Factor Definitions:
All factor data listed on the site comes from Professor Kenneth French’s data library. All of the calculators on this site are long only, reflecting a buy and hold strategy. Although the academic factors are typically defined as long – short (buying top ranked firms and selling poorly ranked firms), short selling isn’t practical for most investors. The factors used on this site are defined as:
- Market Factor: The value-weighted return of all firms.[1] In the US this would be represented by the Vanguard Total Stock Market Fund.
- Value Factor: The value-weighted return of the top 30% of firms based on the ratio of book value to market value.[2] In other words, buying the cheapest firms based on price compared to book value (assets less liabilities on a company’s balance sheet).
- Profitability Factor: The value-weighted return of the top 30% of firms based on the ratio of operating profits to book value.[3] In other words, buying the firms with the highest levels of operating profitability compared to book value.
- Investment Factor: The value-weighted return of the bottom 30% of firms based on asset growth.[4] In other words, buying the firms that are not aggressively investing.
- Momentum Factor: The value-weighted return of the top 30% of firms based on their price change over the last year.[5] In other words, buying companies that have increased in price.
- Small Factor: The value-weighted return of the bottom 30% of firms based on market equity.[6] In other words, buying the smallest firms. When the Small Factor is combined with another factor, Small Value for example, the Small Factor is defined as the bottom 50% of firms based on market equity.
- Combination Factors: When factors such as Value and Profitability are combined, only the firms that rank within the top 30% of both factors are selected. The returns are then value-weighted.
Other Data Sources:
Although we use Professor French’s data set where available, we use other data sources for earlier periods, other countries, and for other asset classes like government bonds, corporate bonds, and gold. Here is an overview of the data sources:
- JST Macrohistory Database: This is the primary source of international market and bond returns from 1871 – 1974. Exchange rate and inflation data are used to calculate returns for international currencies for the full period starting in 1871.[7]
- Damodaran: NYU Professor Aswath Damodaran’s data set on US 10-year Treasury Bonds and US Corporate Bonds is used starting in 1928.[8]
- Piketty: Paris University Professor Thomas Piketty’s data set on gold prices is used from 1833 – 2011.[9] His analysis is continued using Kitco data after 2011.[10]
- Shiller: Yale Professor and Nobel Laureate Robert Schiller’s data on US inflation for the full period starting 1871 and US market data is used for the 1871 – 1926 period.[11]
- Swinkels: Erasmus University Professor Laurens Swinkels data on monthly bond returns is used for Germany starting in 1972, Japan starting in 1974, Australia starting in 1969, Norway starting in 1921, and Sweden starting in 1920.[12]
- DMS: Proffesor’s Dimson, Marsh, and Staunton book Triumph of the Optimists contains real annual return data by decade that is used to fill in missing data from the JST Macrohistory database. Specifics are below:
- Japanese Market data from 1946-1947 is missing. I’ve plugged in a return for 1946 to match DMS Table 26-2 real annualized return for the 1940-1949 period.
- Belgium Government Bond data from 1914 – 1919 is missing. I’ve plugged in a return for 1919 to match DMS Table 19-2 real annualized return for the 1910-1919 period.
- Switzerland Government Bond data for 1915 is missing. I’ve plugged in a return for 1915 to match DMS Table 31-2 real annualized return for the 1910-1919 period.
- Germany Government Bond data from 1944 – 1948 is missing. I’ve plugged in a return for 1945 to match DMS Table 23-2 real annualized return for the 1940-1949 period.
- Denmark Government Bond data for 1915 is missing. I’ve plugged in a return for 1915 to match DMS Table 21-2 for the 1910-1919 period.
- Spain Government Bond data from 1937 – 1940 is missing. I’ve plugged in a return for 1939 and 1940 to match DMS Table 29-2 real annualized return for the 1930-1949 period.
- Simba: This is general historical data from various sources around the web, maintained by the Bogleheads community.[13] We use this to fill in gaps for the historical International total market returns along with US and International government bond returns.
Methodology:
A fine wine’s taste varies by year or vintage, primarily due to the weather that affects the vines throughout the growing season. Similarly, an investor’s return varies due to the timing of their investment and the weather of the business cycle.
Rather than calculate returns from the earliest starting point only, this website calculates returns based on every starting month, or vintage, in the available period. This allows a better understanding of market risks and investment performance over time.
For every month, portfolio returns are calculated using the allocation weights given. If you have a 50% allocation to the US Market and a 50% allocation to US Government Bonds, with returns of 2% and 0% respectively, the return for the month would be 1%. You can properly think about this as monthly rebalancing.
Note that monthly data is used where available. If monthly data is unavailable, monthly returns are calculated from annual data, assuming a constant return over the year. Returns do not include any transaction costs or expenses.
Portfolio returns are calculated in nominal US dollar returns and if necessary converted to local currency using the change in local/USD exchange rates from month to month. If real returns are selected local currency returns are then converted to real returns using the change in the CPI index from month to month.
Global returns are not market cap weighted and are instead calculated using the simple, unweighted average of nominal US dollar returns for all countries with available data. If global currency is selected nominal US dollar returns are converted to a global currency using the average of the changes in all countries local/USD exchange rates from month to month. If real returns are selected for global currency, the nominal returns are converted to real returns using the average of all countries change in the CPI index from month to month.
[1] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_5_factors_2x3.html
[2] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_form_btm.html
[3] Operating Profitability is defined as revenues minus cost of goods sold, interest expense, and selling, general, and administrative expenses. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_port_form_op.html
[4] Asset growth is defined as “the change in total assets from the fiscal year ending in year t-2 to the fiscal year ending in t-1, divided by t-2 total assets at the end of each June”. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_port_form_inv.html
[5] The most recent month is excluded as stocks tend to mean revert in the short term. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_10_port_form_pr_12_2.html
[6] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_port_form_sz.html
[7] https://www.macrohistory.net/database/
[8] https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html
[9] http://piketty.pse.ens.fr/files/capital21c/xls/RawDataFiles/GoldPrices17922012.pdf
[10] https://www.kitco.com/scripts/hist_charts/yearly_graphs.plx?au2010=on&au2011=on&au2012=on&au2013=on&au2014=on&au2015=on&au2016=on&au2017=on&au2018=on&au2019=on&au2020=on&au2021=on&submitauD=View+Data. Data same as Piketty used.
[11] http://www.econ.yale.edu/~shiller/data.htm
[12] https://datarepository.eur.nl/articles/dataset/Data_Treasury_Bond_Return_Data_Starting_in_1962/8152748
[13] https://www.bogleheads.org/wiki/Simba%27s_backtesting_spreadsheet