Appendices for:
An Effective Analysis of the Size and Value Effect
With
A European Stress Test of the Fama and French Three-Factor Model
July 2007
Appendix
Appendix A: Data Selection and excess returns
Country lists and elimination triggers for non-ordinary stock
Datastream list / menomic Firms in list Left after elimination steps
Belgium FBEL 167 113
Belgium dead DEADBD 608 71
Netherlands FHOL 302 137
Netherlands dead DEADNL 382 140
Germany FGER 1 / 2 1248 582
Germany dead DEADBD 1546 231
France FFRA 1083 702
France dead DEADFR 1585 471
United Kingdom LFTALLSH0101 5546 579
United Kingdom dead DEADUK 4781 1566
LISTED 2113
DEAD 2479
TOTAL 4592
Country lists and number of firms
This table describes the number of firms that are in the Datastream lists and the number of firms that is left over after the elimination steps (a to d) that are described in the data section (3.4) are executed. For the average number of firms used, see table 6 and figure 3.
Table A: Country (Datastream) data lists and number of firms in sample.
International ●‘adr’ signals American Depository Receipts; All countries ●‘b’/ ‘c’/ ’d’ ; Class ‘B’ ,‘C’ or ’D’ share,
● Cert; certificate, in some cases these will and in other cases these will not be eliminated,
● (eas) ; EASDAQ share,
● Pf./pref./pref/prf; preferred share, ● (xsq); SEAQ share,
● Dup./dupl../dupl.; Duplicate share, ● % / $; warrant or convertible, ● Wts; warrant,
● Expy/expired/expid/expire/expires; signals a derivative quote, ● (bru)/(par)/(ham)(dus)(stu)(mun)(ber)(xet)/(ams)/(lse); indicate listing outside home country/market Country specific
Belgium vvpr, strip, div, afv, cap, exp. Netherlands rts, div., scripts
Germany .gsh
France rights., adp, ope, op, limited data, ltd data (ex sfi) ex spie)
United Kingdom nrfd, new fully, 1p, warrants arabic number+'p', nrfd, rfd, pp, redeemable shares, red. shares, new nil paid, fully paid, (vxx), br., 'br', pfd
Elimination triggers
This table shows some of the selection criteria and elimination triggers, which were used to divide ordinary form non-ordinary stock. This list is based to a large extent on a similar list in the dissertation by DeMoor (2005). Note that these lists are not extensive and may exlcude some selection criteria.
Excess returns for the 25 size-B/M ratio sorted portfolios.
Book-to-Market Equity Quintiles
Size
Quintiles
Low
2
3
4
High
Low
2
3
4
High
Average Excess Portfolio Return
Standard deviation
Small
-2,59%
-1,66%
-1,15%
-0,70%
0,13%
5,6%
5,1%
4,8%
4,4%
4,8%
2
-1,93%
-1,31%
-0,82%
-0,27%
0,29%
5,6%
5,0%
4,3%
4,2%
4,6%
3
-1,36%
-0,65%
-0,38%
0,09%
0,60%
6,0%
4,8%
4,4%
4,0%
4,1%
4
-0,80%
-0,32%
0,01%
0,32%
0,82%
5,5%
4,7%
4,4%
4,5%
4,5%
Big
0,00%
-0,11%
0,22%
0,46%
1,04%
4,3%
4,6%
5,4%
5,2%
5,5%
Minimum Value weighted Return
Maximum Value weighted return
Small
-20,24%
-20,49%
-20,55%
-15,65%
-16,06%
16,27%
12,30%
12,53%
10,32%
15,33%
2
-22,29%
-23,26%
-17,12%
-17,61%
-19,26%
17,45%
9,75%
10,42%
8,32%
14,56%
3
-24,81%
-17,78%
-19,64%
-17,25%
-15,29%
19,55%
9,16%
10,49%
11,61%
12,67%
4
-21,69%
-19,67%
-18,69%
-16,39%
-14,95%
15,84%
8,52%
11,26%
12,74%
14,07%
Big
-14,09%
-18,46%
-31,86%
-17,94%
-18,51%
11,79%
9,41%
14,82%
15,87%
15,62%
Median
Small
-2,20%
-1,62%
-0,72%
-0,23%
0,02%
2
-1,38%
-0,71%
-0,46%
-0,09%
0,64%
3
-0,44%
-0,17%
-0,03%
0,40%
1,00%
4
-0,24%
0,50%
0,33%
0,89%
1,31%
Big
0,72%
0,91%
1,07%
1,04%
1,29%
These are the descriptive statistics for the excess market returns. In essence this is the same table as table 11, the
difference here is that the riskfree rate is subtracted to come to the excess return values. All values are motnhly
averages for the 192 month period
Appendix B: Robustness tests
Dependent and independent returns for the different time periods
1990-1997
premium
1998-2005
premium
1990-2005
premium
Low
2
3
4
High
Low
2
3
4
High
Low
2
3
4
High
Small
-1,36%
-0,42%
-0,18%
-0,04%
0,70%
2,07%
-3,06%
-2,14%
-1,37%
-0,61%
0,31%
3,37%
-2,21%
-1,28%
-0,77%
-0,33%
0,51%
2,72%
2
-0,58%
-0,23%
-0,10%
0,18%
0,69%
1,27%
-2,53%
-1,65%
-0,78%
0,03%
0,64%
3,17%
-1,55%
-0,94%
-0,44%
0,10%
0,67%
2,22%
3
-0,13%
0,21%
0,22%
0,43%
0,73%
0,85%
-1,84%
-0,75%
-0,24%
0,51%
1,22%
3,06%
-0,98%
-0,27%
-0,01%
0,47%
0,97%
1,96%
4
-0,04%
0,40%
0,32%
0,59%
1,06%
1,10%
-0,80%
-0,29%
0,46%
0,81%
1,33%
2,13%
-0,42%
0,06%
0,39%
0,70%
1,19%
1,62%
Big
0,50%
0,62%
0,67%
1,05%
1,51%
1,01%
0,25%
-0,08%
0,51%
0,61%
1,31%
1,07%
0,37%
0,27%
0,59%
0,83%
1,41%
1,04%
premium
1,86%
1,03%
0,86%
1,10%
0,81%
premium
3,31%
2,07%
1,88%
1,22%
1,00%
premium
2,59%
1,55%
1,37%
1,16%
0,91%
This table shows the value weighted portfolio returns for the first and second half of the original 16 year period, that is 1990-1997 and 1998-2005. Also the returns for the whole 16 year period are shown
for comparison.
Table D: Value weighted monthly portfolio returns for different time periods.
1990-1997 1998-2005 1990-2005
Minimum Maximum Mean St Dev Median Minimum Maximum Mean St Dev Median MinimumMaximumMean St Dev Median
SmB S = (SL+SN+SH)/3 -10,92% 9,93% 0,15% 3,30% 0,10% -17,76% 7,63% -0,64% 5,20% 0,64% -17,76% 9,93% -0,24% 4,36% 0,19% B = (BL+BN+BH)/3 -12,10% 7,96% 0,78% 3,51% 1,38% -17,12% 11,15% 0,43% 5,30% 1,52% -17,12% 11,15% 0,60% 4,49% 1,42% S - B -5,62% 5,64% -0,63% 2,06% -0,96% -8,63% 6,64% -1,06% 2,69% -0,75% -8,63% 6,64% -0,85% 2,40% -0,94% HmL H = (SH+BH)/2 -10,75% 11,25% 0,89% 3,65% 0,96% -16,09% 12,86% 0,87% 4,88% 1,93% -16,09% 12,86% 0,88% 4,29% 1,45% L = (SL+BL)/2 -11,15% 7,02% 0,09% 2,91% 0,66% -16,90% 13,09% -0,93% 5,67% -0,12% -16,90% 13,09% -0,42% 4,53% 0,43% H - L -2,25% 5,92% 0,80% 1,47% 0,62% -14,02% 8,79% 1,80% 3,29% 1,72% -14,02% 8,79% 1,30% 2,59% 0,68%
This table describes the independent returns for the Size (SMB) and Book-to-Market (HmL) factors for the first and second half of the original 16 year period, that is 1990-1997 and 1998-2005. Also the returns for the whole 16 year period are shown for comparison. SmB is the Portfolio formed by the difference between simple average return of the three small market value (MV) portfolios and the three Big (MV) portfolios. HmL is the difference between the simple average return of the two High book-to-market ratio (BM) portfolios and the two low BM portfolios.
Dependent and independent returns for the sample without UK firms and UK firms only
No UK
premium
With UK
premium
UK Only
premium
Low
2
3
4
High
Low
2
3
4
High
Low
2
3
4
High
Returns
Returns
Returns
Small
-1,33%
-0,97%
-0,43%
-0,03%
0,34%
1,67%
-2,21%
-1,28%
-0,77%
-0,33%
0,51%
2,72%
-0,90%
-0,32%
-0,33%
-0,29%
0,17%
1,07%
2
-1,03%
-0,69%
-0,30%
0,17%
0,54%
1,57%
-1,55%
-0,94%
-0,44%
0,10%
0,67%
2,22%
-0,52%
-0,25%
-0,14%
-0,06%
0,15%
0,67%
3
-0,90%
-0,37%
-0,04%
0,35%
0,55%
1,45%
-0,98%
-0,27%
-0,01%
0,47%
0,97%
1,96%
-0,09%
0,09%
0,04%
0,12%
0,42%
0,51%
4
-0,53%
-0,09%
0,25%
0,43%
0,70%
1,23%
-0,42%
0,06%
0,39%
0,70%
1,19%
1,62%
0,10%
0,14%
0,14%
0,27%
0,50%
0,40%
Big
-0,03%
0,07%
0,42%
0,66%
0,79%
0,82%
0,37%
0,27%
0,59%
0,83%
1,41%
1,04%
0,41%
0,20%
0,18%
0,19%
0,63%
0,22%
premium
1,29%
1,03%
0,85%
0,69%
0,44%
2,59%
1,55%
1,37%
1,16%
0,91%
1,31%
0,52%
0,52%
0,49%
0,46%
standard deviation
standard deviation
standard deviation
Small
4,12%
3,94%
3,51%
2,99%
3,28%
5,56%
5,08%
4,77%
4,39%
4,78%
2,77%
2,51%
2,32%
2,33%
2,68%
2
4,04%
3,77%
2,94%
2,83%
3,02%
5,62%
5,01%
4,23%
4,19%
4,60%
2,54%
2,04%
1,98%
2,07%
2,40%
3
3,96%
3,31%
2,84%
2,28%
2,26%
6,01%
4,78%
4,43%
3,99%
4,06%
2,80%
1,99%
2,08%
2,09%
2,43%
4
3,53%
2,72%
2,54%
2,33%
2,65%
5,51%
4,69%
4,37%
4,43%
4,49%
2,55%
2,32%
2,18%
2,48%
2,55%
Big
2,68%
2,97%
3,47%
3,79%
2,82%
4,28%
4,59%
5,42%
5,15%
5,49%
2,13%
2,10%
2,63%
1,96%
3,77%
This table shows the value weighted portfolio returns and standard deviations for the original sample with the UK (middle), without the UK (left) and with the UK firms only (right). Below are the standard
deviations for the portfolio returns. The returns are averages for the monthly returns over the 192 month period from 1990-2005
Table F: Value weighted portfolio returns and standard deviations for the sample with and without the UK
No UK
With UK
UK only
Minimum Maximum Mean
St Dev
Median
Minimum Maximum Mean
St Dev
Median
Minimum
Maximum Mean
St Dev
Median
SmB
S = (SL+SN+SH)/3
-17.76%
7.63%
-0.64%
5.20%
0.64%
-17.76%
9.93%
-0.24%
4.36%
0.19%
-13.99%
6.20%
-0.23%
2.89%
0.21%
B = (BL+BN+BH)/3
-17.12%
11.15%
0.43%
5.30%
1.52%
-17.12%
11.15%
0.60%
4.49%
1.42%
-9.35%
6.87%
0.28%
2.72%
0.62%
S - B
-8.63%
6.64%
-1.06%
2.69%
-0.75%
-8.63%
6.64%
-0.85%
2.40%
-0.94%
-6.52%
5.30%
-0.51%
1.89%
-0.46%
HmL
H = (SH+BH)/2
-16.09%
12.86%
0.87%
4.88%
1.93%
-16.09%
12.86%
0.88%
4.29%
1.45%
-11.11%
9.67%
0.47%
2.41%
0.43%
L = (SL+BL)/2
-16.90%
13.09%
-0.93%
5.67%
-0.12%
-16.90%
13.09%
-0.42%
4.53%
0.43%
-11.23%
10.43%
-0.48%
3.10%
0.07%
H - L
-14.02%
8.79%
1.80%
3.29%
1.72%
-14.02%
8.79%
1.30%
2.59%
0.68%
-9.26%
10.50%
0.94%
2.14%
0.70%
This table describes the independent returns for the Size (SMB) and Book-to-Market (HmL) factors for the sample without the UK (left), with the UK (middle) and for the UK only (right). The values are all
averages for the 192 month period from 1990-2005. SmB is the portfolio formed by the difference between simple average return of the three small market value (MV) portfolios and the three Big (MV)
portfolios. HmL is the difference between the simple average return of the two High book-to-market ratio (BM) portfolios and the two low BM portfolios.
Regression three factor model for the sample without UK firms and UK firms only
Ri – Rf = α + βi (Rm - Rf) + sSmB + hHmL + ε Ri – Rf = α + βi (Rm - Rf) + sSmB + hHmL + ε
No UK Book-to-Market Ratio Quintiles UK only Book-to-Market Ratio Quintiles
Size
Quintiles Low 2 3 4 High Low 2 3 4 High
Size
Quintiles Low 2 3 4 High Low 2 3 4 High
α t-statistic α t-statistic Small -1.02% -0.77% -0.59% -0.35% -0.19% -4,32** -3,98** -3,39** -2,21* -1.19 Small -1.22% -0.62% -0.67% -0.60% -0.16% -8.17** -4.4** -5.46** -5.48** -1.34 2 -0.57% -0.58% -0.59% -0.36% -0.13% -3,52** -3,79** -5,18** -3,2** -1 2 -0.84% -0.59% -0.49% -0.49% -0.31% -7.03** -6.42** -5.18** -5.21** -2.94** 3 -0.50% -0.46% -0.50% -0.33% -0.10% -3,56** -3,63** -4,62** -3,19** -0.93 3 -0.47% -0.29% -0.36% -0.34% -0.07% -3** -3.03** -3.77** -3.48** -0.59 4 -0.39% -0.39% -0.41% -0.35% -0.11% -2,63** -3,47** -3,6** -3,33** -0.86 4 -0.38% -0.34% -0.37% -0.29% -0.10% -2.89** -3.08** -3.59** -2.48* -0.71 Big -0.36% -0.39% -0.48% -0.42% -0.03% -3,83** -3,6** -3,96** -2,99** -0.21 Big -0.09% -0.37% -0.41% -0.44% -0.30% -0.83 -3.57** -2.73** -4.25** -1.41 β t-statistic β t-statistic Small 0.43 0.54 0.52 0.45 0.52 8,73** 13,19** 14,29** 13,54** 15,37** Small 0.35 0.28 0.29 0.32 0.38 10.51** 9.04** 10.86** 13.41** 14.5** 2 0.55 0.61 0.53 0.53 0.53 16,13** 19,06** 21,86** 22,74** 19,73** 2 0.39 0.32 0.29 0.31 0.35 14.64** 15.85** 13.86** 14.94** 15** 3 0.58 0.59 0.55 0.43 0.41 19,75** 22,52** 24,47** 19,73** 18,62** 3 0.44 0.34 0.37 0.36 0.37 12.6** 16.24** 17.41** 16.46** 13.52** 4 0.54 0.51 0.49 0.44 0.48 17,34** 21,64** 20,54** 19,64** 18,05** 4 0.44 0.41 0.39 0.43 0.37 15.24** 16.48** 17.32** 16.42** 12.19** Big 0.43 0.55 0.68 0.75 0.47 21,56** 24,26** 26,6** 25,49** 14,93** Big 0.36 0.34 0.38 0.27 0.39 15.26** 14.69** 11.39** 11.62** 8.26** s t-statistic s t-statistic Small 1.03 1.08 1.20 0.97 1.08 8,38** 10,63** 13,28** 11,87** 12,89** Small 1.22 1.15 1.04 1.16 1.31 10.43** 10.34** 10.91** 13.57** 13.89** 2 1.07 1.08 1.02 0.90 0.95 12,71** 13,59** 17,02** 15,5** 14,17** 2 1.17 0.91 0.90 0.90 1.00 12.47** 12.59** 12.11** 12.3** 11.99** 3 0.78 0.85 0.80 0.49 0.58 10,57** 13,03** 14,27** 9,01** 10,63** 3 0.60 0.58 0.65 0.58 0.67 4.86** 7.73** 8.68** 7.6** 6.77** 4 0.50 0.55 0.43 0.23 0.41 6,51** 9,3** 7,21** 4,12** 6,11** 4 0.24 0.37 0.29 0.27 0.26 2.3* 4.2** 3.62** 2.85** 2.43* Big -0.26 -0.04 -0.08 0.02 0.11 -5,34** -0.71 -1.26 0.23 1.44 Big -0.13 -0.15 0.10 -0.06 0.11 -1.59 -1.81 0.83 -0.76 0.67 h t-statistic h t-statistic Small -0.53 -0.41 0.17 0.29 0.64 -4,09** -3,8** 1,81 3,4** 7,19** Small 0.55 0.49 0.47 0.47 0.58 5.06** 4.81** 5.31** 5.89** 6.62** 2 -0.82 -0.35 0.24 0.48 0.71 -9,2** -4,12** 3,83** 7,81** 10** 2 0.41 0.33 0.39 0.56 0.68 4.72** 4.96** 5.68** 8.39** 8.78** 3 -0.97 -0.22 0.29 0.46 0.51 -12,51** -3,25** 4,88** 8,13** 8,85** 3 0.01 0.12 0.18 0.34 0.47 0.06 1.74 2.62** 4.75** 5.21** 4 -0.76 -0.08 0.35 0.41 0.55 -9,34** -1.35 5,55** 7,08** 7,87** 4 -0.07 0.12 0.13 0.22 0.37 -0.76 1.43 1.76 2.56* 3.71** Big -0.58 -0.32 0.19 0.45 0.37 -11,21** -5,42** 2,82** 5,92** 4,39** Big -0.25 -0.03 0.19 0.30 1.13 -3.29** -0.4 1.71 3.96** 7.37** Adjusted R² Adjusted R² Small 47.10% 60.74% 61.48% 56.79% 62.24% Small 50.05% 46.02% 52.05% 62.04% 64.91% 2 74.58% 73.95% 76.18% 75.89% 71.56% 2 62.06% 64.72% 60.80% 65.78% 66.07% 3 79.94% 77.27% 77.44% 68.23% 67.08% 3 45.70% 59.81% 63.71% 62.65% 54.94% 4 72.13% 73.22% 68.83% 67.62% 64.10% 4 55.20% 59.76% 62.54% 60.97% 48.59% Big 80.49% 79.26% 80.59% 78.81% 55.06% Big 57.81% 57.35% 43.65% 50.64% 44.99%
This table shows the results of the 25 independent regressions for the sample without UK firms and the sample with UK firms only (right) in the 192 month period from January 1990 to December 2005. The dependent variable is the value weighted average stock return of the portfolio sorted by size and book-to-market ratio minus the riskfree interest rate in the period. Size, as measured by market value of the stock, is valued at the beginning of the month and is adjusted each month. The market value is the value of ordinary common stock outstanding (price x amount). The Book/Market ratio is the book value of equity divided by the market value of equity and is changed at the beginning of july each year t to the end of year value of t-1.The riskfree rate is the three month German treasury-bill rate. The independent variables are the market factor, the size factor and the book/market factor. The market factor is the monthly market return of the MSCI Europe Index minus the riskfree rate. The index was shown to have the largest correlation with the total value weighted return of all the firms in the sample. The size factor, SmB, is the average of the returns of the three small size-book/market sorted portfolios minus the average of the three big portfolios.The book/market factor is the difference between the average return in the two large book/market portoflios and the two low book/market portfolios. The
differences are all calulated monthly. β, s and h are the coefficients of the market, size and book/market factor respectively.The intercepts α and the Adjusted R² give an indication of the degree in which the risk factors are able to explain the variation in excess stock returns and whether the factors in the model are able to capture the variance in portoflio returns. The * and **
show a significance (two-tailed) at the 5% and 1% level respectively. The main significance level to see whether the values are significantly different from zero is 5%.
Dependent and independent returns for the sample of listed firms only
Listed Only premium Listed and dead firms premium
Low 2 3 4 High Low 2 3 4 High
Returns Returns Small -1,21% -0,52% -0,37% 0,22% 0,79% 2,00% -2,21% -1,28% -0,77% -0,33% 0,51% 2,72% 2 -0,86% -0,51% -0,30% 0,43% 0,79% 1,65% -1,55% -0,94% -0,44% 0,10% 0,67% 2,22% 3 -0,71% -0,16% 0,29% 0,47% 1,02% 1,73% -0,98% -0,27% -0,01% 0,47% 0,97% 1,96% 4 -0,16% 0,27% 0,42% 0,69% 1,07% 1,23% -0,42% 0,06% 0,39% 0,70% 1,19% 1,62% Big 0,53% 0,36% 0,58% 0,78% 1,46% 0,93% 0,37% 0,27% 0,59% 0,83% 1,41% 1,04% premium 1,74% 0,88% 0,95% 0,57% 0,67% 2,59% 1,55% 1,37% 1,16% 0,91%
standard deviation standard deviation
Small 5,37% 5,50% 4,65% 4,40% 4,89% 5,56% 5,08% 4,77% 4,39% 4,78% 2 6,26% 5,38% 4,70% 4,38% 4,45% 5,62% 5,01% 4,23% 4,19% 4,60% 3 6,01% 5,11% 4,49% 4,31% 3,89% 6,01% 4,78% 4,43% 3,99% 4,06% 4 5,96% 5,03% 4,45% 4,35% 4,35% 5,51% 4,69% 4,37% 4,43% 4,49% Big 4,47% 4,61% 5,74% 5,36% 5,73% 4,28% 4,59% 5,42% 5,15% 5,49% This table shows the value weighted portfolio returns and standard deviations for the original sample with inlisted firms (right),
and with the listed firms only (left). Below are the standard deviations for the portfolio returns. The returns are averages for the monthly returns over the 192 month period from 1990-2005
Table I: Value weighted portfolio returns and standard deviations for the sample with and without the UK
Listed only Listed and dead firms
Minimum Maximum Mean St Dev Median Minimum Maximum Mean St Dev Median SmB S = (SL+SN+SH)/3 -18,73% 8,52% 0,00% 4,38% 0,60% -17,76% 7,63% -0,64% 5,20% 0,64% B = (BL+BN+BH)/3 -18,11% 11,57% 0,62% 4,60% 1,55% -17,12% 11,15% 0,43% 5,30% 1,52% S - B -8,24% 6,16% -0,62% 2,27% -0,59% -8,63% 6,64% -1,06% 2,69% -0,75% HmL H = (SH+BH)/2 -16,06% 14,80% -0,15% 4,69% 0,65% -16,09% 12,86% 0,87% 4,88% 1,93% L = (SL+BL)/2 -17,78% 13,18% 0,87% 4,25% 1,38% -16,90% 13,09% -0,93% 5,67% -0,12% H - L -14,69% 9,78% 1,02% 2,81% 0,64% -14,02% 8,79% 1,80% 3,29% 1,72% This table describes the independent returns for the Size (SMB) and Book-to-Market (HmL) factors for the sample without dead firms (left and the original sample (right) for comparison. The values are all averages for the 192 month period from 1990-2005. SmB is the portfolio formed by the difference between simple average return of the three small market value (MV) portfolios and the three Big (MV) portfolios. HmL is the difference between the simple average return of the two High book-to-market ratio (BM) portfolios and the two low BM portfolios.
Regression three factor model for the sample of listed firms only
Ri – Rf = α + βi (Rm - Rf) + sSmB + hHmL + ε
Book-to-Market Ratio Quintiles
Size
Quintiles
Low
2
3
4
High
Low
2
3
4
High
α
t-statistic
Small
-1,07%
-0,44%
-0,70%
-0,30%
-0,04%
-3,5**
-1,63
-3,15**
-1,47
-0,17
2
-0,27%
-0,46%
-0,65%
-0,26%
-0,18%
-1
-2,17*
-3,74**
-1,66
-1
3
-0,59%
-0,46%
-0,38%
-0,47%
0,11%
-2,62**
-2,35*
-2,19*
-2,74**
0,63
4
-0,23%
-0,26%
-0,42%
-0,29%
0,01%
-0,89
-1,26
-2,41*
-1,58
0,03
Big
-0,09%
-0,36%
-0,48%
-0,37%
0,01%
-0,56
-2,12*
-2,23*
-1,98*
0,04
β
t-statistic
Small
0,73
0,91
0,84
0,82
0,91
10,77**
15,33**
17,18**
17,95**
18,01**
2
0,96
1,00
0,96
0,94
0,91
16,29**
21,13**
25,06**
27,53**
23,4**
3
1,11
1,02
0,94
0,88
0,75
22,04**
23,49**
24,7**
23,09**
18,88**
4
1,06
1,00
0,92
0,86
0,86
18,4**
21,76**
23,74**
21,18**
21,64**
Big
0,79
0,89
1,09
1,05
1,01
23,66**
23,78**
22,72**
25,16**
16,57**
s
t-statistic
Small
1,11
1,05
1,20
1,08
1,15
7,77**
8,37**
11,57**
11,14**
10,7**
2
1,16
1,14
1,15
1,02
0,93
9,36**
11,43**
14,2**
14,11**
11,38**
3
0,91
0,85
0,70
0,61
0,55
8,57**
9,28**
8,66**
7,51**
6,58**
4
0,65
0,65
0,54
0,34
0,36
5,35**
6,72**
6,63**
3,91**
4,22**
Big
-0,29
0,04
-0,13
-0,02
0,33
-4,16**
0,46
-1,32
-0,24
2,54*
h
t-statistic
Small
-0,19
-0,26
0,27
0,39
0,69
-1,75
-2,71**
3,37**
5,29**
8,42**
2
-0,72
-0,21
0,21
0,46
0,69
-7,54**
-2,8**
3,31**
8,35**
11,07**
3
-0,47
-0,05
0,25
0,49
0,49
-5,78**
-0,7
4,04**
7,9**
7,56**
4
-0,42
0,07
0,34
0,37
0,47
-4,48**
0,87
5,35**
5,67**
7,26**
Big
-0,33
-0,08
0,06
0,24
0,75
-6,08**
-1,32
0,8
3,55**
7,62**
Adjusted R²
R²
Small
46,44%
61,32%
63,14%
63,99%
64,38%
47,29%
61,93%
63,72%
64,55%
64,94%
2
70,76%
74,39%
77,84%
80,08%
75,03%
64,94%
74,79%
78,19%
80,39%
75,42%
3
76,86%
75,89%
76,23%
73,92%
65,68%
77,22%
76,27%
76,61%
74,33%
66,22%
4
69,01%
72,09%
74,89%
71,22%
72,35%
69,50%
72,53%
75,28%
71,68%
72,79%
Big
81,46%
78,03%
77,03%
79,75%
62,44%
81,75%
78,38%
77,39%
80,07%
63,03%
This table shows the results of the 25 independent regressions in the 192 month period from January 1990 to
December 2005 for the listed firms only. The dependent variable is the value weighted average stock return of the
portfolio sorted by size and book-to-market ratio minus the riskfree interest rate in the period. Size, as measured by
market value of the stock, is valued at the beginning of the month and is adjusted each month. The market value is
the value of ordinary common stock outstanding (price x amount). The Book/Market ratio is the book value of equity
divided by the market value of equity and is changed at the beginning of july each year t to the end of year value of
t-1.The riskfree rate is the three month German treasury-bill rate. The independent variables are the market factor, the
size factor and the book/market factor. The market factor is the monthly market return of the MSCI Europe Index
minus the riskfree rate. The index was shown to have the largest correlation with the total value weighted return of
all the firms in the sample. The size factor, SmB, is the average of the returns of the three small size-book/market sorted portfolios minus the average of the three big portfolios.The book/market
factor is the difference between the average return in the two large book/market portoflios and the two low
book/market portfolios. The differences are all calulated monthly. β, s and h are the coefficients of the market,
size and book/market factor respectively.The intercepts α and the Adjusted R² give an indication of the degree
in which the risk factors are able to explain the variation excess stock returns and whether the factors in the
model are able to capture the variance in portoflio returns. The * and ** show a significance (two-tailed) at the 5%
and 1% level respectively. The main significance level to see whether the values are significantly different
from zero is 5%.
No Extreme Market Values
No extreme Market Values
With extreme Market Values
Minimum Maximum Mean
St Dev
Median
Minimum Maximum Mean
St Dev
Median
SmB
S = (SL+SN+SH)/3
-17,80%
9,98%
-0,23%
4,37%
0,20%
-17,76%
7,63%
-0,64%
5,20%
0,64%
B = (BL+BN+BH)/3
-17,92%
9,52%
0,54%
4,25%
1,06%
-17,12%
11,15%
0,43%
5,30%
1,52%
S - B
-6,81%
7,24%
-0,77%
1,97%
-0,75%
-8,63%
6,64%
-1,06%
2,69%
-0,75%
HmL
H = (SH+BH)/2
-19,00%
14,82%
-0,53%
4,84%
0,19%
-16,09%
12,86%
0,87%
4,88%
1,93%
L = (SL+BL)/2
-16,83%
12,33%
0,91%
4,19%
1,16%
-16,90%
13,09%
-0,93%
5,67%
-0,12%
H - L
-15,26%
14,83%
1,45%
2,99%
1,13%
-14,02%
8,79%
1,80%
3,29%
1,72%
This table describes the independent returns for the Size (SMB) and Book-to-Market (HmL) factors for the sample with a lower limit and a upper
limit for the market values. The values are all averages for the 192 month period from 1990-2005. SmB is the portfolio formed by the difference
between simple average return of the three small market value (MV) portfolios and the three Big (MV) portfolios. HmL is the difference between
the simple average return of the two High book-to-market ratio (BM) portfolios and the two low BM portfolios.
January Effect;
jan feb march april may june july aug sep oct nov dec feb-dec January 'Premium'
Portfolio 1 2,09% -0,5% -3,1% -2,1% -0,7% -3,3% -4,2% -2,4% -5,6% -4,1% -2,2% -0,4% -2,6% 4,70% 2 1,84% -0,5% -2,6% 0,6% -1,6% -1,6% -1,6% -1,4% -4,4% -1,6% -1,8% -0,6% -1,6% 3,41% Small 3 3,59% 0,5% -1,8% -0,7% -0,1% -1,7% -2,3% -1,0% -3,2% -1,4% -0,3% -0,9% -1,2% 4,76% 4 3,15% 0,6% -1,3% 1,6% 1,3% -1,5% -0,9% -1,4% -2,5% -1,4% -0,5% -0,9% -0,6% 3,79% 5 4,32% 1,9% 0,4% 2,6% 2,1% -0,8% -1,4% -0,6% -2,9% 0,2% 0,3% 0,0% 0,2% 4,16% average 3,00% 0,4% -1,7% 0,4% 0,2% -1,8% -2,1% -1,4% -3,7% -1,7% -0,9% -0,6% -1,2% 4,16% 6 2,65% -0,1% -3,0% -1,0% -0,7% -3,7% -2,9% -1,9% -4,6% -1,6% -1,7% 0,0% -1,9% 4,58% 7 2,04% -0,3% -1,4% 0,6% 0,0% -1,4% -1,8% -1,8% -4,3% -1,1% -1,5% -0,3% -1,2% 3,25% 8 2,89% 0,2% -0,5% 1,3% 1,0% -1,3% -1,6% -1,7% -3,3% -0,9% -0,7% -0,6% -0,7% 3,63% 9 2,22% 1,0% 0,5% 2,0% 0,9% -0,8% -1,2% -0,8% -3,0% 0,3% 0,3% -0,3% -0,1% 2,31% 10 3,73% 2,1% 0,3% 2,4% 1,5% -0,2% -0,4% -0,1% -2,5% 0,4% 0,6% 0,1% 0,4% 3,34% average 2,70% 0,6% -0,8% 1,1% 0,5% -1,5% -1,6% -1,3% -3,6% -0,6% -0,6% -0,2% -0,7% 3,42% 11 1,71% 0,4% -2,0% 0,1% -0,5% -2,2% -2,6% -1,7% -4,7% -0,5% -0,2% 0,5% -1,2% 2,94% 12 2,75% 0,5% -0,7% 0,8% 0,5% -1,4% -1,2% -1,0% -4,1% 0,0% 0,2% 0,3% -0,5% 3,30% medium 13 2,57% 0,5% 0,2% 1,6% 1,1% -1,4% -1,4% -1,0% -3,4% 0,6% -0,3% 0,8% -0,2% 2,81% 14 1,83% 1,7% 0,5% 2,3% 2,0% -0,2% -0,6% -0,5% -3,1% 0,1% 0,5% 1,1% 0,3% 1,49% 15 2,96% 1,2% 1,1% 3,0% 1,6% 0,1% -0,2% -0,3% -1,7% 1,2% 1,5% 1,2% 0,8% 2,17% average 2,37% 0,9% -0,2% 1,6% 0,9% -1,0% -1,2% -0,9% -3,4% 0,3% 0,4% 0,8% -0,2% 2,54% 16 2,24% 0,5% -2,0% 0,9% 0,1% -2,2% -1,2% -1,1% -4,4% 0,6% 0,3% 1,3% -0,7% 2,91% 17 2,61% 1,0% 0,2% 1,7% 0,9% -1,1% -1,0% -0,9% -4,0% 0,9% -0,2% 0,6% -0,2% 2,78% 18 2,27% 1,9% 0,7% 2,3% 1,6% -0,6% -0,4% -1,2% -3,7% 0,2% 0,6% 0,9% 0,2% 2,05% 19 2,23% 1,9% 0,9% 2,4% 2,0% -0,7% -0,6% -1,2% -3,0% 0,9% 2,0% 1,5% 0,6% 1,67% 20 2,75% 2,3% 1,5% 3,3% 1,9% 0,0% 0,1% 0,0% -2,0% 1,2% 2,0% 1,3% 1,1% 1,70% average 2,42% 1,5% 0,2% 2,1% 1,3% -0,9% -0,6% -0,9% -3,4% 0,8% 0,9% 1,1% 0,2% 2,22% 21 0,36% 1,3% -0,8% 2,0% 1,3% 0,0% -0,8% -0,7% -3,1% 1,3% 1,5% 2,1% 0,4% -0,01% 22 0,68% 0,7% 0,7% 1,7% 1,1% -0,6% -1,3% -0,6% -3,4% 1,3% 1,5% 1,5% 0,2% 0,44% Big 23 1,04% 0,5% 0,5% 2,7% 1,6% 0,2% 0,1% -1,6% -5,1% 3,0% 2,4% 1,7% 0,6% 0,49% 24 2,21% 1,0% 0,5% 2,5% 1,2% -0,4% 0,8% -1,0% -3,7% 3,3% 2,4% 1,1% 0,7% 1,50% 25 4,04% 1,7% 0,8% 1,4% 1,8% -0,7% 1,4% 0,2% -1,4% 2,8% 4,0% 1,0% 1,2% 2,87% average 1,67% 1,0% 0,3% 2,1% 1,4% -0,3% 0,0% -0,7% -3,3% 2,3% 2,4% 1,5% 0,6% 1,06% Jan Feb-Dec
Independent Factors SmB small3 0,83% -0,51%
big3 0,92% 0,53%
-0,08% -1,04%
HmL hi2 1,31% 0,68%
lo2 0,62% -0,59%
0,69% 1,27%
This table shows the value weighted returns of the 25 portfolios sorted by size and B/M ratio for the different months. The values are monthly averages for the 192 month period from 1990-2005. Below are the return values for the independent returns for the Size (SMB) and Book-to-Market (HmL) factors for January and February till December. SmB is the portfolio formed by the difference between simple average return of the three small market value (MV) portfolios and the three Big (MV) portfolios. HmL is the difference between the simple average return of the two High book-to-market ratio (BM) portfolios and the two low BM portfolios.
