# FF5.monthly: Fama-French 5 Factors Data Set In JustinMShea/ExpectedReturns: Reproduction of Key Functionality from Antti Ilmanen's Expected Returns

## Description

FF4.monthly is the Fama-French five-factor monthly data series on U.S. stock market from 1963-07 to 2020-06. The data set also includes the risk-free rate on 1-month U.S. T-Bill during the same period.

## Usage

 1 data("FF5.monthly") 

## Format

An xts object containing observations of Fama-French Factors on U.S. Stock Market.

• Frequency: Monthly.

• Date Range: 1963-07 to 2020-06.

• Data updated: 2020-08-19 21:56:26 CEST.

• RF: A numeric. The risk-free rate on 1-month U.S. T-Bill. See 'RF variable' section below.

• MKT.RF: A numeric. The market portfolio proxy return net of risk-free rate factor. See 'MKT.RF factor' section below.

• SMB: A numeric. The "Small Minus Big" factor. See 'SMB factor' section below.

• HML: A numeric. The "High Minus Low" factor. See 'HML factor' section below.

• RMW: A numeric. The "Robust Minus Weak" factor. See 'RMW factor' section below.

• CMA: A numeric. The "Conservative Minus Aggressive" factor. See 'CMA factor' section below.

The object consists of 684 rows and 6 columns.

## Details

In addition to column definitions, this section contains a glimpse into factors construction and their underlying variables.

## Fama-French Five Factors Construction

The Fama-French factors are constructed using the six value-weight portfolios formed on size, the six value-weight portfolios formed on size and operating profitability, and the six value-weight portfolios formed on size and investment.

## Market Equity Variable

Market equity, also referred to as size and denoted ME, is a firms' financial variable calculated as the product of price times shares outstanding. The stock price is from CRSP, whereas shares outstanding are from Compustat (if available) or CRSP.

## BE variable

Book equity, denoted BE, is a firms' financial variable that Fama-French construct from Compustat data or is collected from the Moody's Industrial, Financial, and Utilities manuals. BE is the book value of stockholders' equity, plus balance sheet deferred taxes and investment tax credit (if available), minus the book value of preferred stock. Depending on availability, they use the redemption, liquidation, or par value (in that order) to estimate the book value of preferred stock. Stockholders' equity could be reported by Moody's or Compustat, otherwise the authors measure stockholders' equity as the book value of common equity plus the par value of preferred stock, or the book value of assets minus total liabilities (in that order).

## BM ratio

The book-to-market ratio of a firm is defined as the ratio between its market equity and book equity:

BM = BE/ME

## Six Size/Book-to-market Portfolios

The portfolios, which are constructed at the end of each June, are the intersections of 2 portfolios formed on size (ME) and 3 portfolios formed on the BM.

The size breakpoints for year t is the median NYSE market equity at the end of June of year t (see K. R. French's Detail for ME Breakpoints).

The BM for June of year t is the book equity for the last fiscal year end in t-1 divided by ME for December of t-1. The BM breakpoints are the 30th and 70th NYSE percentiles (see K. R. French's Detail for BM Breakpoints).

## Operating Profitability Ratio

The operating profitability ratio (OP) used to form portfolios in June of year t is annual revenues minus cost of goods sold, interest expense, and selling, general, and administrative expense divided by the sum of book equity and minority interest for the last fiscal year ending in t-1.

## Six Size/Operating Profitability Portfolios

The portfolios, which are constructed at the end of each June, are the intersections of 2 portfolios formed on size (market equity, ME) and 3 portfolios formed on profitability (OP). The size breakpoint for year t is the median NYSE market equity at the end of June of year t (see K. R. French's Detail for ME Breakpoints). OP for June of year t is annual revenues minus cost of goods sold, interest expense, and selling, general, and administrative expenses divided by book equity for the last fiscal year end in t-1. The OP breakpoints are the 30th and 70th NYSE percentiles (see K. R. French's Detail for Operating Profitability Breakpoints).

## Investment variable

The investment ratio used to form portfolios in June of year t is 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.

## Six size/investment portfolios

These portfolios are constructed at the end of each June and represent the intersections of 2 portfolios formed on market equity, denoted ME, and 3 portfolios formed on investment (INV). The size breakpoint for year t is the median NYSE market equity at the end of June of year t (see K. R. French's Detail for ME Breakpoints). Investment is 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. The investment ratio breakpoints are the 30th and 70th NYSE percentiles (see K. R. French's Detail for Investment Breakpoints).

## RF variable

The RF variable refers to the risk-free rate. It depends on the period been considered and on the country. For example, for U.S. monthly data series is the one month T-Bill return. The RF data series distributed by K. R. French with the Fama-French factors data are usually obtained from Ibbotson Associates Inc. (Morningstar).

## MKT.RF factor

With MKT.RF we indicate the excess return on the market portfolio return proxy, net of the risk-free rate RF calculated on the same period t, that is

MKT.RF = MKT - RF

or, as it is also commonly denoted in the literature,

MKT.RF = R_{m} - R_{f}

MKT is obtained by Fama-French as the value-weight return of all CRSP firms that are incorporated in the U.S. and listed on the NYSE, AMEX, or NASDAQ securities markets. These firms must have a CRSP share code of 10 or 11, good shares and price data, at the beginning of the period.

## SMB factor

The SMB (Small Minus Big) factor return variable is the average return on three (nine) small portfolios minus the average return on three (nine) big portfolios. Where the number (three or nine) and type (small or big) of portfolios in factors construction depends on whether the model being considered is the Fama-French's Three-factor model or the Fama-French's Five-factor model, respectively. In formulas, for the Three-factor model we express the SMB factor as

SMB = \frac{1}{3}[(Small Value + Small Neutral + Small Growth) - (Big Value + Big Neutral + Big Growth)]

For the Five-factor model the process is analogous, except that in this case an SMB factor has to be built for each one of the three sets of portfolios based on specific firms' financial fundamentals. Once that is accomplished, their weighted average is taken. We thus obtain

SMB = \frac{1}{3}[SMB_{(B/M)} + SMB_{(OP)} + SMB_{(INV)}]

## HML factor

The HML (High Minus Low) factor return variable is the average return on the two value portfolios minus the average return on the two growth portfolios. That is,

HML = \frac{1}{2}[(Small Value + Big Value) - (Small Growth + Big Growth)]

## RMW factor

The RMW (Robust Minus Weak) is the average return on the two robust operating profitability portfolios minus the average return on the two weak operating profitability portfolios,

RMW = \frac{1}{2}[(Small Robust + Big Robust) - (Small Weak + Big Weak)]

## CMA factor

The CMA (Conservative Minus Aggressive) is the average return on the two conservative investment portfolios minus the average return on the two aggressive investment portfolios,

CMA = \frac{1}{2}[(Small Conservative + Big Conservative) - (Small Aggressive + Big Aggressive)]

## Potentially Missing Data

In the Fama-Franch factors data series missing data are indicated by -99.0, -99.99 or -999. Which value is actually used really depends by the context and the data set at hand, we recommend looking any of those values with suspicion, especially for real-world business use cases when even one basis point count.

## Underlying Data Providers

Most of the Fama-French factor data series are constructed from data provided by CRSP/Compustat. Remarkably, these include all data regarding stock prices and firms' fundamentals. In particular, see Changes in CRSP Data, where Prof. K. R. French explains which data changes from the database have affected the data series constructed and used in their research.

There are many other providers involved, examples are Bloomberg, Ibbotson Associates Inc., Morgan Stanley Capital International, Moody's. They are mentioned at the occurence.

All the data series downloaded from Prof. Kenneth R. French's online data library at https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html are under the most recent (c) Kenneth R. French.

## References

Fama, Eugene F and French, Kenneth R (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics. Fama, Eugene F and French, Kenneth R (2015). A five-factor asset pricing model. Journal of Financial Economics.

Davis, Fama, and French (2000). Characteristics, Covariances, and Average Returns: 1929-1997. Journal of Finance.

The series was generated with GetFactors().
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