Things have changed a bit since then, so I figured I would update his info with what I've found. If you haven't done any regressions yourself yet, you might want to get some practice on the US side before reading on. Here's a great tutorial to start with. I suggest starting by running a few US funds, since the factors are much easier to come up with, so there are less ways to make a mistake. OK, moving on:
Basically, the difficulty with EAFE is that Prof. French gives us research factors for the US, and more recently for several regions: Global, North America, Europe, Asia-Pacific ex-Japan, and Japan. But if you want EAFE, it's problematic trying to derive it from the above. That's because the size and value thresholds for Europe, Asia, and Japan are different and vary with respect to each other, so you can't simply do a market-cap-weighted average or some such to get EAFE factors.
So, what do we do instead? You can get the Mkt and HmL factors from Kenneth French's website:
Robert T wrote:For Non-US Developed Market - Mkt factor:
- I use the Mkt data from the Ind_all file under Intl. Index Portfolios from from Ken French’s website
(Among other places, you can get the risk-free rate from French's website as well. They're in the list of US Fama-French factors, or in the developed market factors.)Robert T wrote:For Non-US Development Mkt - Risk Free Rate [Rf]:
- I use US T-bills as the risk free rate for all international FF3F regressions as did Sinquefield in this article and Fama-French in this one.
The tricky one is SmB:
I wasn't able to access the S&P citigroup data via Robert's link, and couldn't find it elsewhere on their site; I assume it is no longer public, although if I'm wrong and someone can point me to it, that'd be great. (Edit: found it still up on their old site, but apparently it's going to be pay-only as of the end of this month. Anyway, the MSCI method works fine.)Robert T wrote:For Non-US Developed Market - SmB factor
- We're on our own:
Here are two options: From the MSCI website just use EAFE small cap index minus EAFE or from the S&P/citigroup website use Small (less than 1 billon) minus Big (greate than 5 billion). The latter has a longer total return series of monthly returns – back to 1989. The magnitude of the small cap premium was similar using the two measures (larger with the S&P/citigroup data) and they have a fairly high correlation coefficient (0.91).
Fortunately, the MSCI method worked pretty well. The Fama-French methodology for calculating SmB is to take the returns of the smallest 10% of the given region by market cap and subtract the returns of the largest 90%. We can't do exactly that, but we can come close.
The MSCI EAFE Std index (the one tracked by VEA and EFA) covers the top 84% by market cap, and the small-cap index (tracked by SCZ) covers the next 14%. (There is now a micro-cap index as well, which will allow a slight improvement on this technique in the future, but it only has a few years' data right now.) So if you take the returns of the small-cap index minus those of the EAFE index, you get something close to the definition of SmB.
You can get the MSCI index performance data here.
You'll want to choose Developed Markets, USD. For size, you want the standard, which will show up in the list as "EAFE", and the small-cap, which will be "EAFE SC". Run the search and click on the name in the list. When the chart comes up, set the term to Full History, the Index Level to 'gross' (which means total returns including dividends, gross of withholding taxes,) and the frequency to monthly. Update, then click 'Download Data' at the top.
Once you've done that for both the standard and small indices, you can crunch SmB. For each month, you want to calculate the change from the previous month and express it as a percentage. ie (C/P - 1)*100, where C=current month value and P=previous month value. Do that for the 'small' and 'big' indices, then subtract the values in your big list from the ones in your small list. The result is your SmB!
Note: The MSCI small index has gross returns data back to Dec. 2000. If you want to go earlier than that you can set it to 'price' to get earlier values instead. It's not technically perfect, but we're already saying 14% = 10%, so whatever, right? I actually did it both ways to check, and the SmB results for the two sets had a correllation of 0.998 - so if you want to use price it doesn't really matter.
These are the correlations between the SmB calculated as above and the various global SmB factors on Prof. French's site, since Jan. 2001:
Code: Select all
Global Europe Asia-Pac Ex-J Japan North America
0.845 0.816 0.428 0.570 0.370
So, here's what I came up with:
Code: Select all
Mkt-Rf HmL SmB RF
199007 1.52 -0.15 0.68
199008 -10.94 -1.02 0.66
199009 -14.42 1.87 0.60
199010 15.63 -3.77 0.68
199011 -6.62 1.00 0.57
199012 0.79 -2.23 0.60
199101 2.72 -0.07 0.52
199102 9.48 5.37 0.48
199103 -5.69 -0.66 0.44
199104 1.10 -0.10 0.53
199105 -1.00 -0.57 0.47
199106 -7.33 0.17 0.42
199107 4.45 1.40 0.49
199108 -2.57 -0.99 0.46
199109 5.05 1.13 0.46
199110 1.33 -3.02 0.42
199111 -4.76 -2.12 0.39
199112 4.70 -1.04 0.38
199201 -3.03 3.95 0.34
199202 -3.61 0.31 0.28
199203 -6.79 1.12 0.34
199204 -0.03 7.25 0.32
199205 6.28 -0.88 0.28
199206 -4.78 0.10 0.32
199207 -2.96 -3.82 0.31
199208 6.05 -5.59 0.26
199209 -2.69 0.30 0.26
199210 -5.80 0.24 0.23
199211 1.11 -0.45 0.23
199212 0.14 0.91 0.28
199301 -0.02 3.38 1.869 0.23
199302 2.85 0.27 1.459 0.22
199303 9.57 5.72 1.804 0.25
199304 8.79 3.61 2.185 0.24
199305 2.33 -1.60 4.530 0.22
199306 -3.36 -1.27 -3.848 0.25
199307 4.48 1.43 0.813 0.24
199308 5.03 0.86 0.351 0.25
199309 -3.13 0.50 0.019 0.26
199310 2.15 -0.23 -3.384 0.22
199311 -8.65 1.62 -1.241 0.25
199312 6.56 3.53 1.450 0.23
199401 9.90 3.21 2.745 0.25
199402 -1.08 1.68 2.294 0.21
199403 -3.70 1.79 2.170 0.27
199404 3.59 0.77 0.094 0.27
199405 -1.06 1.79 -0.573 0.32
199406 1.55 1.03 0.757 0.31
199407 0.45 -0.51 -0.654 0.28
199408 1.75 -0.19 -1.246 0.37
199409 -3.51 0.28 -0.326 0.37
199410 3.28 0.65 -1.788 0.38
199411 -5.64 -0.71 -2.048 0.37
199412 0.63 -1.06 0.796 0.44
199501 -4.44 -0.04 0.133 0.42
199502 -0.78 -0.49 -0.906 0.40
199503 5.20 -0.57 -4.033 0.46
199504 3.80 -2.06 -1.397 0.44
199505 -1.84 0.70 -0.984 0.54
199506 -1.99 0.30 -0.335 0.47
199507 5.36 -0.46 0.322 0.45
199508 -3.55 -0.08 1.133 0.47
199509 0.65 -0.90 -2.092 0.43
199510 -2.13 -0.15 -1.181 0.47
199511 1.83 0.28 -1.424 0.42
199512 3.37 0.85 -0.485 0.49
199601 -0.14 1.79 2.737 0.43
199602 0.17 0.89 0.726 0.39
199603 1.52 -0.72 -0.010 0.39
199604 2.43 1.01 2.467 0.46
199605 -1.48 -0.73 -0.064 0.42
199606 0.16 -0.61 -0.559 0.40
199607 -3.37 0.23 -2.481 0.45
199608 -0.49 0.22 0.250 0.41
199609 2.56 -0.17 -2.057 0.44
199610 -1.75 -0.27 -0.628 0.42
199611 3.63 2.57 -2.566 0.41
199612 -1.46 1.37 -2.035 0.46
199701 -4.22 0.94 1.608 0.45
199702 1.17 0.13 0.362 0.39
199703 0.22 -0.80 -2.752 0.43
199704 0.05 -2.62 -3.732 0.43
199705 6.71 0.99 1.204 0.49
199706 5.00 -1.87 -3.588 0.37
199707 1.30 0.10 -5.020 0.43
199708 -7.53 1.77 1.202 0.41
199709 5.17 -1.78 -7.586 0.44
199710 -7.61 3.15 2.269 0.42
199711 -1.40 -4.04 -5.823 0.39
199712 -0.07 -0.44 -6.573 0.48
199801 4.47 6.91 1.807 0.43
199802 5.97 4.37 2.673 0.39
199803 2.66 1.64 -0.747 0.39
199804 0.30 -0.50 -0.864 0.43
199805 -0.15 -0.24 0.930 0.40
199806 -0.16 -2.77 -4.617 0.41
199807 0.56 -0.62 -2.262 0.40
199808 -12.44 -3.04 -0.799 0.43
199809 -2.83 -1.99 -1.394 0.46
199810 9.79 -0.79 -2.270 0.32
199811 4.75 0.23 -0.218 0.31
199812 3.27 -2.44 -3.438 0.38
199901 -0.60 -1.58 -0.846 0.35
199902 -2.81 2.51 1.240 0.35
199903 3.90 5.98 1.363 0.43
199904 4.12 7.63 3.500 0.37
199905 -4.89 -0.93 1.636 0.34
199906 3.42 2.99 1.535 0.40
199907 2.96 2.44 0.203 0.38
199908 0.87 2.12 1.874 0.39
199909 0.71 -0.34 -1.205 0.39
199910 3.60 -3.86 -5.004 0.39
199911 4.38 -7.91 -2.826 0.36
199912 8.86 -5.39 -7.951 0.44
200001 -6.98 0.72 6.564 0.41
200002 2.44 -12.76 -0.138 0.43
200003 3.17 6.85 -1.409 0.47
200004 -5.89 3.82 -2.158 0.46
200005 -3.66 8.29 2.335 0.50
200006 3.64 3.60 4.994 0.40
200007 -4.55 1.55 -2.002 0.48
200008 0.88 -0.78 3.958 0.50
200009 -5.11 3.53 -0.780 0.51
200010 -3.40 3.27 -4.492 0.56
200011 -3.59 7.59 3.553 0.51
200012 2.55 3.20 -3.120 0.50
200101 -0.18 3.25 3.061 0.54
200102 -7.92 4.67 5.499 0.38
200103 -7.57 0.15 -0.926 0.44
200104 7.02 -0.06 1.575 0.39
200105 -3.71 -0.03 3.294 0.32
200106 -4.28 0.31 1.124 0.28
200107 -2.50 1.50 -2.292 0.30
200108 -2.82 2.99 3.606 0.31
200109 -10.35 -4.85 -3.237 0.28
200110 2.78 0.84 2.560 0.22
200111 3.35 1.46 0.168 0.17
200112 0.06 -0.68 -3.050 0.15
200201 -5.04 -1.71 2.958 0.14
200202 0.64 -1.52 0.962 0.13
200203 5.66 1.40 1.195 0.13
200204 0.61 -0.61 2.946 0.15
200205 1.42 4.09 3.128 0.14
200206 -4.21 -2.75 0.235 0.13
200207 -9.09 1.62 2.154 0.15
200208 -0.53 0.19 -1.073 0.14
200209 -10.70 -2.89 2.947 0.14
200210 5.35 -1.07 -6.617 0.14
200211 4.54 3.82 -1.669 0.12
200212 -3.14 0.31 1.498 0.11
200301 -3.82 3.61 2.755 0.10
200302 -2.37 -0.15 1.493 0.09
200303 -1.96 -1.94 1.377 0.10
200304 9.56 3.53 -0.425 0.10
200305 6.34 4.81 2.466 0.09
200306 2.26 1.61 2.894 0.10
200307 2.43 3.64 0.678 0.07
200308 2.41 2.04 4.177 0.07
200309 3.45 3.44 2.902 0.08
200310 6.26 3.90 1.749 0.07
200311 2.08 -0.09 -2.644 0.07
200312 7.51 0.71 -1.716 0.08
200401 1.71 2.07 3.663 0.07
200402 2.36 1.30 0.524 0.06
200403 0.52 0.68 3.543 0.09
200404 -2.39 0.51 -0.821 0.08
200405 0.12 0.17 -1.993 0.06
200406 2.01 1.44 3.186 0.08
200407 -3.25 0.81 -1.278 0.10
200408 0.14 0.87 0.265 0.11
200409 2.42 1.24 -0.235 0.11
200410 3.39 0.64 0.346 0.11
200411 6.74 1.62 1.114 0.15
200412 4.46 0.90 0.608 0.16
200501 -1.57 1.10 3.805 0.16
200502 3.88 0.45 -0.316 0.16
200503 -2.76 0.94 0.895 0.21
200504 -2.71 -2.00 -0.060 0.21
200505 -0.71 0.08 -0.102 0.24
200506 1.57 -0.42 1.350 0.23
200507 2.97 1.87 1.451 0.24
200508 2.73 0.08 0.353 0.30
200509 3.37 -0.17 -0.341 0.29
200510 -2.61 1.62 -0.349 0.27
200511 1.80 -1.10 0.757 0.31
200512 4.82 -1.09 3.345 0.32
200601 5.75 -0.34 0.683 0.35
200602 -0.46 3.04 -1.008 0.34
200603 2.94 -0.42 1.520 0.37
200604 4.40 -0.20 -0.461 0.36
200605 -4.85 -0.10 -1.922 0.43
200606 -0.33 -1.08 -2.198 0.40
200607 0.71 1.26 -3.697 0.40
200608 2.14 0.26 0.034 0.42
200609 -0.06 2.06 0.246 0.41
200610 3.63 1.26 -0.226 0.41
200611 2.52 0.65 1.283 0.42
200612 2.97 1.73 0.198 0.40
200701 0.34 1.11 1.410 0.44
200702 0.50 -0.51 0.860 0.38
200703 2.42 -0.77 0.660 0.43
200704 3.68 -0.04 -0.763 0.44
200705 1.42 0.72 -1.122 0.41
200706 -0.06 -0.53 -0.339 0.40
200707 -2.03 -2.26 1.083 0.40
200708 -2.03 -1.15 -3.605 0.42
200709 5.08 -1.73 -4.233 0.32
200710 3.73 0.14 2.302 0.32
200711 -3.92 -3.91 -3.924 0.34
200712 -2.59 1.07 -1.213 0.27
200801 -8.76 1.50 -0.528 0.21
200802 1.77 -2.93 2.798 0.13
200803 -1.40 2.21 0.739 0.17
200804 5.08 -1.20 -3.140 0.18
200805 1.22 -3.91 0.601 0.18
200806 -7.96 -3.73 -0.016 0.17
200807 -3.67 2.59 -1.358 0.15
200808 -4.42 1.02 0.200 0.13
200809 -14.05 3.18 -2.692 0.15
200810 -20.09 -2.03 -3.561 0.08
200811 -5.43 -1.61 0.945 0.03
200812 6.52 -1.01 0.823 0.09
200901 -9.69 -3.18 3.402 0.00
200902 -9.93 -1.93 0.981 0.01
200903 5.82 5.38 0.177 0.02
200904 12.34 17.03 2.477 0.01
200905 12.77 2.62 2.277 0.00
200906 -0.20 -0.41 2.514 0.01
200907 9.03 4.84 -1.501 0.01
200908 4.77 6.01 2.643 0.01
200909 4.16 0.11 1.158 0.01
200910 -1.42 -2.03 -0.520 0.00
200911 2.08 -1.54 -2.013 0.00
200912 1.22 -0.12 -0.689 0.01
201001 -3.66 0.49 3.419 0.00
201002 -0.96 -0.18 -0.711 0.00
201003 6.36 1.37 1.045 0.01
201004 -0.94 1.94 3.479 0.00
201005 -11.22 -1.70 -1.007 0.01
201006 -0.97 -1.41 0.579 0.01
201007 9.57 2.13 -0.853 0.01
201008 -3.31 -1.01 0.208 0.01
201009 10.12 -0.06 1.602 0.01
201010 4.06 0.04 0.249 0.01
201011 -4.88 -1.92 1.223 0.01
201012 8.39 1.89 3.547 0.01
201101 2.21 4.74 -1.578 0.01
201102 3.05 0.20 -1.048 0.01
201103 -1.69 -3.07 2.133 0.01
201104 6.16 -1.09 -0.761 0.00
201105 -2.65 -2.03 0.336 0.00
201106 -1.20 -0.37 -0.408 0.00
201107 -1.34 -2.78 0.535 0.00
201108 -8.89 -3.12 0.808 0.01
201109 -9.72 0.73 -0.835 0.00
201110 8.51 -1.05 -2.446 0.00
201111 -4.69 -1.93 -0.575 0.00
201112 -1.25 0.30 -0.967 0.00
201201 2.925
201202 0.247
201203 0.533
201204 1.409
201205 -0.329
201206 -2.966
201207 -0.759
201208 -0.013
Code: Select all
First, a sanity check:
Factor Loadings
Fund Mkt-Rf SmB HmL Alpha
MSCI EAFE All-Cap Index 1.01 0.03 0.03 -0.50%
t-values 130.40 1.13 1.94 -0.86
R^2 = 0.998 (2007/12 - 2011/12)
Looks pretty good. Bit of negative alpha there, but not statistically significant.
Fund Mkt-Rf SmB HmL Alpha MER
VEA 1.05 -0.34 0.08 -0.10% 0.12%
t-values 39.55 -3.88 1.52 -0.05
R^2 = 0.976 (2007/08 - 2011/12)
(Note VEA tracks the MSCI EAFE 'standard' AKA 'large + mid' index, so the negative size loading is expected.)
Fund Mkt-Rf SmB HmL Alpha MER
SCZ 1.07 0.50 0.05 -0.45% 0.40%
t-values 32.93 4.31 0.84 -0.18
R^2 = 0.973 (2008/02 - 2011/12)
Fund Mkt-Rf SmB HmL Alpha MER
PXF 1.07 -0.30 0.48 -1.23% 0.75%
t-values 33.94 -2.96 7.57 -0.53
R^2 = 0.972 (2007/08 - 2011/12)
Fund Mkt-Rf SmB HmL Alpha MER
EFV 1.04 -0.30 0.35 -3.26% 0.40%
t-values 39.71 -3.86 6.67 -1.95
R^2 = 0.968 (2005/09 - 2011/12)
Now there's some negative alpha...
And again over a shorter time period to compare with PXF:
Fund Mkt-Rf SmB HmL Alpha MER
EFV 1.03 -0.35 0.38 -3.39% 0.40%
t-values 32.62 -3.51 5.96 -1.46
R^2 = 0.969 (2007/08 - 2011/12)
Edit: Forgot DFA!
Factor Loadings
Fund Mkt-Rf SmB HmL Alpha MER
DFA Int'l Vector 1.08 0.22 0.19 -1.03% 0.54%
t-values 34.48 2.16 3.42 -0.49
R^2 = 0.984
(Includes some EM which may throw it off a BIT, but R^2 still very high.)
Edit: Note: these factors are only appropriate for profiling funds that invest across EAFE. For specific country or smaller regional funds (like Europe), it's better to use the regional or country data from Prof. French's site. For World Ex-US or Emerging, Jason Hsu provides factors that should be fairly comparable to the FF ones here: http://www.jasonhsu.org/research-data.html
Edit 2: it should be noted that making the approximations described here does have some effects on the eventual results, which I discuss in a post below.