of companies included in the sample, the black coloured bars, is 433 in 1990 with the number peaking to 667 in 1997. The number then falls to 566 companies at the end of the sample.
86 88 90 92 94 96 98 00 02 04 06 08 10 12 14 Number of companies 200 300 400 500 600
700 Number of companies in the sample
3.2.
Limitations to the data
Datatream proves to be a useful resource since it covers a great deal of the data under investigation within this paper. Just as every coin has two sides, however, so do databases with their limitations. One of those limitations is that databases use very different definitions for what should be the same variable. An example of this, is how gross profits are defined under Compustat and Datastream. Another limitation is that in the United Kingdom three systems are used to determine closing prices.3 One of these uses the midpoint price as the closing price. This particular system is responsible for the majority of stocks traded on the Alternative Investment Market (AIM). Consequently, through this system estimating effective spreads or price impacts would be a difficult task at the best of times. That said, transaction costs are estimated based on the quoted spread and I expect these to be relatively large since the quoted spread is often used as a starting point for negotiations and does not represent the price of the trade. Another way to cope with such an issue, and suggestion for further research, is to use the sample covariances of daily price changes to estimate the transaction costs as proposed by Hasbrouck (2009)4. Yet, I consider such a solution beyond the scope of this paper. Other limitations emerge from differences in accounting standards between companies and over time. To cope with this Novy-Marx (2013) uses gross profitability instead of earnings or operating profitability, he argues that: “gross profits is
3The stock exchange electronic trading systems (SETS) is used for all main exchanges and some liquid AIM stocks. The market making is electronic and it uses an auction period to determine the closing prices. Whereas, the Stock Exchange Automated Quotation (SEAO) is used for some stocks traded on the AIM, is non-electronic and defines the closing price as the last midpoint price.
the cleanest measure of true economic profitability, the farther down the income statement one goed, the more polluted the measures become”. In regard to these limitation I present my data.
3.3.
Independent variables
When defining the profitability premium, the independent variables are different proxies for profitability. I calculate the book value of equity as total assets minus total liabilities and gross profits are defined as revenue minus costs of goods sold (COGS). In the default specification gross-profits are scaled by total assets, as in the gross profitability definition outlined by Novy-Marx (2013). For operating profitability, the definition utilised is provided by Fama and French (2015), where operating profits are deflated by the book value of equity. In the alternative specifications both the proxies are broken down according to the DuPont model. This results in a measure of how profitable companies are in relation to their revenue and a proxy for asset or capital efficiency. In doing so, either gross profits or operating profits are scaled by revenue to generate a measure of profitability relative to sales. Further, I deflate revenue by either gross profits or operating profits, to create a measure of how efficiently a company is employing its assets or equity to generate sales. This is specified in equation in (3) and (4).
Table 1: Descriptive statistics for the independent variables
This table presents the descriptive statistics for the variables utilised in the asset pricing tests. The accounting variables are deflated by total assets and the book value of equity to create the ratios described in the literature. r12,2is the prior year’s returns excluding those of the last month. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015.
Percentiles
Variable Mean SD 5th 25th 50th 75th 95th
Accounting variables scaled by total book assets
Gross profits 0.31 0.23 0.03 0.15 0.26 0.41 0.71
Revenue 1.16 0.80 0.13 0.59 1.05 1.53 2.74
Accounting variables scaled by book value of equity
Operating profits 0.21 0.22 -0.08 0.10 0.19 0.29 0.54
Revenue 2.43 1.46 1.20 1.63 2.07 2.68 4.80
Accounting variables scaled by revenue
Gross profits 0.29 0.29 0.05 0.17 0.28 0.41 0.66
Operating profits 0.09 0.12 -0.02 0.04 0.08 0.14 0.29
Other variables
Market value of equity (£106) 1074 3154 20 56 159 602 5471 Book equity-to- market equity 0.72 0.63 0.13 0.31 0.53 0.89 1.93
r12,2 0.05 0.38 -0.64 -0.14 0.09 0.28 0.59
3.4.
Risk factors
Table 2: Spearman rank correlations
This table presents the Spearman rank correlations between the independent variables utilised in the asset pricing tests. The numbers and variables correspond to those in table 1. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2014.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Accounting variables scaled by total assets
(1) Gross profits 1.00
(2) Revenue 0.60 1.00
Accounting variables scaled by book value of equity
(3) Operating profits 0.50 0.45 1.00
(4) Revenue 0.13 0.38 0.48 1.00
Accounting variables scaled by revenue
(5) Gross profits 0.45 -0.33 0.11 -0.20 1.00
(6) Operating profits 0.09 -0.33 0.48 -0.11 0.51 1.00
Other variables
(7) Market value of equity -0.03 -0.10 0.31 0.19 0.09 0.33 1.00
(8) Book equity-to- market equity -0.35 -0.22 -0.57 -0.24 -0.16 -0.24 -0.46 1.00
(9) Prior year’s performance (r12,2) 0.05 0.05 0.06 0.03 0.02 0.05 0.11 -0.15 1.00
Rm (market return) is specified as the value-weighted return of companies in the
data-set. Note that the time-series Pearson correlation of Rm with the FTSE All Share Index
is 0.90. This is consistent with Gregory et al. (2013) as Rf (risk free rate) is the return
on the three month Treasury Bills as the return on the one month Treasury Bills is only available from March 2000. SMB, HML and RMW are constructed according to Gregory et al. (2013), UMD follows Carhart (1997) and PMU is defined as is Novy-Marx (2013). Hence, HML, PMU and RMW are all constructed similarly and adhere to the breakpoints discussed earlier. Appendix A.2 stipulates this routine.
3.5.
Construction of test portfolios
For example, Fama and French (2015) wrestle with this in their 2 × 2 × 2 × 2 sorts. In view of the data characteristics and research objective, however, portfolio sorts have a better fit. Nonetheless, the results should be the same, as Cochrane (2011) argues that portfolio sorts are really the same thing as nonparametric cross-sectional regressions.
For each of the profitability measures earlier described, ten ranked portfolios are con-structed. Accounting figures for the end of fiscal year end of year t are matched with stock returns from July of year t+1, until June of year t+2, to avoid look ahead bias Fama and French (1993). Following Gregory et al. (2013) the decile sorts employ breakpoints based on the 350 largest companies and monthly value-weighted returns to minimize the impact of the small tail in the data-set. The discussion between equal-and-value-weighted returns is partly analogous to the discussion about sorts and regression. Most literature considers value-weighting, but there are exceptions, such as Fama and French (2008) who provides results for both methods. To come full circle to I present value-weighted results in the paper and back those up with their equal-weighted counterparts in the appendix.
As to the two-way sorts, I first sort on size and secondly on the profitability variable. Again, the portfolios are rebalanced monthly to maintain value weights. Gregory et al. (2013) advocate a similar strategy to determine breakpoints. They equally divide the 350 largest stocks over size groups two, three, four and five. The smallest size groups contains all stocks excepts those of the 350 largest for a particular year. For the second sorting variable they again use the breakpoints of the 350 largest stocks. However, since my sample is smaller, a 433 stock minimum, I feel it is more efficient to use equally dived breakpoints. Hence, the portfolios consist of an approximately equal number of companies and for that reason the approach slightly differs from Fama and French (1992, 1993).
3.6.
Regressions for the test portfolios
After having created portfolios sorted on profitability the key is to determine if these returns are attributable to the known risk factors such as size and value or if they generate an alpha unexplainable by other risk exposures. Further, I compute the Durbin -Watson statistic to research the presence of auto-correlation. DW-statistic can be an addition to R2 since the presence of auto-correlation implies that there is still explanatory power in the
3.7.
Monotonic patterns in the returns of the portfolio sorts
When sorting stocks into portfolios based on their profitability, I expect the returns on the profitable portfolio to be larger than those of the unprofitable portfolio. In addition, one also expects that the returns on the profitable portfolio are larger than those of the second portfolio and so on. However, according to Patton and Timmermann (2010), there is little attention given to analysing such patterns in asset pricing. When sorting stocks into portfolios it is common practice to utilise a t-test to consider the the mean return spread between the value and growth portfolio. Although, comparing the returns of the top and bottom portfolios is not a valid way to make conclusions about the monotonic pattens and only takes part of the data into account. For that reason, I employ the test for monotonic patterns in assets returns as proposed by Patton and Timmermann (2010). Their MR-test follows a nonparametric approach that tests of a monotonic relation between all inequalities. A further strength is that it does not require the relation to be known or specified. This is especially useful since the data does not follow a normal distribution. The MR-test starts with the returns of ten portfolios sorted on profitability measures (r1,t, ..., r10,t). Where the
theory suggest that:
E[r10,t] > E[r9,t] > ... > E[r1,t] (5)
If then: ∆i = E[ri,t] − E[ri−1,t] for i = 2,...,10, equation (5) can be rewritten as: ∆i > 0 for
i = 2,...,10. Where the MR-tests assay the returns differentials, ∆M R = [∆1, ..., ∆N], for a
weakly decreasing pattern under the null hypothesis and strictly increasing pattern under the alternative hypothesis. Thus, H0 : ∆M R ≤ 0 and H1 : ∆M R> 0.
3.8.
Gibbons-Ross-Shanken test
Running regression on the portfolios sorted on profitability, leads to a number of inter-cepts equal to the number of portfolios tested. The t-statistic indicates if each of the alphas are different from zero, but does not indicate whether the intercepts are jointly equal to zero. That is where the test of Gibbons, Ross, and Shanken (1989), hereafter referred to as GRS, is applicable since it tests whether the estimated intercepts from the multivariate regression are jointly zero. It is not only very advantageous that it yield in one single number, but also necessary, because sorting sotcks reduces the power of regressions. As the GRS-test requires unbiased estimates of the covariance matrices, I utilise Newey-West standard errors to compute the regressions (Newey and West, 1987).
Equation (6) displays the static, where T is the number of time-series observations, N the number of tested assets and L the number of risk factors. ˆα is a N x 1 vector of the alpha estimations, ˆP is the covariance matrix of the residuals, ¯µ is a L x 1 vector of the factor portfolio means and ˆΩ is the covariance matrix of the factor portfolios.
3.9.
Transaction costs
To further the understanding of the profitability anomaly, I also take into account the transaction costs. Although profitability strategies are characterized by a low turnover, being dependent on trading expensive stocks could still make it an expensive system. I form strategies on PMU and RMW long-short self-financing tertile, quintile and decile portfolio sorts and measure the impact of transaction cost. As with Novy-Marx (2013), I now use equal weighted returns since it is more common practise to invest equally-weighted rather than value weighted. The portfolios are monthly rebalanced whilst the underlying data is only updated on a yearly frequency. This results in a strategy that has a relatively large turnover once a year and smaller turnovers for the individual months. For the full sample result, breakpoints are based on the 350 largest companies, whereas for a sample of larger stocks, those with a market capitalisation which exceeds £1 billion equally divided breakpoints are used. For the sample with large companies I use equally divided breakpoints.
χt= 0.5 × Nt X i |wi,t− ˜wi,t−1| (7) ˜ wi,t−1= wi,t(1 + ri,t) PNt i wi,t(1 + ri,t) (8)
The turnover, similar to the turnover formulae used by Barroso and Santa-Clara (2015), is defined in equation (7). Nt is the number of stocks at time t, wi,t is the weight of stock
i in the portfolio at time t and ri,t is the return of asset i at time t. Equation (8) explains
˜
wi,t−1 as the weight in the current period right before rebalancing.
Quoted half spreadi,t = 0.5 × 1 12 0 X τ =−12 (Ask(i, t + τ ) − Bid(i, t + τ )) 1 2(Ask(i, t + τ ) + Bid(i, t + τ )) (9)
Table 3: Descriptive statistics for the risk factors
This table reports descriptive statistics for the Carhart (UMD), Fama-French (SMB, HML, RMW) and Novy-Marx (PMU) factors. Rm is the market return, Rf is the risk-free rate and Rm− Rf is the market risk premium. The hit rate is defined as the percentage of months with returns larger than zero. The SMB and HML factors are formed from six intersecting portfolios using yearly market capitalization and book-to-market ratios. The other factors are constructed in similar fashion utilising the variables described in table 1. This method corresponds to the descriptions on the websites of Ken French and Robert Novy-Marx. The statistics are based on value-weighted returns and the portfolios are rebalanced monthly while while the accounting data is only updated on a yearly frequency. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015.
Rm-Rf Rm Rf SMB HML UMD PMU RMW Mean (%) 0.41 0.79 0.38 0.05 0.09 0.58 0.26 0.14 Std dev (%) 4.15 4.12 0.26 2.05 2.81 4.75 2.18 1.73 Min (%) -15.38 -14.99 0.02 -8.10 -8.34 -35.60 -10.40 -6.39 Median (%) 0.94 1.39 0.41 0.11 0.01 1.01 0.31 0.17 Max (%) 11.50 12.23 1.30 7.37 11.67 11.12 9.70 6.16 Hit rate (%) 62.67 66.67 100.00 52.33 50.33 64.33 57.67 55.00 Skewness -0.75 -0.74 0.53 0.08 0.25 -2.04 -0.20 -0.17 Kurtosis 4.51 4.54 3.63 4.17 4.26 14.98 6.31 4.56 Jarque-Beta statistic 57 57 19 17 23 2002 139 32
spread over the year as an estimate for the quoted spread of the company.5
4.
Results
The method discussed throughout the paper is to form portfolios sorted on profitability and examine if these portfolios yield returns that are not explained by other risk factors. First, I discuss the one-way sorted portfolios, examine if these portfolios generate alphas and if adding a profitability factor helps explaining their returns. Next, the two-way sorts are considered which examines the interaction with size, and finally, I discuss if arbitrage is limited by transaction costs.
4.1.
Risk factors
Table 3 and figure A.2 present the risk factors, as described by Fama and French (1993) and Gregory et al. (2013), although, this provides preliminary evidence for a profitability premium, the aim here is to introduce the Fama and French factors that will later be used in the regressions. It is notable is how the market return tanked in 2001 and 2008 and
Fig. 2: Profitability portfolio returns
This figure visualises the monthly average value-weighted returns of portfolios sorted on gross profits-to-total assets (PMU) and operating profits deflated by the book value of equity (RMW). The results are summarized in the second and third column of table 3. Portfolios are formed each year at the end of June and are value-weighted. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015. Unprofitable 2 3 4 5 6 7 8 9 Profitable Average return (%) 0 0.5 1
1.5 PMU portfolio returns (Novy-Marx, 2014), 1990-2015
Weak 2 3 4 5 6 7 8 9 Robust
Average return (%)
0 0.5 1
1.5 RMW portfolio returns (Fama and French, 2015), 1990-2015
consequently corresponded to the momentum crash in 2008. The return of the value factor demonstrates how growth stocks outperformed value stocks during the technology bubble and that the value premium did not yield returns over the last five years. This is in direct contrast to the profitability factors that performed enormously well after the recent financial crisis. Moreover, throughout the course of the sample, the average value premium is smaller than either PMU or RMW. The kurtosis of PMU is clearly out of line with those of HML and RMW factors and none of the data is normally distributed. The correlations between my risk factors and those of Gregory et al. (2013) are 0.70, 0.60, 0.89, 0.99 and 0.90 for ,respectively, SMB, HML, UMD, Rf and Rm. Note that they use the FTSE 1000 as definition for the market return. Figure A.1 and table A.1 expound on the relationships between the risk factors. The PMU and RMW have a correlation of 0.69 and are both correlated to the size premium. In contrast, they seem to relate little to the HML and UMD premiums.
4.2.
One-way sorts
ref-erence of figure 2, assuming that the returns are a linear function of PMU and RMW, and that those variables are normally distributed, one would expect to find an s-shaped pattern. This shape is visible in the lower portfolios but to a lesser extend in the more profitable portfolios. Thus, so far profitability seems to be dependent on the extreme portfolios and is more about avoiding unprofitable companies than it is about investing in the profitable ones.
In table 4, column 2 and 3 present results of the PMU and RMW portfolio sorts from figure 2, whereas the other columns present the results for portfolios sorted on variables according to the DuPont decompositions of equations (3) and (4). For all the variables, except revenues divided by book equity, the t-test depicts that the long/short portfolio is significantly different from zero. However, the MR-test only confirms monotonicity for portfolios sorted on operating profits divided by book equity. This is in contrast to Novy-Marx (2013) who finds that the gross profits-to-total assets is driven by the asset turnover, the results are not clear about whether the profitability premiums are either driven by capital and assets turnovers or margins. However, none of those variables generates returns larger than either one of the profitability factors. As table 4 and Novy-Marx (2013) suggest, there little evidence of a profitability premium in the years before 2000. Panel C and D of the table extrapolate on this further. Although, there seems to be a difference in the high and low portfolios, the monotonicity tests do not support evidence for a profitability premium in the period before 2000.
Table 5, panel A reports the regression results for 10 portfolios are sorted on gross profits-to-total assets. The unprofitable portfolio has negative exposure to the SMB factor and are associated with a value tilt, whereas the more profitable portfolios seem to be more inclined towards smaller growth stocks. Remarkable is that the first portfolio has different factor loadings than the second portfolios, which may be due to outliers. As the alphas, GRS-statistic and R2 indicate, the three-factor model does not fully explain the portfolio returns. The long/short portfolio generates alpha and only has small exposure to the market factor. However, a side-note here is that the R2 is only 0.02.6
Panel C shows the regression results for the RMW portfolios. The low portfolio is tremen-dously tilted towards smaller stocks and is not explained by the value factor in contrast to
Table 4: One-way sorts on profitability metrics and their DuPont decompositions This table presents monthly value-weighted average returns for the profitability factors and their decompo-sitions according to the DuPont model. GP-AT stands for gross profits-to-total assets, OP-BE is operating profits-to-book equity, GP-REV is gross profit margin, OP-REV is the operating profit margin, REV-AT is revenue-to-total assets and REV-BE is revenue-to-book equity. The portfolios are rebalanced monthly while while the accounting data is only updated on a yearly frequency. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015. *Only in this case MR-UP-tests concludes that the MR-test has enough explaining power to support of reject the hypotheses.
profitability factors profit margins capital turnover
Portfolio GP-AT OP-BE GP-REV OP-REV REV-AT REV-BE
(1) (3) (5) (6) (2) (4)
Panel A: average returns, full sample
Low 0.30 0.12 0.51 0.19 0.44 0.64 2 0.71 0.41 0.70 0.53 0.71 0.55 3 0.71 0.77 0.77 0.79 0.87 0.80 4 0.78 0.69 0.64 0.56 0.81 0.88 5 0.79 0.80 0.57 0.67 0.74 0.74 6 0.93 0.73 0.68 0.66 0.65 0.79 7 0.85 0.89 0.95 0.78 0.84 0.79 8 0.77 0.72 0.95 0.82 0.81 0.77 9 1.07 0.76 1.07 0.89 0.88 0.75 High 0.90 0.97 0.78 0.92 0.84 0.75
Panel B: tests of monotonicity, full sample
High-Low 0.59 0.85 0.26 0.73 0.40 0.11
t-statistic 2.50 2.47 1.40 1.96 1.61 0.39
t-test p-value 0.01 0.01 0.08 0.03 0.05 0.35
MR p-value 0.12 0.07* 0.52 0.20 0.23 0.02
Panel C: average returns, July 1990 - July 2000
Low 0.52 0.60 0.72 0.46 0.60 0.75 2 0.75 0.36 0.88 0.69 0.90 0.53 3 0.74 0.96 0.63 0.92 0.87 1.09 4 1.03 0.65 0.59 0.38 0.89 0.86 5 0.76 1.06 0.56 0.71 0.81 0.77 6 0.81 0.82 0.82 0.69 0.62 0.99 7 0.94 0.84 1.02 0.92 0.76 0.69 8 0.79 0.83 0.78 1.01 0.90 0.85 9 1.18 0.62 1.33 0.87 1.01 0.72 High 0.77 1.02 0.71 0.92 0.80 0.65
Panel D: tests of monotonicity, July 1990 - July 2000
High-Low 0.25 0.42 -0.01 0.46 0.20 -0.10
t-statistic 0.73 0.93 -0.02 0.85 0.50 -0.26
t-test p-value 0.23 0.18 0.51 0.20 0.31 0.60
Table 5: Regression results for ten PMU and RMW portfolios
This table uses the three-factor model to explain the returns of the portfolios ranked on gross profits scaled by total assets and operating profits deflated by the value of book equity. For each set of low to high portfolio regressions the GRS tests if the intercepts are jointly equal to zero. |A| stands for the absolute average. The risk factors refer to those of Novy-Marx (2013); Fama and French (1993, 2015). The regression models are:
Panel A: RP M U (t)− RF t= ai+ bi(Rit− RF t) + siSM Bt+ hiHM Lt+ eit Panel C: RRM W (t)− RF t = ai+ bi(Rit− RF t) + siSM Bt+ hiHM Lt+ eit
Panel A: Regression results for 10 portfolios sorted on gross profits-to-total assets Coefficients t-statistics a (%) b s h t(a) t(b) t(s) t(h) R2 DW Low -0.19 1.15 0.34 0.01 -1.13 27.49 3.67 0.19 0.77 1.87 2 0.28 0.98 -0.28 0.40 2.11 25.59 -2.41 4.83 0.81 2.04 3 0.31 0.93 -0.20 0.25 3.14 25.32 -1.84 4.24 0.82 2.28 4 0.41 0.89 -0.29 0.06 3.75 34.90 -4.47 1.19 0.81 2.10 5 0.38 1.00 -0.02 -0.07 3.87 26.98 -0.33 -1.13 0.85 2.10 6 0.50 1.02 0.21 -0.12 3.88 20.86 1.54 -1.26 0.79 1.82 7 0.38 1.11 0.14 0.00 3.32 23.06 1.15 -0.02 0.81 2.41 8 0.32 1.07 0.57 -0.27 2.62 26.22 3.65 -1.97 0.75 2.34 9 0.70 0.88 0.32 -0.13 5.95 17.64 2.33 -1.09 0.71 2.17 High 0.46 1.03 0.42 -0.11 2.78 21.86 3.65 -0.97 0.74 1.88 High-Low 0.65 -0.12 0.08 -0.12 2.65 -1.98 0.53 -0.92 0.02 1.71 Panel B: Summary statistics for the low to high portfolios of panel A
|A| 0.39 1.01 0.28 0.14 3.25 24.99 2.50 1.69 0.00 0.78 2.10 GRS 27.34
Panel C: Regression results for 10 portfolios sorted on operating profits-to-book equity Low -0.46 1.27 1.11 -0.02 -1.67 14.13 6.35 -0.10 0.65 1.81 2 -0.11 1.18 0.28 0.23 -0.70 26.68 2.49 2.55 0.75 2.24 3 0.27 1.12 0.04 0.34 1.40 16.27 0.44 5.70 0.77 1.83 4 0.26 0.99 -0.23 0.29 2.31 24.69 -2.67 5.22 0.81 2.08 5 0.38 0.97 0.02 0.04 3.05 32.04 0.20 0.66 0.82 1.70 6 0.33 0.95 -0.06 0.10 2.51 22.28 -0.54 1.20 0.75 2.14 7 0.49 0.96 -0.19 0.06 3.91 24.10 -2.67 0.86 0.79 2.10 8 0.31 0.97 -0.02 0.10 2.25 28.19 -0.18 0.92 0.79 1.92 9 0.33 1.01 0.31 -0.05 2.58 18.74 3.38 -0.93 0.80 2.09 High 0.57 1.03 0.43 -0.48 4.15 24.20 3.04 -4.19 0.80 1.87 High-Low 1.02 -0.25 -0.68 -0.46 3.62 -2.46 -4.02 -4.51 0.25 1.82 Panel D: Summary statistics for the low to high portfolios of panel C
Table 6: Two-way sorts on size and profitability
This table reports monthly value-weighted average returns of portfolios sorted on the profitability metrics, and their DuPont decompositions, and size. The portfolios are rebalanced monthly while while the accounting data is only updated on a yearly fre-quency. The full sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015. Panel C and D use a sample period until 2000.
Panel A: Market equity x gross profits-to-total assets
Gross profits-to-total assets MR Joint Market equity Unprofitable 2 3 4 Profitable p-value p-value Small 0.44 0.65 0.54 0.84 1.21 0.24 2 0.08 0.83 0.88 0.87 1.16 0.06 3 0.76 0.61 0.50 0.79 1.06 0.18 0.22 4 0.46 0.97 0.92 0.67 0.93 0.53 Big 0.52 0.73 0.82 0.93 0.90 0.06 MR p-value 0.96 0.93 0.95 0.58 0.01 Joint MR p-value 0.95 0.86
Panel B: Market equity x operating profits-to-book equity
Operating profits-to-book equity MR Joint Market equity Weak 2 3 4 Robust p-value p-value Small 0.25 0.70 0.96 0.75 1.07 0.48 2 0.03 0.83 0.95 0.93 1.03 0.03 3 0.32 0.92 0.83 0.79 0.82 0.11 0.11 4 0.55 0.81 0.77 0.75 1.05 0.05 Big 0.68 0.64 0.80 0.78 0.93 0.04 MR p-value 0.61 0.36 0.04 0.53 0.45 Joint MR p-value 0.28 0.09
the high portfolio. The extreme values in this portfolio results in a long/short portfolio with a large alpha and negative SMB factor loading. These results line up with the correlations in table 2 and the hypotheses, as they show a negative relationship between both the value profitability and the value factor. Furthermore, the growth tilt exhibited by the long/short portfolios is due to the growth bias of the profitable portfolios. However, the three-factor model is not able to explain the profitability anomaly, which raises the question, for further research, if the profitability factors can explain average returns?7
4.3.
Two-way sorts
This section elaborates on the previous one by exploring the nexus between size and profitability. Table 6 presents the two-way sorts on profitability and size. As the two-way sorts consist of a lot of inequalities, the test is broken down into a series of conditional tests to better understand the economic interpretation of the results. Panel A shows that
the return on gross profit-to-assets portfolios is increasing with profitability. Although the profitability effect is observable, interaction with size is only significant for the profitable portfolios. The difference between my results and that of Novy-Marx (2013) is that he finds more evidence for the intersection with size and gross profits-to-total assets than my research. To provide more clarity, table 6 uses the MR-test to examine the patterns in expected returns by keeping one sorting variable constant, while varying the other. The panel exposes a profitability premium among size group two and five. Overall, the joint tests do not find statistical evidence that supports a size and profitability effect, notwithstanding, every profitable portfolio, small or big, outperforms its unprofitable counterpart. Comparing this to the findings of Fama and French (2015) yield a similar conclusion consistent with panel A; they come across stronger support for the intersection with size. The MR-test proves the existence of a monotonic pattern in profitability among all size groups. This aligns with the earlier hypotheses, as I predicted a stronger profitability effect among small companies. Again, there is no overall evidence for monotonic patterns. The outliers in the unprofitable and weak bins may come across as rare, for instance, both the second unprofitable and weak portfolio. That said, assuming that the profitability variables are normally distributed, one expects extreme values in the high and low bins. In addition to that, 25 portfolios in relation to the sample size is on the high side and thus, an individual company might have a relatively large impact on the performance of the portfolio. Both the value-weighted and the equal-weighted results, in table A.2, lead to the same conclusions. Profitable companies, for both the variables, do yield higher returns than unprofitable companies, but I only evidence clear monotonic patterns for the RMW variable. Secondly, the table suggests that profitability varies with size but evidence to this is lacked through the MR-test.8
4.4.
Investability
Figure 3 demonstrates the relation between the size and quoted spreads for companies in the data-set and the Worldscope database. Each year at the end of June, companies are ranked on their value of market equity and matched with a quoted spread estimation from the twelve preceding months. As the long tail of small stocks in the data has been an issue throughout the paper, it again has its impact on trading costs. Trading of stocks with a below median market value of equity is expensive at the best of times. However, the quotes half spread (QHS) for companies in the Worldscope data-set is even larger, hence, the data filtering introduces a bias towards the cost with lower trading costs. As described in the
data section, the quoted spread is a limit measure compared to the effective spread and it often is referred to as a starting point for negotiations. Consequently, this causes the spreads displayed in figure 3 to be tremendous. Moreover, the figure also shows the importance for a trading strategy focused on profitability to mitigate transaction cost. Not surprisingly, this can be easily implemented by only trading larger stocks. However, this is at odds with previous results that illustrated profitability as being at its strongest amongst smaller stocks.
Table 7 reports profitability results for self-financing long/short strategies and are con-structed through simple decile, quintile and tertile sorts, in panel A, B and C respectively. For each panel the table presents the gross returns (column 1), the alpha relative to the Fama-French three-factor model (column 2), the average turnover of the long and short leg (column 3), the transaction costs (column 4), the returns accounting for transaction costs (column 5) and the net alpha (column 6). Although the strategy rebalances monthly, to maintain equal weights, the turnover is quite low since the sorting variables are only updated at the end of June of each year. Hence, the strategies exhibit a relatively large turnover at the beginning of July and smaller turnovers, only to maintain weights, during the other months. Figure A.3 visualises this for RMW tertiles.9 The transaction costs relatively high in relation to the
9I only show these plots RMW tertiles as all the strategies exhibit approximately similar patterns in of the transaction costs and turnovers.
Fig. 3: Average quoted half spread
This figure reports the relation between size and the quoted spread. Each year at the end of June stocks are ranked on their market capitalization and matched with an estimation of their quoted half spread. The estimation is based on monthly observations in the twelve months before the stocks are sorted on size. Interesting but not shown it that average spreads have slightly decreased over time. The sample period starts in July 1990 and ends in July 2015.
Market capitalization rank (descending)
0 50 100 150 200 250 300 350 400 450 500
Quoted half spread (%) 0
1 2
3 Time series averages of the quoted half spread, full sample
Market capitalization rank (descending)
0 100 200 300 400 500 600 700 800 900 1000
Quoted half spread (%) 0
2 4 6 8
Table 7: Returns and transaction costs
This table reports monthly equal-weighted returns for self-financing long/short portfolios constructed using equally divided breakpoints and decile, quintile and tertile sorts in panel A, B and C, respectively. In each panel the strategies’ gross return, alpha relative to the Fama-French three-factor model, the average turnover over the long and short portfolio, the transaction cost based on the observed quoted spread, the net returns and the net alpha are shown. The t-statistics are between the parentheses. The portfolios are rebalanced monthly while while the accounting data is only updated on a yearly frequency. The sample period begins in July 1990 and uses the using the accounting variables from 1989. The sample is concluded at the end of June 2015.
Panel A: Long-short decile portfolios E[re
gross] αgrossF F 3 TO T-costs E[rnete ] αF F 3net
PMU 0.59 0.65 11.67 0.43 0.16 0.21
[2.84] [2.65] [2.84] [0.91]
RMW 0.85 1.02 12.47 0.46 0.39 0.56
[2.94] [3.62] [1.37] [2.04]
Panel B: Long-short quintile portfolios
PMU 0.49 0.58 10.63 0.37 0.12 0.20
[2.55] [3.08] [2.55] [1.14]
RMW 0.67 0.84 11.41 0.40 0.27 0.44
[2.29] 2.89 [0.93] [1.51]
Panel C: Long-short tertile portfolios
PMU 0.41 0.51 9.91 0.33 0.08 0.17
[1.98] 2.35 [1.98] [0.82]
RMW 0.64 0.72 10.43 0.34 0.30 0.37
[2.28] [2.39] [1.06] [1.23]
turnover due to using the observed bid-ask spread in the market as a proxy. Hence, almost none of the strategies are able to deliver significant returns after accounting for these costs. Further, all the alphas are larger than the observed returns, mainly because of the negative HML loadings of the strategies.
Figure 4 plots the strategies of table 7 over time. The upper line is the gross return as presented in the second column of table 7 and the lower line represents the net return of column 7. As in the table the transaction costs are tremendous. In accordance to the results of table 4 and Novy-Marx (2013), the strategies gather most of their returns after 2000. Moreover, the strategies have a tendency to perform well during and right after the tech bubble and the recent financial crisis.
to maintain equal weights. The figure corresponds to earlier results since most of the most of the returns come from the short leg of the portfolio. Thus, again, profitability is more about avoiding the unprofitable companies than about investing in the profitable ones. The trans-action costs do not have an huge impact on the effectiveness of the strategies, profitability is profitable on its own. Still the transaction costs evidenced by Novy-Marx and Velikov (2014) are considerably lower as the use the effective bid-ask spread and have a sample with larger companies. Further, this leads to the surprising conclusion that a profitability strategy is more present in large stocks than in smaller stocks after accounting for transaction costs.
4.5.
Limitations and further research
Fig. 4: Profitability strategy performance, full sample
This figure presents returns for the profitability strategies constructed using simple decile and quintile sorting procedures and is rebalanced monthly to maintain equal weights. The upper line is the gross return corresponding to column two in table 7, whereas the lower line in very plot is the return net of transaction costs as shown in column 6 of table 7. The transaction cost are based on the observed bid-ask spreads. The cumulative returns are defined as the sum of the log returns. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015.
91 94 97 00 03 06 09 12 15 Cum. return (%) -1 -0.5 0 0.5 1 1.5
2 PMU long-short decile
91 94 97 00 03 06 09 12 15 Cum. return (%) -1 0 1 2 3 RMW long-short decile 91 94 97 00 03 06 09 12 15 Cum. return (%) -0.5 0 0.5 1
1.5 PMU long-short quintile
Fig. 5: Profitability strategy performance, large company sample
This figure presents returns for the profitability strategies based on investable universe of companies with a market capitalisation larger than£1 billion. The strategy is constructed using simple tertile sorting procedure and is rebalanced monthly to maintain the equal weights. The market return is the value-weighted return of the large company investable universe. The difference between the gross and net returns in the left plot are the transaction costs based on quotes spread estimates. The cumulative returns are defined as the sum of the log returns. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015.
91 94 97 00 03 06 09 12 15 Cum. return(%) -1 0 1 2 3
Long/short RMW quintile portfolio for large companies
high portfolio market return low portfolio 91 94 97 00 03 06 09 12 15 Cum. return(%) -0.2 0 0.2 0.4 0.6 0.8
1 Net returns long/short RMW quintile portfolio
Gross return Net return 91 94 97 00 03 06 09 12 15 Cum. return(%) -1 0 1 2 3
Long/short PMU quintile portfolio for large companies
high portfolio market return low portfolio 91 94 97 00 03 06 09 12 15 Cum. return(%) -0.5 0 0.5 1
1.5 Net returns long/short PMU quintile portfolio
5.
Conclusions
I began this paper referring to Warren Buffet and Joel Greenblatt and their measures for a good company at a good price. Fama and French (1993) come up with a factor to measure the price of a company, but there has only been recent academic support for the use of the profitability factor to determine the quality of a company (Fama and French, 2015; Novy-Marx, 2013). Since all the literature regarding the profitability premium is focused on the United States, this paper examined the effect on equity markets in the United Kingdom for the period 1990-2015. I explain the premium from difference perspectives in fiance and in turn, pursue the hypothesis that profitable companies should yield higher returns than unprofitable companies and that the effect is stronger among smaller companies.
Consequently my research shows the emergence of a relative profitability risk premium within equity markets in the United Kingdom after 2000. The one-way sorts indicate that ranking stocks on profitability does matter. Sorting on operating income scaled by the value of book equity, yields a monotonic pattern in average returns whilst ranking on gross profits-to-total assets does not. Further, this effect is more so exacerbated due to the unprofitable companies than outperforming of profitable companies. This premium is only observed during the recent millennium and I do not find evidence that the profitability premiums are fully driven by either asset and capital turnovers or profitability margins. Correlations and regression expound on the negative relation between value and profitability and indicate that the profitability premium is larger among smaller companies. The two-way sorts confirm the latter, but nonetheless show the premium is present across the whole size spectrum. The MR-test only supports overall monotonic patters for the 25 portfolios sorted on size and operating profits-to-book equity. I then show that even after accounting for transaction costs a profitability strategy yields results. A sample of large companies learns that, although the premium is weaker among large companies this is largely offset by the lower transaction costs those companies face relative to smaller companies. Further, it again shows that most of the performance of the premium is due to underperformance unprofitable companies instead of profitable companies. Hence, the profitability premium is about avoiding unprofitable companies.
quality. This paper hopes to contribute to this currently ambiguous definition, however, it in no way imposes conclusive parameters and is rather, a call for further research. The final conclusion of this paper is that Buffett (1989) is right: “It’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price”.
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Appendix
The paper focuses on the profitability premium in the United Kingdom’s (UK) equity markets during the period January 1989 through July 2015. This appendix intends to discuss the data selection process. All the data is from the Worldscope database, accessed through Thompson Reuters Datastream. Parentheses are used to refer to Datastream codes. The results for the traditional Fama and French (1993) factors corresponds to what Gregory et al. (2013) evidenced.
A.1.
Data and universe selection
The data comes from the Worldscope UK database [WSCOPEUK], which starts in 1985. I use the Worldscope database instead of all UK stocks [FBRIT] in combination with all the so called ’dead’ stocks [DEADUK] because of the better availability of accounting data in the early years of the sample. At the time of writing the Worldcope UK database consists of 5,359 stocks whereas the a combination of [FBRIT] and [DEADUK] counts 10,329 stocks over the same period. An advantage of the Worldscope database is that it includes dead stocks and therefore is relatively free of survivor-ship bias. Starting with the Worldscope UK database I exclude all non-equities, all non-British stocks, companies not traded in London and those companies of which the provided listing is not their main listing. Further, financial companies, those with SIC codes starting with six, are also excluded (Novy-Marx, 2013). Datastream’s total returns index [RI] is used to gather returns, [MV] as proxy for the market value. Book value of equity is total assets [WC02999] minus total liabilities [WC03351]. Gross profits are defined as [WC01100] and revenue as [WC01001]. Operating income [WC01250] or EBIT represents the difference between sales and total operating expenses.10 In line with
Gregory et al. (2013), I use the monthly return on three month Treasury Bills [UKTBTND] as proxy for the risk-free rate since this data is available from January 1985 whereas monthly return on one month Treasury Bills is only available form March 2000. Datastream’s total return index [RI] becomes stuck on the last traded day in the case a company goes into administration, it is not revised to zero. Using [X(RI)*(X(PT)/X(PT] instead of [RI] helps to overcome this obstacle.
A.2.
Construction of anomalies
The key methodology employed is the rank portfolio approach. The considered strate-gies are based on time-series of equally-weighted and value-weighted returns on long/short portfolios. For the strategies based on annual data, accounting figures for fiscal-year end of year t are matched with stock returns data from July of year t+1 until June of year t+2 to avoid look ahead bias Fama and French (1993). Although the accounting figures are only refreshed once a year all the portfolios are monthly rebalanced to maintain their weights. The risk factors of table 3 is according to description on the websites of Ken French and Robert Novy-Marx (Carhart, 1997; Fama and French, 1993, 2015; Novy-Marx, 2013).
Anomalies
• Size (SMB) according to Fama and French (1993).
Refreshed annually, rebalanced monthly. At the end of June of each year, companies are ranked on their market capitalization.
• Value (HML) according to Fama and French (1993).
Refreshed annually, rebalanced monthly. At the end of June of each year, companies are ranked on book equity from the previous fiscal year divided by their market equity at that moment.
• Momentum (UMD) according to Jegadeesh and Titman (1993).
Rebalanced monthly. At the end of each month, companies are ranked on their per-formance in the pertaining twelve months, skipping the latest month.
• Gross profits to total assets (PMU) according to Novy-Marx (2013).
Refreshed annually, rebalanced monthly. At the end of June of each year, companies are ranked on their gross profits-to-asset ratio from the previous fiscal year.
• Operating profits to the market value of equity (RMW) according to Fama and French (2015).
Table A.1: Factor correlations
This table reports average the Pearson correlations for the re-turns to the risk factor portfolios. The SMB and HML factors are formed from six intersecting portfolios using yearly market capitalization and book-to-market ratios. The other factors are constructed in similar fashion utilising the variables described in table 1. This method corresponds to the descriptions on the websites of Ken French and Robert Novy-Marx. The statistics are based on value-weighted returns and the portfolios are rebal-anced monthly while while the accounting data is only updated on a yearly frequency. The sample period begins in July 1990 and uses the using the accounting variables starting from 1989. The sample is concluded at the end of June 2015.
Rm-Rf SMB HML UMD PMU RMW Rm-Rf 1 SMB -0.18** 1 HML 0.17* 0.45* 1 UMD -0.32* -0.07 -0.39 1 PMU -0.18* 0.69* 0.15* 0.03 1 RMW -0.24* 0.62* 0.06 0.08 0.69* 1
Table A.2: Two-way sorts on size and profitability, equally-weighted returns
This table reports monthly equally-weighted average returns to portfolios sorted on the prof-itability metrics and size. Further, it shows the MR test and decompositions of it. The sample period begins in July 1990 and uses the using the accounting variables from 1989. The sample is concluded at the end of June 2015.
Panel A: Market equity x gross profits-to-total assets
Gross profits-to-total assets MR Joint Market equity Unprofitable 2 3 4 Profitable p-value p-value
Small 0.51 0.78 0.66 1.06 1.14 0.21 2 0.03 0.67 0.87 0.77 1.20 0.16 3 0.76 0.59 0.55 0.62 1.02 0.21 0.46 4 0.49 0.98 0.90 0.65 1.04 0.77 Big 0.53 0.62 0.83 0.95 0.95 0.01 MR p-value 0.98 0.95 0.91 0.86 0.06 Joint MR p-value 0.97 0.91
Panel B: Market equity x operating profits-to-book equity
Operating profits-to-book equity MR Joint Market equity Weak 2 3 4 Robust p-value p-value
