Cash flows and market-timing: the Fama French
five-factor model revisited
Roeland Holscher (s2038811)
University of Groningen Supervisor: dr. A. Plantinga
Table of Contents
1 Introduction . . . 3
2 Background . . . 5
2.1 The Fama French five-factor model . . . 5
2.2 Investor timing, dollar-weighted returns and cash flows . . . 7
1
Introduction
In 1992 Eugene Fama and Kenneth French published one of the most influential papers in finance. Expanding on the capital asset pricing model (CAPM), they designed the Fama French three-factor model (FF3 model) to capture the cross-sectional variation in stock returns. They find that size and book-to-market equity, in addition to the CAPM market risk factor, describe this variation in returns well. Additionally, Fama & French (1993) extended their paper by also capturing variation in bond returns. The results reinforce their 1992 paper. They find that the default spread and term structure explain the variation in returns for bonds. These factors are uncorrelated with size and book-to-market equity; the differences in stock returns are best explained by the latter.
Their research initially met a lot of criticism. Black (1993) accuses Fama & French (1992) of data mining: simply looking for statistical relations in their data without proper theoreti-cal interpretation. Furthermore, he states they rely too much on previous findings of others, without questioning whether these results were merely a lucky outcome. The criticism of MacKinlay (1995) is similar. He states that the fit of the FF3 model is a result of data-snooping: choosing an inference method after examining the data, as opposed to before. Asness (2015), one of the founders of AQR capital and a former assistant to Fama, nicely states: “Our most potent weapon in addressing data mining is the out-of-sample test. If a re-searcher discovered an empirical result only because she tortured the data until it confessed, one would not expect it to work outside the torture zone.”1In the past two decades, scholars
have used other samples to test the FF3 model outside of this zone. Barber & Lyon (1997) used only financial firms. These companies were excluded from their analysis by Fama & French (1992). Barber & Lyon find similar results for financial firms, concluding that the model cannot be a result of data-snooping alone. Overall, empirical evidence supporting the model has been considerable, although book-to-market performs better than size does out-of-sample.
Recently, Fama & French (2015) have extended their factor model by adding two new factors. The first new factor captures the relationship between returns and a company’s operating profitability, the second between the returns and the company’s investments. Al-though the model does not pass the Gibbons-Ross-Shanken test (GRS), a joint test to examine whether all intercepts are jointly zero, it does explain more variation in returns than FF3. In the past two years, scholars have taken the FF5 model outside of the torture zone. Kubota & Takehara (2017) analyze the model´s capability to explain stock pricing in Japan. Similarly, Lin (2017) tests its performance in the Chinese stock market. These out-of-sample tests, mostly using stock data from markets in Europe and Asia-Pacific, do not yield unambiguous results. Therefore, it is relevant to impose a different kind of test. How does the FF5 model fare capturing patterns in a metric other than returns? Dichev (2007) provides such a metric. In his influential paper he suggests an alternative measure of investors´ returns: dollar-weighting. The theory behind this method will be discussed
1 Asness, C., June 2 2015.
more extensively in the following section of this paper. Dollar-weighting regards investing in stocks as several separate cash flows. This can provide a better estimate of how the av-erage investor in those stocks performed, in contrast to a traditional buy-and-hold return on capital, which depends on a geometric average. Using this measure, Dichev finds that investors mistime the market on a level of national market aggregation. These results are, however, disputed by other scholars. Using alternative tests, they find Dichev’s results to be statistically insignificant. Although the results found by Dichev are challenged, the notion of using distributions between companies and investors to assess performance is not.
2
Background
2.1 The Fama French five-factor model
The CAPM was the first coherent model to explain the relationship between a stock’s risk and its expected return. It was created in the 1960s by several scholars, among whom Nobel laureate William Sharpe. The CAPM draws on the diversification theory by Harry Markowitz. It distinguishes two types of risks: systematic risk and unsystematic risk. The latter is stock specific and can be diversified away, so only systematic market risk matters. The FF3 model was designed as an extension of the CAPM. Fama & French (1992) found that the CAPM failed to explain two return patterns that were already widely documented in 1992: the size and book-to-market equity effect. As stated in the introduction, they were accused of data mining. While other scholars tested the FF3 model out-of-sample, Fama & French (1995) tried to validate the two new factors with economic reasoning. The explanation for the size effect is straightforward: small firms have a larger growth potential. They state the book-to-market effect is likely to be caused by persistent financial distress. However, this explanation for the value factor is not persuasive. Dichev (1998) used bankruptcy risk as a proxy for financial distress. He finds that higher bankruptcy risk does not result in higher stock returns and thus does not explain the value premium.
Investigating this hypothesis, Fama & French (2008) tested return anomalies. They state a robust relationship between both factors and returns is absent. However, in 2015, work by previous scholars led them to believe that these two variables nonetheless might capture much of the variation in returns. Novi-Marx (2013) reports that a gross profitability factor has as much explanatory power as the book-to-equity factor does. Because profitable firms behave differently from value firms, adding gross profitability to the FF3 model improves its performance. Hou, Xue & Zhang (2012) propose a four-factor model with an investment factor and a factor similar to profitability. They exclude the value factor from their model, given its lack of economic intuition. Hou et al. show that the model outperforms the FF3 model. Therefore, Fama & French (2015) extended their model into a five-factor model.
To test their model, Fama & French (2015) sort U.S. stocks into portfolios based on size, the book-to-market ratio, profitability and investment. They calculate operating profitabil-ity as revenue minus cost of goods sold and operating and interest expenses. To make the profitability comparable across companies, everything is scaled to the book value of equity. Investment is defined as the growth in total assets over the previous year. At first glimpse, this seems a quite surprising proxy for expected investment. In their 2008 paper, they state asset growth is not a robust proxy. In their 2015 model, they use asset growth as a replace-ment for growth in book value. Although both proxies seem to yield the same results, they do not provide a clear-cut theoretical explanation for the use of asset growth over book equity growth. Based on these criteria, the stocks are annually re-allocated to portfolios. Different frameworks are used to calculate the factors. They use 2 x 2 portfolios sorted on size and one of the other factors with the medians as breakpoints. Also, 2 x 3 portfolios are used in which size is controlled for. The 30th and 70th percentile function as breakpoints for the book-to-market ratio, profitability and investment. Furthermore, 2 x 2 x 2 x 2, 2 x 4 x 4 and 5 x 5 portfolios are used to determine the factors. There is some greatness in simplicity, as the 2 x 3 portfolios perform as well as the other frameworks.
With the additional factors, the FF5 model is indeed able to capture more variation in U.S. stock returns. One of the more interesting findings is that the value factor is statis-tically redundant in the five-factor model. When explaining the pattern in excess returns, the book-to-market effect is captured by the new factors. In a more recent article, Fama & French (2017) perform the same analysis using international stock data. In addition to the 1963 to 2013 sample of U.S. stocks, they use a 1990 to 2015 sample for North America, Europe, Japan and Asia Pacific. The results are similar, except for Japan. In Japan the prof-itability and investment factors add little explanatory power. However, the 25 year horizon is relatively short. Kubota & Takehara (2018) extend this period from 1978 to 2014, which is more comparable to the original U.S. data. Similar to the 25 year horizon used by Fama & French, the new factors are not statistically significant using long-term Japanese stock data. The FF3 model explains Japanese stock prices far better.
far more variation in returns than the FF3 model. In India, the value factor preserves its explanatory power. The sample, however, only consists of 491 listed companies. The model’s performance with stocks traded on the Australian Securities Exchange (ASX) is equal. Chai, Chiah, Li & Zhong (2016) find the FF5 model captures more variation than the FF3 model. Again, book-to-market equity is not redundant. Chai et al. also test other models, including the Carhart four-factor model (CH4). The FF5 outperforms all other asset pricing models. Lastly, Lin (2017) tests the FF5 model using stocks traded on the Shanghai Stock Exchange (SHSE) and Shenzen Stock Exchange (SZE). The model captures considerably more vari-ation in returns than the FF3 model does. However, the total asset growth is not the best proxy for expected investment in China or developing countries for that matter. Lin states that with a dense shareholder concentration, which is governmental in China, managers could be compelled to invest more. Profitability has greater explanatory power than invest-ment in such an environinvest-ment.
On average, both theory and the international tests support the FF5 model. Profitabil-ity and investment add a lot of explanatory power to the FF3 model, both statistically and economically. The value factor seems to be only redundant using U.S. stock data, in other regions it remains significant with the added factors. Nevertheless, the factor lacks an in-stinctive economical explanation for its premium. The economic reasoning behind the new factors is more convincing. However, the international tests merely duplicate the analysis using different samples. These samples are relatively short compared to the U.S. stock data. This makes an out-of-sample test relying indirectly on the same data the more relevant. In addition, the international tests are aimed at purely capturing excess returns. If the model is able to capture patterns in a different metric indirectly by explaining portfolio returns, it is truly taken outside of the torture zone. Does the FF5 model tell a convincing story capturing patterns in cash flows between companies and investors? To answer this question, it is important to first lay down an expectation of such pattern. The next section attends to the matter.
2.2 Investor timing, dollar-weighted returns and cash flows
The concept of using dollar-weighted returns to assess investment performance is known among scholars. Bodie, Kane & Marcus (1996) contrast it to the geometric average return, also known as the time-weighted return. They state that the dollar-weighted or internal rate of return allows periods in which more money was invested to have greater influence on the overall performance, resulting in the effective rate of return. Zweig (1997) uses the concept of dollar-weighting to evaluate the performance of mutual funds. He argues that the timing of cash flows is of utmost importance; an investor is able to lose money even if the fund he invests in is doing well.
positive correlation between the cash flows and future returns. He finds that, on average, investors in the US stock market mistime the market, resulting in a significantly lower re-turn than a buy-and-hold strategy. He also finds a significant difference between the two returns for other major international stock markets. His research suggests the concept of dollar-weighting can be used further, for example at lower levels of aggregation, in venture capital investing and in assessing the performance of different types of investors.
In another paper, Dichev (2011) addresses the performance of hedge fund investors us-ing the same methodology. The distributions enable to distus-inguish hedge funds returns from investor performance. He finds that investors in hedge funds lose around 5% by mistiming the cash flows. In a recent paper, Friesen and Nguyen (2018) assess not only the perfor-mance of fund investors, but also their learning ability. By splitting up their sample into different sub periods, they find investors do learn. Investors increasingly avoid high-risk and high-expense funds. However, they still mistime their cash flows. Pouring in capital after periods of superior returns, the dollar-weighted returns for fund investors remain lower than the buy-and-hold returns.
Dichev’s 2007 paper has met strong criticism. Keswani & Stolin (2008) argue that the period used by Dichev does not represent investors realistically. An investment horizon con-sisting of 77 years is too long. When this horizon is divided into periods of approximately 25 years, they find that the dollar-weighted returns are no longer significantly different from a buy-and-hold strategy. Keswani & Stolin’s findings are reinforced by Hatem, Johnston &Paul (2015). Replicating Dichev’s research with several time periods, they find that the market capitalization both at the beginning and end largely define the gap between the dollar-weighted returns and the buy-and-hold benchmark. However, they criticize Dichev’s results, not his method of calculating cash flows or the notion of using these cash flows to assess investor performance.
In order to employ the capital flows to test the FF5 model, it is important to distinguish the most prominent components and it is essential to determine how they are related to the factors in the model. Using cash distributions to assess investors’ historical performance can be considered as looking at managers’ timing from an opposite perspective. The subject of managers timing a firm’s equity flows is well-covered within the existing literature. Divi-dends, although becoming less common according to Bildik & Fatemi (2012), are expected to be a key driver and are closely related to net profits. They find that large, profitable firms with fewer investment opportunities pay more dividends on average. This results in cash flows from the companies to the investor. Reversely, smaller firms with high growth potential and weaker profitability will declare fewer dividends. These companies rather use internal funding to expand, than pay out dividends.
to repurchase company shares. However, the literature does not bring forward a motive for repurchasing shares directly related to the FF5 factors.
On the opposite side, initial public offerings (IPOs) and seasoned equity offerings (SEOs) cause cash flows from investors to companies. Loughran & Ritter (1995) analyze stock per-formance after both IPOs and SEOs. They use a sample of 4,753 IPOs and 3,702 SEOs on the major American Stock exchanges between 1970 and 1990, provided by CRSP. Their results are both statistically and economically significant. Following an IPO, the average issuing firm has a five-year return of 15.7% whereas the matching firms yield a 66.4% return. Firms conducting an SEO perform even worse compared to their matching firms. The results sug-gest managers issue equity when the firm is currently overvalued by the market. Loughran & Ritter provide an explanation for the underperformance. They state that investors too often believe, or want to believe, they have found the next Microsoft. As early as 1995 it was widely published that IPOs were poor long-term investments. Due to higher subjective probabilities, investors tend to overvalue growth-stocks. Basically Loughran & Ritter state that the manager can time the market because the average investor cannot.
Similarly, Brav, Geczy & Gompers (2000) find that this underperformance is greater for small growth stocks. Managers of smaller firms often use flexible accounting to boost earn-ings preceding an IPO, which explains part of the underperformance. Bushee, Cedergren & Michels (2018) relate the underperformance following IPOs to news coverage. They use various databases, including CRSP, for IPO data and combine it with financial news arti-cles. Bushee et al. conclude that intensive news coverage amplifies investor activity, which drives up the security price following an IPO. This overreaction results in underperformance. These results are less profound for SEOs. Lin & Wu (2013) also investigate SEO timing. Alternatively, they do not attribute the lower returns following an SEO to overvaluation but to liquidity risk. Managers issue equity when a firm’s liquidity risk is minimal. In turn, investors require a lower return following the offering. They do not find stocks to underper-form in the long run after an SEO.
The existing literature shows that the cash flows between investors and companies are closely related to firm size and the new profitability and investment factors. Large, prof-itable companies with lower growth potential invest less and distribute more cash to in-vestors. Small companies with weak profitability or a lot of investment opportunities will retain more of their earnings. Moreover, these firms are likely to visit the capital market on a more regular basis to attract additional funding. This implies a clear expectation of the distributions. Stated from an investor’s perspective: cash is more likely to be distributed to small companies with weak profitability that invest a lot. Cash is more likely to be received from large companies with robust profitability and low investment opportunities.
3
Methodology
Capital flows from and to stock investors are the most important input for assessing the performance of the FF5 model. In order to derive these cash flows, it is necessary to obtain dividends and stock repurchases. However, as Dichev (2007) states, case-specific data is also required depending on the level of aggregation. On the market level, for example, the list-ing and delistlist-ing of companies are cash flows, while on lower levels of aggregation mergers, acquisitions and spin-offs are important capital flows. This large data requirement compli-cates calculations, if there is sufficient data in the first place. Therefore, Dichev provides an alternative —and less cumbersome—method to derive these cash flows. For an index, the distribution of cash flows to the investor is equal to
Distributionst= M Ct−1(1 + rt) − M Ct (1)
where M Ctis the market capitalization at time t and rtis the value-weighted return
includ-ing dividends on that index. This formula can be easily adapted for individual stocks, by defining rt as the holding return including dividends. M C is calculated by multiplying the
number of shares outstanding by the share price. Divide it by thousand to obtain the M C in millions of U.S. dollars, given that the number of shares outstanding is already denominated in thousands. Positive distributions flow from the company to the investor, negative distri-butions from the investor into the company. On average, the literature leads us to believe that investors experience poor market timing. They tend to invest more after periods of superior returns and withdraw money before periods of high returns. Therefore, the distri-butions are expected to have a negative relationship with the past returns and a positive relationship with future returns. Under the null hypothesis, the returns and distributions are uncorrelated. Both the Pearson and Spearman correlation will be examined to test this hypothesis, thus replicating Dichev (2007) in this respect.2
The distributions enable an out-of-sample test of the FF5 model by sorting the stocks in three portfolios based on the size and sign of the cash flows. The securities are allocated to a low, medium and high distribution portfolio with the 30th and 70th percentiles as break-points. These portfolios are rebalanced on a monthly basis. The returns on these portfolios are used to estimate
Rit− RF t= ai+ bi(RM t− RF t) + siSM Bt+ hiHM Lt+ riRM Wt+ ciCM At+ eit (2)
where bi, si, hi, ri and ci are the coefficients that capture variation in returns, ai is the
zero-value intercept and eit is the residual. Rit is the return of portfolio i for period t, RM t
is the return on the market portfolio and RF t is the risk-free return. SM Bt (small minus
2 The Pearson correlation measures a linear correlation, whereas the Spearman correlation assesses
big) is the return of a portfolio of small stocks minus the return on a portfolio of big stocks. HM Lt(high minus low) is the return of a portfolio consisting of stocks with a high
book-to-market ratio minus the return on a portfolio with a low book-to-book-to-market ratio. RM Wt(robust
minus weak) and CM At (conservative minus aggressive) respectively are the difference in
returns between portfolios with robust and weak profitability stocks and the difference in returns between portfolios with low and high investment companies. All of these portfolios are diversified. Furthermore, the returns of the portfolios sorted on distributions are used to estimate the FF3 model, to examine whether the profitability and investment factors add explanatory power. The FF3 is given by equation (2), minus the RM W and CM A factors and their coefficients. The new profitability and investment factors tell a more intuitive story about distributions than the book-to-market equity. Moreover, Fama & French find the HM L factor to be statistically redundant with the added factors. Therefore, a Fama & French four-factor model (FF4) lacking HM L will also be estimated. Lastly, the returns are used to estimate the CH4 model, equal to
Rit− RF t= ai+ bi(RM t− RF t) + siSM Bt+ hiHM Lt+ uiU M Dt+ eit (3)
where uiis the coefficient and U M Dt(up minus down) is the return on a portfolio of stocks
that had a high return in the previous year minus the return on a portfolio of stocks that had a low return in the previous year. As a robustness check, the above will be repeated using the 10th and 90th percentiles as breakpoints for the three portfolios.
Theory suggests that large, profitable companies with lower investment opportunities would distribute more cash to the investors. Therefore, we expect a positive factor loading on HM L, RM W and CM A, and a negative factor loading on SM B for the high-distribution portfolio. Similarly, we would expect small businesses, growth firms and companies with weak profitability or high investment opportunities to visit the capital market on a regular basis to attract funding. Therefore, we expect a negative factor loading on HM L, RM W and CM A and a positive factor loading on SM B for the low-distribution portfolio. Because Dichev (2007) reports a negative correlation between past returns and distributions, we expect a negative factor loading on U M D for the high-distribution portfolio and a positive loading for the low-distribution portfolio. However, literature leads us to believe the relationship between the distributions and the two new Fama & French factors is stronger. Therefore, the FF5 model is expected to outperform the CH4 model.
Lastly, the variance inflation factors (VIFs) are calculated to detect multicollinearity. The VIF is equal to V IF = 1 1 − R2 f (4) where R2
f is the coefficient of determination of factor f on the other factors. A VIF of 1
4
Data
Basic stock information is needed for the calculation of the cash flows. CRSP provides a large database which includes this information on all common stocks listed on the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX) and the NASDAQ.3The
database was obtained from the Wharton Research Data Services (WRDS). The main benefit of using CRSP is its completeness. CRSP has been providing security prices, holding returns including dividends and information concerning volume since December 1925. Missing closing prices are substituted by the average of the bid/ask prices on a trading day. The NYSE stocks cover the entire period, AMEX and NASDAQ stocks have been included from 1962 and 1973 respectively. The dataset contains all data needed to compute the distributions, both on aggregate and individual stock level. Therefore, it is not surprising Dichev also utilizes CRSP-data until 2002 for his analysis. The market capitalization and NYSE market cap breakpoints from CRSP are also used by Fama & French to compose the SMB factor portfolio.
Appendix A contains the descriptive statistics for the CRSP database from 1926 to 2017. Given the sheer size of the table, it has not been included here. N is the year-end number of listed firms for which the stock information necessary to calculate the distributions is available. The market cap is also presented at year-end, in millions of U.S. dollars. The number of listed companies increases steadily until 1997, with large jumps in 1962 and 1973 when the AMEX and NYSE stocks join the sample. After 1997 there is a drop in the number of firms, followed by a relatively stable level since 2002. Although the number of firms remained more or less the same, the market capitalization has continued to rise since 2002. Table 1 contains a summary of the descriptive statistics in table 7.
The average annual return for the U.S. stock markets has been 11.6%, with a standard deviation of 19.8%. On average, both the absolute and scaled distributions are positive; cash flows mainly from companies to the investors. This indicates dividends and share repurchases could be the most important component of the distributions. Most notably, the negative dis-tributions seem to correspond with financial crises. The stock market crash of 1929, early 1990s recession, Asian and Russian financial crisis, dot-com bubble and 2008 global financial crisis all coincide with a negative distribution in the following year. The correlation matrix in table 2 supports this pattern. The distributions are significantly negatively correlated with past returns. After a period of high returns, investors tend to invest extra capital. Alter-natively, they withdraw capital after a period of low or negative returns. Additionally, the distributions are significantly positively correlated with future returns. Investors withdraw money before periods of high returns and invest before periods of low returns. This suggests that investors indeed experience mistiming on average. Additional fundamental informa-tion on the companies is needed for the factor portfolios. S&P Global Market Intelligence has been providing this kind of information since 1950 for the U.S. and Canadian market. Similar to CRSP, the Compustat fundamental data can be accessed through WRDS. They even provide a merged database, connecting the more extensive CRSP data with the annual
3
Table 1: Summary statistics and correlation matrix for annual returns and annual distributions
Annual return Annual distribution Dist./MC
Sum 5652800
Mean 0.116 0.014
Std. 0.198 0.037
Dist./MC Future return Past return
Dist./MC * 0.509 -0.127 (\textless0.001) (0.227) Future return 0.232 * 0.227 (0.092) ( 0.109) Past return -0.277 0.0273 * (0.043) (0.053)
The annual return is the weighted return, computed by compounding the monthly value-weighted returns. The annual distribution is the sum of the monthly distributions, calculated using Distributionst= M Ct−1(1 + rt) − M Ct where rt is the monthly value-weighted return. Dist./MC
is the annual distribution divided by the average of the beginning and ending market cap of the corresponding year. Past return is the average of the annual returns three years preceding an annual distribution, future returns the average of the three years following the distribution (N = 90). Spearman correlations are below, Pearson correlations above. The p-values in parentheses.
Compustat data. However, as we do not possess the license for the merged data, both sets have to be merged manually by linking the identifying company codes (cusips). Because the company information is annual data and has been available from 1950, there are less obser-vations for the fundamentals. In total, CRSP contains 4,248,429 obserobser-vations for stocks with a price, the number of shares outstanding and a return. In contrast, Compustat contains 258,575 observations for both cash dividends and share repurchases. The book value per share and total market value, combined with the number of shares outstanding from CRSP, are used to construct the HM L value portfolios. This reduces the sample size to 91,659 observations. For the RM W portfolios, the revenues are needed in combination with either the costs of goods sold, general expenses or interest expenses. As such, the sample contains 201,301 observations. The CM A portfolios are constructed using total asset growth. 258,549 observations include information on total assets. The value-weighted returns of all stocks in CRSP are used as the market return and the one-month Treasury bill rate as the risk-free return. CRSP provides the NYSE breakpoints and market caps for the SM B portfolios. French maintains a data library containing all factors from the FF3-, CH4- and FF5 mod-els.4 The library also includes sorted portfolios for these factors, industry portfolios and
international stock data. Because French provides monthly factors based on the same data used to determine the distributions, these factors are used in our analysis.
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5
Results
Table 2 presents the regression results for the portfolio of stocks with a low distribution. For these stocks, investors either pour in extra capital or less cash flows from companies to in-vestors than on average. One of the first things to stand out is that the adjusted R-squared is close to one. This can be ascribed to M ktRF . Fama & French use the value-weighted return of all stocks in CRSP as the market return. The returns of the portfolio closely resemble the market return, because the portfolio contains 30% of these stocks. Although this causes the R-squared to be less reliable in assessing overall fit, it can still be used to measure a model’s performance relative to other models. U M D is not significant, thus the CH4 model adds no explanatory power to the FF3 model. The Fama French factors, however, are all highly significant. For SM B, the coefficient is positive. This means the stocks in the portfolio on average behave like small stocks. The factor loading on HM L is negative, which indicates that the securities in the portfolio act like growth stocks. Directly related are the negative coefficients for RM W and CM A. The stocks behave like firms with weak profitability and a lot of investment opportunities. This confirms our expectation. Securities with a low dis-tribution of cash to the investors are likely to be small companies with weak profitability and high growth potential. The adjusted R-squared indicates that the FF4 model, lacking
Table 2: Regression results - portfolio with stocks sorted on distributions, percentiles 1 to 30 (low)
the HM L factor, captures less variation in returns than the FF5 model does. This means the two new factors do not fully capture the value effect. The multicollinearity matrix in the appendix B supports this finding. The VIF of the HM L factor is lower than 2, showing only a weak correlation with the new factors. The correlation between CM A and the other factors is the strongest, albeit with a VIF of 2.18, indicating weak multicollinearity.
Table 3 contains the results for the portfolio of stocks with large cash flows to the in-vestors. Similar to the low-distribution portfolio, the momentum factor is not significant; whether the stock price has recently been increasing or decreasing appears to be unrelated to the distributions of cash. All Fama French factors are highly significant. The results ex-hibit the inverse pattern of the low distribution portfolio. The factor loading on SM B is negative, meaning the stocks in the portfolio behave like big stocks. HM L has a positive coefficient, as do RM W and CM A. This indicates that the securities in the portfolio behave
Table 3: Regression results - portfolio with stocks sorted on distributions, percentiles 71 to 100 (high) (1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 0.9765 0.9744 0.9885 0.9891 (0.0065)*** (0.0063)*** (0.0055)*** (0.0064)*** SMB -0.0772 -0.0771 -0.0603 -0.0596 (0.0101)*** (0.0100)*** (0.0076)*** (0.0093)*** HML 0.0594 0.0555 0.0307 (0.0125)*** (0.0126)*** (0.0104)** UMD -0.0111 (0.0075) RMW 0.0765 0.0811 (0.0105)*** (0.0161)*** CMA 0.0622 0.0928 (0.0155)*** (0.0145)*** Constant 0.0921 0.1018 0.0546 0.0547 (0.0220)*** (0.0222)*** (0.022)** (0.0222)** Observations 654 654 654 654 Adjusted R-squared 0.982 0.983 0.984 0.984 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
investment factors do not fully capture the explanatory power of the value factor. The ad-justed R-squared of the FF5 model is slightly higher than for the FF4 model.
In table 4 the regression results are displayed for the low-distribution stocks using the 10th and 90th percentiles as breakpoints. Although it is still highly significant, the signif-icance of the market factor has decreased because the portfolio now contains 10% of the CRSP stocks. This results in a lower R-squared. The SM B factor has become insignificant. Other than that, the results support the previous findings. The coefficients are bigger than before, meaning securities in the portfolio act more like stocks with weak profitability and high growth potential than previously. Moreover, the FF5 model has a better fit than the FF4 model, indicating that HM L has explanatory power and is not redundant. This sug-gests the findings using the 30th and 70th percentiles as breakpoints are robust. Table 5
Table 4: Regression results - portfolio with stocks sorted on distributions, percentiles 1 to 10 (low)
(1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 1.0337 1.0354 0.9997 0.9984 (0.0163)*** (0.0150)*** (0.0130)*** (0.0127)*** SMB 0.0216 0.0215 -0.0255 -0.0267 (0.0219) (0.0217) (0.0249) (0.0251) HML -0.1426 -0.1395 -0.0594 (0.0349)*** (0.0387)*** (0.0303)* UMD 0.0090 (0.0215) RMW -0.2131 -0.2219 (0.0483)*** (0.0489)*** CMA -0.1807 -0.2399 (0.0536)*** (0.0498)*** Constant 0.0679 0.0600 0.1739 0.1736 (0.0506) (0.0483) (0.0458)*** (0.0459)*** Observations 654 654 654 654 Adjusted R-squared 0.934 0.934 0.943 0.942 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
The distributions allow a different approach of isolating the investors’ timing. By subtract-ing the dividends, we take out an important cash flow from the company to investors. The
Table 5: Regression results - portfolio with stocks sorted on distributions, percentiles 91 to 100 (high) (1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 0.9504 0.9492 0.9777 0.9793 (0.0096)*** (0.0095)*** (0.0084)*** (0.0089)*** SMB -0.1369 -0.1368 -0.0926 -0.0911 (0.0178)*** (0.0176)*** (0.0134)*** (0.0144)*** HML 0.1264 0.1240 0.0679 (0.0225)*** (0.0237)*** (0.0177)*** UMD -0.0066 (0.0171) RMW 0.1982 0.2082 (0.0231)*** (0.0245)*** CMA 0.1260 0.1936 (0.0279)*** (0.0246)*** Constant 0.1526 0.1584 0.0617 0.0621 (0.037)*** (0.0416)*** (0.0344)* (0.0350)*** Observations 654 654 654 654 Adjusted R-squared 0.949 0.949 0.959 0.958 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
portfolios. As tables C5 to C8 show, this results in the same pattern. The coefficients for the momentum factor are highly significant and the CH4 model has the most explanatory power.
6
Conclusion
This research has tested the performance of the FF5 model and in particular the validity of the new profitability and investment factors. By allocating stocks into portfolios based on the cash flows between investors and companies, the FF5 model can explain the cross-sectional variation in returns and identify the average stock characteristics of the portfolio. We find that the RM W and CM A coefficients are connected with the distributions of cash. On average, stocks that distribute more cash to the investor behave like large, mature and profitable companies. Securities that receive more cash from the investor behave like small companies with weak profitability and high growth potential. Dividends appear to be the most important determinant of the cash flows. When they are included in the distributions, the FF5 model outperforms the other tested models. The HM L factor improves the fit, thus is not redundant. When dividends are excluded, the momentum factor becomes highly significant causing the CH4 model to outperform the other models.
On average, the international tests showed that the FF5 model performs well out-of-sample and that the value factor retains explanatory power. Our results are in line with the existing literature. The model is able to capture a pattern in the cash flows. This pat-tern conforms to the economic theory behind these cash flows; big companies with robust profitability and limited growth potential pay out more dividends. If the RM W and CM A factors were purely a result of data mining, we would not expect them to explain such a pattern with an economically reasonable story. However, RM W and CM A capture patterns in dividends more convincingly than other factors. This does not imply the FF5 model out-performs other asset pricing models in different frameworks. Moreover, the results are in favour of the momentum factor. The relationship between U M D and the distributions sup-ports Dichev’s (2007) findings. Investors allocate more capital to stocks that have recently increased in price and withdraw money from stocks that incurred losses.
The thesis has some obvious shortcomings. We were only able to test RM W and CM A because theory predicted a clear pattern in the cash flows. In recent years, scholars have suggested the addition of other factors, for example liquidity risk and return on equity. Because the literature does not provide a clear expectation of the relationship between these factors and cash flows, our methodology cannot be used to test these factors. Another limitation is the use of a single time period. Although the FF5 model explains the variation in cash flows, it does not show changes in this pattern. Literature suggest dividends are becoming less common and the amount of open market share purchases is increasing. This could signify the pattern to be different in recent years. Dividing the single horizon in multiple sub periods would have allowed to capture changes in cash flows.
7
References
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A
Descriptive statistics
Table A1: Descriptive statistics (1926-2017)
Year N Market cap
Table A1 continued from previous page
Year N Market cap
Table A1 continued from previous page
Year N Market cap
in million $ Annual return Annual distribution Distribution/ market cap 1998 8636 13576473 0.218 -96474 -0.008 1999 8302 17611942 0.259 -461155 -0.030 2000 8107 16116305 -0.110 -528342 -0.031 2001 7409 14227508 -0.115 40600 0.003 2002 6991 11304530 -0.209 -67182 -0.005 2003 6641 14991372 0.332 49437 0.004 2004 6679 16949600 0.132 20110 0.001 2005 6696 17992192 0.076 240733 0.014 2006 6798 20397436 0.164 514528 0.027 2007 6939 21150058 0.080 881068 0.042 2008 6772 12649595 -0.384 509050 0.030 2009 6511 16613949 0.318 -36697 -0.003 2010 6543 19355294 0.173 102842 0.006 2011 6654 18694354 -0.016 357538 0.019 2012 6598 21303068 0.155 282103 0.014 2013 6732 27436898 0.300 221470 0.009 2014 7005 30101880 0.100 84553 0.003 2015 7176 28722278 -0.018 854007 0.029 2016 7029 31223444 0.122 906952 0.030 2017 7014 36800916 0.209 948425 0.028 Sum 5652800 Mean 0.116 0.014 Std. 0.198 0.037
N is the number of listed firms at the end of the year. The market cap is the market capitalization at the end of the year in millions of U.S. dollars. The annual return is the value-weighted return, computed by compounding the monthly value-value-weighted returns. The annual distribution is the sum of the monthly distributions, calculated using Distributionst =
M Ct−1(1 + rt) − M Ctwhere rtis the monthly value-weighted return. Distribution/ market
B
Multicollinearity
Table B1: VIF matrix
Variable FF3 CH4 FF5 FF4 MktRF 1.15 1.19 1.31 1.31 SMB 1.08 1.08 1.20 1.20 HML 1.07 1.13 1.95 UMD 1.07 RMW 1.22 1.20 CMA 2.18 1.20
The variance inflation factor measures the collinearity with other factors in the model. VIF = 1 means no correlation, 1<VIF<5 slight multicollinearity and VIF>5 indicates problematic
multicollinearity.
C
Regressions excluding dividends and share repurchases
Table C1: Regression results - portfolio with stocks sorted on distributions excluding dividends, percentiles 1 to 30 (low) (1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 0.9237 0.9378 0.9236 0.9230 (0.0173)*** (0.0163)*** (0.0164)*** (0.0169)*** SMB 0.0035 0.0025 0.0009 0.0003 (0.0281) (0.0257) (0.0287) (0.0296) HML -0.0242 0.0019 -0.0272 (0.0362) (0.0327) (0.0428) UMD 0.0745 (0.0205)*** RMW -0.0111 -0.0150 (0.0452) (0.0477) CMA 0.0069 -0.0202 (0.0552) (0.0480) Constant -0.7663 -0.8313 -0.7638 -0.7638 (0.0494)*** (0.0487)*** (0.0546)*** (0.0545)*** Observations 648 648 648 648 Adjusted R-squared 0.910 0.915 0.910 0.910
Table C2: Regression results - portfolio with stocks sorted on distributions excluding dividends, percentiles 1 to 10 (low) (1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 0.9295 0.9448 0.9278 0.9271 (0.0183)*** (0.0173)*** (0.0176)*** (0.0181)*** SMB -0.0594 -0.0605 -0.0647 -0.0655 (0.0302)* (0.0274)** (0.0301)** (0.0310)** HML -0.0347 -0.0063 -0.0347 (0.0383) (0.0344) (0.0449) UMD 0.0812 (0.0217)*** RMW -0.0231 -0.0282 (0.0486) (0.0515) CMA 0.0004 -0.0342 (0.0580) (0.0509) Constant -0.7530 -0.8238 -0.7452 -0.7452 (0.0544)*** (0.0533)*** (0.0599)*** (0.0597)*** Observations 648 648 648 648 Adjusted R-squared 0.895 0.901 0.895 0.895
Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
Table C3: Regression results - portfolio with stocks sorted on distributions excluding dividends, percentiles 71 to 100 (high) (1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 1.0322 1.0180 1.0297 1.0290 (0.0128)*** (0.0133)*** (0.0122)*** (0.0123)*** SMB -0.0460 -0.0449 -0.0508 -0.0515 (0.0211)** (0.0187)* (0.0233)* (0.0231)** HML -0.0362 -0.0625 -0.0317 (0.0316) (0.0313)* (0.0280) UMD -0.0753 (0.0203)*** RMW -0.0212 -0.0259 (0.0523) (0.0529) CMA -0.0095 -0.0411 (0.0519) (0.0520) Constant 0.7252 0.7908 0.7342 0.7342 (0.0486)*** (0.0482)*** (0.0535)*** (0.0508)*** Observations 648 648 648 648 Adjusted R-squared 0.932 0.936 0.931 0.931
Table C4: Regression results - portfolio with stocks sorted on distributions excluding dividends, percentiles 91 to 100 (high) (1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 1.0389 1.0240 1.0336 1.0326 (0.0143)*** (0.0149)*** (0.0136)*** (0.0136)*** SMB -0.1251 -0.1240 -0.1355 -0.1365 (0.0223)*** (0.0210)*** (0.0255)*** (0.0254)*** HML -0.0563 -0.0838 -0.0474 0.0347 (0.0348)** (0.0311) UMD -0.0787 (0.0225)*** RMW -0.0458 -0.0527 (0.0574) (0.0580) CMA -0.0189 -0.0661 (0.0578) (0.0572) Constant 0.8013 0.8699 0.8205 0.8205 (0.0541)*** (0.0539)*** (0.0596)*** (0.0597)*** Observations 648 648 648 648 Adjusted R-squared 0.917 0.921 0.917 0.917
Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
Table C5: Regression results - portfolio with stocks sorted on distributions excluding dividends and repurchases, percentiles 1 to 30 (low)
(1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 0.9252 0.9394 0.9354 0.9344 (0.0197)*** (0.0187)*** (0.0184)*** (0.0189)*** SMB -0.0090 -0.0085 -0.0077 -0.0075 (0.0320) (0.0295) (0.0339) (0.0348) HML -0.0166 0.0084 -0.0538 (0.0392) (0.0359) (0.0477) UMD 0.0689 (0.0218)*** RMW 0.0190 0.0113 (0.0439) (0.0469) CMA 0.0856 0.0303 (0.0639) (0.0515) Constant -0.7203 -0.7818 -0.7449 -0.7438 (0.0552)*** (0.0532)*** (0.0593)*** (0.0591)*** Observations 564 564 564 564 Adjusted R-squared 0.906 0.910 0.906 0.906
Table C6: Regression results - portfolio with stocks sorted on distributions excluding dividends and repurchases, percentiles 1 to 10 (low)
(1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 0.9293 0.9447 0.9391 0.9380 (0.0205)*** (0.0196)*** (0.0193)*** (0.0198)*** SMB -0.0687 -0.0681 -0.0706 -0.0703 (0.0337)** (0.0307)** (0.0349)** (0.0360)* HML -0.0215 0.0057 -0.0602 (0.0411) (0.0375) (0.0494) UMD 0.0748 (0.0230)*** RMW 0.0075 -0.0010 (0.0466) (0.0499) CMA 0.0906 0.0287 (0.0667) (0.0545) Constant -0.7014 -0.7682 -0.7228 -0.7216 (0.0602)*** (0.0573)*** (0.0644)*** (0.0642)*** Observations 564 564 564 564 Adjusted R-squared 0.892 0.896 0.892 0.891
Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
Table C7: Regression results - portfolio with stocks sorted on distributions excluding dividends and repurchases, percentiles 71 to 100 (high)
(1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 1.0431 1.0262 1.0408 1.0399 (0.0144)*** (0.0150)*** (0.0137)*** (0.0136)*** SMB -0.0381 -0.0387 -0.0424 -0.0421 (0.0247) (0.0215)* (0.0271)* (0.0267)* HML -0.0593 -0.0892 -0.0548 (0.0340)* (0.0334)*** (0.0306)* UMD -0.0822 (0.0213)*** RMW -0.0175 -0.0253 (0.0568) (0.0570) CMA -0.0085 -0.0648 (0.0611) (0.0581)* Constant 0.7188 0.7923 0.7270 0.7281 (0.0565)*** (0.0556)*** (0.0602)*** (0.0604)*** Observations 564 564 564 564 Adjusted R-squared 0.925 0.930 0.925 0.924
Table C8: Regression results - portfolio with stocks sorted on distributions excluding dividends and repurchases, percentiles 91 to 100 (high)
(1) (2) (3) (4) Variables FF3 CH4 FF5 FF4 MktRF 1.0495 1.0318 1.0439 1.0425 (0.0161)*** (0.0166)*** (0.0150)*** (0.0150)*** SMB -0.1118 -0.1124 -0.1239 -0.1236 (0.0266)*** (0.0244)*** (0.0296)*** (0.0293)*** HML -0.0850 -0.1161 -0.0755 (0.0368)** (0.0369)*** (0.0336)** UMD -0.0856 (0.0231)*** RMW -0.0489 -0.0596 (0.0615) (0.0618) CMA -0.0166 -0.0942 (0.0676) (0.0634) Constant 0.7903 0.8667 0.8116 0.8131 (0.0621)*** (0.0615)*** (0.0657)*** (0.0660)*** Observations 564 564 564 564 Adjusted R-squared 0.910 0.916 0.911 0.910
