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Construction:
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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
rate.
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 region.
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
stock portfolios,
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
B/M portfolios,
HML = 1/2 (Small Value + Big Value)
– 1/2 (Small Growth + Big Growth).
The 2x3 sorts on size and lagged momentum to construct WML are similar, but
the size-momentum portfolios are formed monthly. For portfolios formed at
the end of month t–1, the lagged momentum return is a stock's cumulative
return for month t–12 to month t–2. The momentum breakpoints for a region
are the 30th and 70th percentiles of the lagged momentum returns of the big
stocks of the region.
The developed portfolios use developed size breaks, but we use the momentum
breakpoints for the four regions to allocate the stocks of these regions to
the developed portfolios. The independent 2x3 sorts on size and momentum
produce six value-weight portfolios, SL, SN, SW, BL, BN, and BW, where S
and B indicate small and big and L, N, and W indicate losers, neutral, and
winners (bottom 30%, middle 40%, and top 30%).
WML is the equal-weight average of the returns for the two winner
portfolios for a region minus the average of the returns for the two loser
portfolios,
WML = 1/2 (Small High + Big High)
– 1/2 (Small Low + Big Low).
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