# Interpreting Fama-French factors for the German stock market

I calculated the Fama-French five factors myself for the German market. Most of my results align well with prior research, except one thing: When i do the calculations for the sub-period from 2011 to 2018, i get a negative mean for the HML factor albeit with a statistically non-significant t-statistic (<0.5). Before that and for the entire period (1990-2018) i get a positive mean and a statistically significant t-statistic (>2).

Can that be or am I doing something wrong? How should i interpret a negative HML factor return and what could be the reason for this change? All HML factors I have seen in international studies had a positive mean.

EDIT:

On my factor calculations: I use Thomson Reuters Datastream and followed Schmidt's et al. (2015) recommendation to clean my data from Datastream, but I didn't use their breakpoints. I used the breakpoints suggested by Fama/French (2016): Small is lower 10% of June market cap, big is upper 90% of June market cap. Then, the 30th and 70th percentile of the big group as breakpoints for other variables (HML, RMW, CMA). My book-to-market ratio for June of year $$t$$ is common equity (WC03501) + deferral taxes (WC03263) of fiscal year end $$t-1$$ divided by the december market value (MV) of $$t-1$$. Is there anything wrong with it?

Each June i sort them into big (top 90% aggregated market cap) and small (lower 10%). Independently, i calculate the 30th and 70th percentile breakpoints for the book-to-market ratio based on the big group and sort my companies into three groups: L(ow), M(edium), H(igh). The intersection of these two sorts generate six portfolios: SL, BL, SM, BM, SH, BH. I hold these portfolios from July of year $$t$$ until June of year $$t+1$$. Then, i re-sort my portfolios etc.

I calculate the monthly value-weighted returns. HML-return for month $$t$$ is: $$HML_r = \frac{r_{SH} + r_{BH}}{2} - \frac{r_{SL} + r_{BL}}{2}$$

EDIT:

On what stocks I exclude: As I said, I use Schmidt's et al (2015) paper to clean my data, both their static screens and their dynamic screen. I exclude companies with a lower market capitalization than 5 million euros though and i exclude all financial companies (SIC code between 6000 and 6999). Furthermore, to be included in my June sort of year $$t$$, i demand from the company to have all the return and the market value data from July of year $$t$$ until June of year $$t+1$$. I know that not all researchers do it like this, but some do (like Hanauer et al (2011)) and i think it's better to have more balanced portfolios like that.

• Besides US-evidence, the SMB-return in Germany is negative (i.e. large companies generate higher returns), but the other factor-returns and therefore HML-return should be positive in the german stock market (see table three here, similarly results in other studies hold up to the year 2018). Could you please describe in detail your steps on calculating the HML-return and provide details on what data set you have and what stocks you are excluding prior to any calculations? Nov 18, 2018 at 10:50
• I edited my post. I am aware of this table. the weird thing is if I calculate the mean and t-statistics for the period 1996 until 2018 my HML factor is positive and highly significant with comparable values. also for 1996 until 2011. but not from 2011 until 2018. is smth wrong? Nov 18, 2018 at 11:00
• I meant 1990* until 2018 Nov 18, 2018 at 11:09
• I added a new edit for further clarification. Nov 18, 2018 at 11:13
• What are you regressing against? I mean, what is the stream of returns that you use as your portfolio? Nov 19, 2018 at 13:23

### Preliminary

This answer provides evidence (and confirms your supposition!) that the HML factor in Germany is no longer rewarded with higher returns in the cross-section of German stocks. From July 1992 - December 2018, the average HML-premium is 0.49% (2.26) per month, but insignificantly -0.28% (-1.01) from July 2011 - December 2018. Momentum (WML) and operating profitability (RMW) are the most significant factors in Germany both in the total period (1,28% and 0.55% per month) and since 2011 (1,38% and 0.73% per month), whereas the investment style portfolio CMA may have its economic source in only some sup-portfolios or firms. Momentum and op. profitability are robust throughout the cross-section of German stocks.

### Introduction

Fama/French (2015) test a five-factor asset pricing model that adds profitability and investment factors to the market, size, and value-growth factors of the Fama/French (1993) three-factor model. There is strong evidence that the size affect is not prevalent in integrated European markets and also reversed in some countries like Germany (Fama/French (2017) and Hanauer et al. (2011)). I replicated the Fama/French five-factor model for the German stock market and will extensively address this part of your question:

When i do the calculations for the sub-period from 2011 to 2018, i get a negative mean for the HML factor albeit with a statistically non-significant t-statistic (<0.5). Before that and for the entire period (1990-2018) i get a positive mean and a statistically significant t-statistic (>2). Can that be or am I doing something wrong?

### Data

I use monthly financial data from Thomson Reuters Datastream and yearly accounting data from Worldscope from January 1990 - December 2018 for the German stock market. All data are denominated in euro and total returns (i.e. reinvesting dividends; adjustment for corporate equity activities) of any investment is assumed. To avoid the survivorship bias, all common stocks (stock type EQ, major flag Y, type of share C) including yet delisted stocks are considered in the sample. I start the stock selection with Worldscope lists (WSCOPEBD), dead lists (DEADBDX) and research lists (FGERX). Any financial company having SIC-codes between 6,000 - 6,999 is excluded prior to the analysis.

Data from Thomson Reuters Datastream has to be screened and corrected prior to any analysis. I follow Ince and Porter (2006) and Campbell et al. (2010) and exclude certain identifier within the company name to catch non-common stocks like ADR, REIT's or preferred shares. To mitigate the influence of tiny, illiquid stocks, i follow Ang et al. (2009) and exclude stocks with the lowest 5% of market capitalization or having an un-adjusted closing price lower than 1€ at the portfolio formation date. I apply the dynamic filters DS09 and DS10 from Schmidt et al. (2015) and set all return data to NA if it is greater than 990% per month or if the return $$r_t$$ at the end of month $$t$$ is greater than 300% and $$(1 + r_t)(1 + r_{t-1}) < 50%$$ (we delete then both $$r_t$$ and $$r_{t-1}$$. Further, to mitigate the impact of outliers in accounting information, we winsorize all firm-level (accounting) ratios at the 1% and 99% levels at the portfolio formation date.

### Fama-French Portfolios and the Momentum Factor

I follow Fama and French (1992), (1993) and (2015) and build portfolios at the end of each June. Firms with a negative book-value of equity are excluded and book-value of equity is defined as in Schmidt et al. (2015), i.e. i do not consider deferred taxes (unreported results are similar as what follows). With regard to OP, we do not include selling, general and administrative expense, as this item is not broadly available among international firms. The return predictability of operating profitability is, however, not affected by this adjustment. Momentum (WML) is the cumulative prior 12-month gross stock return, skipping the most recent month, see Jegadeesh and Titman (1993) and the WML definition on Kenneth French's data-library.

### Summary statistics

A typical firm in our sample has a market capitalization of 1,228.35 million euro and a book-to-market ratio of 0.75. Typically, total assets growth with a rate of 24% per year and the operating profitability is 1.22. On average, there are 440 stocks with sufficient data to be included in the portfolio sort:

Table 1
Summary statistics for firm characteristic, July 1992 to December 2018
----------------------------------------------------------------------
Market Cap.   B/M-Ratio  Investment Profitabilty |  N
1. Qu.          745.9        0.59        0.06         1.10     | 322
Median         1092.3        0.71        0.09         1.24     | 450
Mean           1228.4        0.75        0.24         1.22     | 440
3. Qu.         1413.1        0.87        0.21         1.38     | 534
Std.            604.2        0.23        0.36         0.19     | 111.71



Table 2 reports summary statistics for the factor returns of the Fama/French five-factor model for the German capital market:

Table 2
Summary statistics for monthly factor returns, July 1992 to December 2018
-------------------------------------------------------------------------
MKT     SMB     HML    CMA    RMW     WML
Mean            0.53   -0.37   0.49    0.39   0.55   1.28
Std.            5.00    3.39   3.19    3.16   2.85   5.67
t-statistic     1.73   -2.09   2.26    1.83   3.11   4.36
-------------------------------------------------------------------------
This table reports average monthly returns, standard deviations of monthly
returns, and Newey and West (1987) adjusted t-statistics for the average
returns using a lag of six.


Over the sample period from 1992 to 2018, the average market premium amounts to 0.53% per month. All factor returns besides the market premium yield economically and statistically significant return premiums. Especially momentum is most relevant with an average premium of 1.28% per month in Germany.

The following Table reports the summary statistic for the sub-period 2011-2018:

Table 3
Summary statistics for monthly factor returns, July 2011 to December 2018
-------------------------------------------------------------------------
MKT     SMB     HML     CMA    RMW     WML
Mean            0.51   -0.02   -0.28   -0.20   0.73   1.38
Std.            4.48    3.12    2.45    2.23   2.17   3.09
t-statistic     1.13   -0.07   -1.01   -0.68   2.81   5.36
-------------------------------------------------------------------------
This table reports average monthly returns, standard deviations of monthly
returns, and Newey and West (1987) adjusted t-statistics for the average
returns using a lag of six.


Comparing the total period to the sub-period of Table 3 shows, that the HML-factor reverses, but - carefully and precisely interpreted - becomes insignificant and not distinguishable from zero. The same interpretation holds for the CMA-factor return, while RMW remains its stability and WML both becomes statistical and economical larger. The following figure shows the growth of a buy-and-hold strategy, which invests 1€ at the end of June 1992 until December 2018 in each of the factor portfolios (with logarithmic ordinate):

As the figure shows, an initial investment of 1€ in the WML-portfolio results in a total portfolio wealth of 33.51€, whereas the SMB-investment results in a remaining 0.26€. Table 4 provides the total portfolio value of the initial buy-and-hold strategy starting in June 1992, as well as starting in June 2011:

Table 4
Buy-and-hold portfolio wealth of an initial 1€ investment in each factor portfolio
and the risk-free rate of interest RF
----------------------------------------------------------------------------------
Panel A: June 1992 - December 2018

Portfolio:            MKT     SMB     HML     CMA     RMW     WML      RF
Total wealth:        3.60    0.26    4.07    2.94    5.07    33.51    1.96
Geom. return:        0.40   -0.43    0.44    0.34    0.51     1.11    0.21

Panel B: June 2011 - December 2018

Portfolio:            MKT     SMB     HML     CMA     RMW     WML      RF
Total wealth:        1.45    0.94    0.76    0.82    1.89     3.29    1.01
Geom. return:        0.41   -0.07   -0.31   -0.22    0.71     1.33    0.01


Table 4 shows the strong prevalence of momentum in Germany, but together with the figure one can see that the momentum portfolio is largely hit by economic shocks and looses significantly in times of a crisis like the dotcom-crisis in the early 2000's or the financial-crisis in 2009. As already seen in Table 2 and Table 3, the HML-investment as well as the CMA-investment had negative performances after 2011.

### Fama/MacBeth

Besides the non-parametric portfolio strategy in the previous section, i additionally apply the Fama/MacBeth (1973) regression approach. Table 5 reports the average coefficients (i.e. risk premia) of the following regression model:

$$r_{i,t+1} = \alpha_i + \beta_{i,t} + size_{i,t} + bm_{i,t} + inv_{i,t} + op_{i,t} + mom_{i,t} + \epsilon_t$$

where $$\beta_{i,t}$$ denotes the market beta of stock $$i$$, measured with monthly (excess) returns of the previous three years, i.e. 36 month with a minimum of 24 observations required, regressed on the monthly market premium. $$size$$ is the natural logarithm of firm size at the end of June $$t$$ and held constant until June of $$t+1$$. $$bm$$, $$inv$$, $$op$$ are the book-to-market ratio, the change in total assets and the operating profitability of a firm and updated yearly. $$mom$$ is the monthly updated gross return using 12 month and skipping the most recent month. I winsorize each month any independent variable on both sides on a level of 0.5% to mitigate the influence of outliers.

Table 5 presents the average coefficient estimates from monthly cross-sectional regressions of one month-ahead stock returns on the Fama/French risk-factor returns, firm beta and firm momentum for the total period of July 1992 to December 2018. All regressions are estimated using two different weighting schemes, equal-weights and value-weights. The equal-weighted cross-sectional regression approach corresponds to forming equal-weighted portfolios, whereas the value-weighted cross-sectional regression approach corresponds to forming value weighted portfolios. In summary, the value-weighting regression is based on the WLS-approach (weighted least squares) with the market capitalization of the previous month as weightings (see Asparouhova et al. (2013)):

Table 5
Cross-sectional regressions of one-month ahead stock returns on
Fama/French factor returns, firm beta and firm momentum from
July 1992 - December 2018.
-----------------------------------------------------------------
Panel A                      Panel B
Equal-weighted                Value-weighted
-----------------------------------------------------------------
Intercept  |       0.24 (0.85)                   -0.50 (-0.88)
Beta       |      -0.15 (-0.71)                  -0.16 (-0.48)
Size       |       0.02 (0.47)                    0.06 (0.90)
BM-Ratio   |       0.12 (1.66)                    0.64 (2.12)
Investment |      -0.69 (-3.25)                  -0.02 (-0.06)
Op. Prof.  |       0.06 (1.50)                    0.15 (1.51)
Momentum   |       1.42 (5.18)                    1.04 (2.18)
------------------------------------------------------------------
t-statistics are provided in parenthesis and are Newey and West (1987)
adjusted using a lag of six.


Panel A of Table 5 provides evidence, that in an equal-weighted setting, the book-to-market ratio, Investment and Momentum have a strong influence on the one-month-ahead future stock return. In fact, firms with a high book-to-market ratio, high previous stock returns and low investments gain higher future returns. The value-weighted setting in Panel B shows, that the influence of investment diminishes, so the investment risk is strongly linked to small, tiny firms. The average size-premium is not significantly different from zero in both settings, although having a significant performance of -0.37% (-2.09) in the portfolio sort in Table 1. A more detailed analysis shows, that the size-effect is nearly completely located in the high performance of few large firms. While momentum has the most effect on return predictability, the market-beta of a firm is not significant.

### Factor redundancy test

If a factor’s average return is captured by its exposures to the other factors in a model, that factor adds nothing to the model’s explanation of average returns and therefore can be dropped. In this section, i regress each of factors on the others to examine which return factor possesses unique information about expected returns and which factors may be redundant. The intercept in this regression provides the average return that is left unexplained by the exposures to the other five factors:

Table 6
Using five factors in regressions to explain monthly returns on the sixth


Panel A: July 1992 - December 2018

Dependent |   MKT   |   SMB   |   HML   |   CMA   |   RMW   |   WML   |
-----------------------------------------------------------------------
Intercept |   0.77  |   0.13  |   0.46  |   0.25  |   0.38  |   1.19  |
|  (2.68) |  (0.65) |  (2.35) |  (1.21) |  (2.14) |  (4.15) |
MKT       |         |   -0.49 |  -0.04  |  -0.07  |   0.00  |  -0.51  |
|         | (-11.97)| (-0.49) | (-1.13) |  (0.06) | (-3.90) |
SMB       |  -0.93  |         |   0.00  |   0.00  |  -0.01  |  -0.43  |
| (-12.04)|         |  (0.01) |  (0.01) | (-0.09) | (-3.35) |
HML       |  -0.05  |  0.00   |         |   0.11  |   0.12  |  -0.13  |
| (-0.50) | (0.02)  |         |  (0.76) |  (1.28) | (-1.01) |
CMA       |  -0.10  |  0.00   |   0.12  |         |  -0.08  |   0.41  |
| (-1.10) | (0.02)  |  (0.77) |         | (-0.83) |  (2.47) |
RMW       |   0.01  | -0.00   |   0.15  |  -0.10  |         |   0.37  |
|  (0.06) |-(0.09)  |  (1.40) | (-0.84) |         |  (2.12) |
WML       |  -0.25  | -0.11   |  -0.05  |   0.15  |   0.11  |         |
| (-5.25) |(-3.88)  | (-1.01) |  (2.31) |  (2.55) |         |
-----------------------------------------------------------------------
adj. R^2  |   0.51  |  0.45   |   0.02  |   0.10  |   0.05  |   0.23  |
-----------------------------------------------------------------------


Panel B: July 2011 - December 2018

Dependent |   MKT   |   SMB   |   HML   |   CMA   |   RMW   |   WML   |
-----------------------------------------------------------------------
Intercept |   0.70  |   0.47  |   0.11  |   0.09  |   0.67  |   1.56  |
|  (1.17) |  (1.31) |  (0.42) |  (0.32) |  (2.58) |  (4.08) |
MKT       |         |  -0.48  |  -0.14  |  -0.10  |   0.08  |  -0.33  |
|         | (-7.00) | (-1.27) | (-1.62) |  (1.14) | (-2.92) |
SMB       |  -0.93  |         |  -0.37  |   0.09  |  -0.11  |  -0.31  |
| (-5.96) |         | (-2.76) |  (1.01) | (-1.19) | (-2.90) |
HML       |  -0.23  |  -0.32  |         |   0.22  |  -0.14  |  -0.18  |
| (-1.21) | (-2.57) |         |  (3.90) | (-1.32) | (-1.74) |
CMA       |  -0.23  |   0.10  |   0.28  |         |  -0.21  |  -0.03  |
| (-1.63) |  (0.99) |  (3.11) |         | (-1.79) | (-0.19) |
RMW       |   0.17  |  -0.13  |  -0.18  |  -0.21  |         |  -0.09  |
|  (1.03) | -(1.22) | (-1.34) | (-1.84) |         | (-0.67) |
WML       |  -0.32  |  -0.16  |  -0.10  |  -0.01  |  -0.04  |         |
| (-3.11) | (-2.32) | (-1.45) | (-0.19) | (-0.69) |         |
-----------------------------------------------------------------------
adj. R^2  |   0.57  |  0.54   |   0.15  |   0.21  |   0.18  |   0.07  |
-----------------------------------------------------------------------
Dependent indicates the dependent variable in the regression. Newey and
West (1987) adjusted t-statistics for the coefficients are given in
parentheses. R^2 is adjusted for degrees of freedom.


As Table 6 shows, a linear combination of SMB, HML, CMA, RMW and WML is not able to generate the market risk premium, as 0.77% per month are left unexplained in the total period of July 1992 - December 2018. The SMB return however is strongly determined by the market premium and momentum. If the overall market moves 1% up in a month, the SMB return on average decreases 0.49%. The value-effect however is not rendered insignificant in presence of the other factor returns, as the intercept of 0.46% per month is significantly different from zero (t-statistic 2.35).

The sub-period of July 2011 - December 2018 (Panel B) provides evidence, that the HML (as well as SMB) return is subsumed by other risk premiums. The HML risk-factor is mostly explained by the SMB-return and CMA-return, left only an insignificant intercept of 0.11% (0.42) per month. This is interesting, because both SMB and CMA also may not add information about expected returns beyond that provided by the simultaneous influence of other factor risk premia. For this subperiod, the RMW and WML return are the only ones, which can not be explained by other factor returns.

### Conclusion

I provide evidence that the Fama/French five-factor returns on the German stock market capture certain risk exposures in the total period of 1992-2018. Firm characteristics like size, book-to-market ratio, investment style and operating profitability are valid proxies for the exposure towards latent risk factors, which are cross-sectionally highly correlated with these firm-level variables. In contrast to the USA, the size effect in Germany is reversed, i.e. large stocks outperform small stocks.

The ability to capture risk-exposures however weakens in recent time. The value factor (HML) generates 0.49% per month overall, but an insignificant return of -0.28% per month since 2011. The only factors which are still highly significant (both statistically and economically) are WML and RMW, so momentum and operating profitability are strong risk exposures for German stocks. The parametric Fama/MacBeth (1973) regression shows, that the CMA return may have its economic roots in only some sub-portfolios rather than in the cross-section of the overall stock market.

### References

Ang et al. (2009), High idiosyncratic volatility and low returns: international and further U.S. evidence. Journal of Financial Economics (91).

Asparouhova et al. (2013), Noisy prices and inference regarding returns. Journal of Finance (68).

Campbell et al. (2010), Multi-country event-study methods. Journal of Banking and Finance (34).

Fama/MacBeth (1973), Risk, Return, and Equilibrium: Empirical Tests, Journal of Political Economy, 81 (3).

Fama/French (1992), The Cross-Section of stock returns, The Journal of Finance 47(2).

Fama/French (1993), Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33(1).

Fama/French (2015), A five-factor asset pricing model, Journal of Financial Economics (116).

Fama/French (2017), International tests of a five-factor asset pricing model, Journal of Financial Economics (123).

Hanauer et al. (2013), Risikofaktoren und Multifaktormodelle für den deutschen Aktienmarkt (risk factors and multi-factor models for the german stock market), Betriebswirtschaftliche Forschung & Praxis (65).

Ince/Porter (2006), Individual equity return data from Thomson Reuters Datastream: Handle with care!, Journal of Financial Research (29).

• This may be a slight deviation from the original topic, but would be able to point me to Newey and West (1987) adjustment with lags? Since you use R, it would be great to if there is R implementation. Thanks!
– AK88
Sep 18, 2019 at 15:42
• Sure, i use a combination of the packages sandwich and lmtest. If you have a regression model reg <- lm(y ~ x) (here is y a time series of returns and x=1, that is an intercept only model) you get Newey/West (1987) robust standard errors by applying coeftest(reg, NeweyWest(reg, lag = l, prewhite = FALSE)) with l being an appropriate value (here: 6). Sep 19, 2019 at 5:35

Can I suggest a much more pedestrian explanation? HML is a "risk premium"... so it doesn't always pay off; and there are regimes in which it can pay off negatively by a significant degree for a significant time because the conditions are all wrong, right ;-)

Consider the cliche that large-caps tend to be multi-national exporters more than smaller-caps who tend to be more domestically-exposed. See above: the former just got a 33% currency deval, which is a 66% appreciation for everyone else. Good for large-caps and their international competitiveness.

The 2011 cut-off is also interesting. 2010 was the last hurrah of the ECB's inflation-mania. They raised rates into spiking oil prices, weeks before a(nother) bank-sovereign solvency crisis, only to reverse course in short order. They even published an ECB op-ed saying that the US inflation of the 1970s had nothing to do with oil prices (WTF???); but was all to do with too loose monetary policy ;-) Of course in the summer of 2011, Draghi junked all that; and committed to whatever looseness was required for the monetary union to survive. So the currency, that was historically biased hawkish/strong (to the benefit of Small/Mid-Caps), tanked. Good for exporters...

Also in 2011, Germany was the "safe haven" in Europe, given Europe's problems. Tanking the currency for the sake of the currency bloc to alleviate the risks on the others removes that premium (in prices) from domestic German exposures. And more recently, Germany is now leading the Eurozone aggregates into recession. From being "safe haven", domestic Germany (ie their smaller-caps) has now become the risk factor.

So maybe it's not such a surprise that the ex-post factor risk premium on German HML realised negative 2011-18?