Data Sources and Universes
The data sources are the merged CRSP/Compustat for US simulations, merged Datastream/Worldscope
for Global Developed and Emerging markets. The “risk free” rate is defined as the yield of 3-Month US
Treasury Bills as published by the St. Louis Federal Reserve Bank.
Global developed market includes Australia, Austria, Belgium, Canada, Denmark, Finland, France,
Germany, Greece, Hong Kong, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway,
Portugal, Singapore, Spain, Sweden, Switzerland, United Kingdom, and United States.
Global emerging market includes Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt,
Hungary, India, Indonesia, Israel, Korea (South), Malaysia, Morocco, Mexico, Pakistan, Peru, Philippines,
Poland, Russian Federation, South Africa, Thailand, Turkey, and Taiwan.
Global Factors
2x3 Size and Value Portfolios
Size and Value portfolios are reconstituted annually at the end of June. All listed stocks in the specified
universe are partitioned into 2 size portfolios (Small and Big) and 3 value portfolios (Value, Neutral, and
Growth), ranked by Market Value (ME) and Book-to-Market Value ratio (BE/ME). The six portfolios are
the intersections of the size and the value portfolios. Constituents of each of the six portfolios (Small
Value, Small Neutral, Small Growth, Big Value, Big Neutral, and Big Growth) are weighted by their
Market Value.
For the reconstitution in June of year T, only companies that have reported financial information for
fiscal year T-1 and T-2, and with active market data, are included.
ME is the reported market capitalization without free-float adjustment at the time of reconstitution.
BE/ME for June of year T is defined as the book value of common equity for fiscal year that ends in year
T-1, divided by the market value at the end of year T-1.
The top 20 percentile of companies ranked by ME are partitioned into Big, the bottom 80 percentile of
companies ranked by ME are partitioned into Small; The top 30 percentile of companies ranked by
BE/ME are partitioned into Value, the bottom 30 percentile of companies ranked by BE/ME are
partitioned into Growth, the middle 40 percentile of companies ranked by BE/ME are partitioned into
Neutral.
30th BE/ME
percentile
70th BE/ME
percentile
Big Growth
Big Neutral
Big Value
Small Growth
Small Neutral
Small Value
80th ME
percentile
2x3 Size and Momentum Portfolios
Size and Momentum portfolios are reconstituted monthly. All listed listed stocks in the specified
universe are partitioned into 2 size portfolios (Small and Big) and 3 momentum portfolios (Up, Medium
or Down companies), ranked by Market Value (ME) and 1-year momentum (PR1YR). Constituents of
each of the size portfolios (Small Up, Small Medium, Small Down, Big Up, Big Medium, Big Down) are
weighted by their Market Value.
For the reconstitution in June of year T, only companies with active market data for the last 12 months
are included.
ME is the reported market capitalization without free-float adjustment at the time of reconstitution.
PR1YR is defined as cumulative total return for the last one year excluding the last month (month t-12 to
t-2).
The top 20 percentile of companies ranked by ME are partitioned into Big, the bottom 80 percentile of
companies ranked by ME are partitioned into Small; The top 30 percentile of companies ranked by
PR1YR are partitioned into Up, the bottom 30 percentile of companies ranked by PR1YR are partitioned
into Down, the middle 40 percentile of companies ranked by PR1YR are partitioned into Medium.
30th PR1YR
percentile
70th PR1YR
percentile
Big Down
Big Medium
Big Up
Small Down
Small Medium
Small Up
80th ME
percentile
Market, Size, Value, Momentum Factor Returns
The Market Factor (Mkt-RF) is the total return of a market portfolio, in excess of the risk-free rate. The
market portfolio is the Market Value weighted portfolio of all listed stocks in the specified universe.
The Size Factor (SMB) is defined as the average of total returns of the three Small portfolios, minus the
average of the total returns of the three Big portfolios.
1
𝑆𝑀𝐵 = (𝑆𝑚𝑎𝑙𝑙 𝑉𝑎𝑙𝑢𝑒 + 𝑆𝑚𝑎𝑙𝑙 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝑆𝑚𝑎𝑙𝑙 𝐺𝑟𝑜𝑤𝑡ℎ)
3
1
− (𝐵𝑖𝑔 𝑉𝑎𝑙𝑢𝑒 + 𝐵𝑖𝑔 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝐵𝑖𝑔 𝐺𝑟𝑜𝑤𝑡ℎ)
3
The Value Factor (HML) is defined as the average of the total returns of the Big and Small Value
portfolios, minus the average of the total returns of the Big and Small Growth portfolios.
1
1
𝐻𝑀𝐿 = (𝐵𝑖𝑔 𝑉𝑎𝑙𝑢𝑒 + 𝑆𝑚𝑎𝑙𝑙 𝑉𝑎𝑙𝑢𝑒) − (𝐵𝑖𝑔 𝐺𝑟𝑜𝑤𝑡ℎ + 𝑆𝑚𝑎𝑙𝑙 𝐺𝑟𝑜𝑤𝑡ℎ)
2
2
The Momentum Factor (Mom) is defined as the average of the total returns of the Big and Small Up
portfolios, minus the average of the total returns of the Big and Small Down portfolios.
1
1
𝑀𝑜𝑚 = (𝐵𝑖𝑔 𝑈𝑝 + 𝑆𝑚𝑎𝑙𝑙 𝑈𝑝) − (𝐵𝑖𝑔 𝐷𝑜𝑤𝑛 + 𝑆𝑚𝑎𝑙𝑙 𝐷𝑜𝑤𝑛)
2
2
Reference:
Carhart, Mark M. 1997. "On Persistence in Mutual Fund Performance." Journal of Finance, vol. 52, no.
1 (March): 57-82.
Fama, Eugene F., and Kenneth R. French. 1993. "Common Risk Factors in the Returns on Stocks and
Bonds." Journal of Financial Economics, vol. 33, no. 1 (Feburary): 3-56