All returns are in U.S. dollars, include dividends and
capital gains, and are not continuously compounded. Market is the return on
a region's value-weight market portfolio minus the U.S. one month T-bill
To construct the SMB and HML factors, we sort stocks in a region into two
market cap and three book-to-market equity (B/M) groups at the end of each
June. Big stocks are those in the top 90% of June market cap for the
region, and small stocks are those in the bottom 10%. The B/M breakpoints
for a region are the 30th and 70th percentiles of B/M for the big stocks of
The developed portfolios use developed size breaks, but we use the B/M
breakpoints for the four regions to allocate the stocks of these regions to
the developed portfolios.
Similarly, the developed ex us portfolios use developed ex us size breaks and regional B/M breakpoints.
The independent 2x3 sorts on size and B/M produce
six value-weight portfolios, SG, SN, SV, BG, BN, and BV, where S and B
indicate small or big and G, N, and V indicate growth (low B/M), neutral,
and value (high B/M).
SMB is the equal-weight average of the returns on the three small stock
portfolios for the region minus the average of the returns on the three big
SMB = 1/3 (Small Value + Small Neutral + Small Growth)
– 1/3 (Big Value + Big Neutral + Big Growth).
HML is the equal-weight average of the returns for the two high B/M
portfolios for a region minus the average of the returns for the two low
HML = 1/2 (Small Value + Big Value)
– 1/2 (Small Growth + Big Growth).