SY4.monthly: Stambaugh–Yuan Four-Factors Data Set

Description Usage Format Details Stambaugh-Yuan (2017) Factors Construction RF variable MKT.RF factor SMB factor MGMT factor PERF factor Source References Examples


SY4.monthly is the Stambaugh–Yuan (2017) four-factors monthly data series on U.S. stock market from 1963-01 to 2016-12. The data set also includes the risk-free rate on 1-month U.S. T-Bill during the same period.




An xts object containing observations of Stambaugh–Yuan (2017) four-factors data set on U.S. Stock Market, and the risk-free rate on 1-month U.S. T-Bill.

The object consists of 648 rows and 5 columns.


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

Stambaugh-Yuan (2017) Factors Construction

Stambaugh-Yuan (2017) consider 11 anomalies. Anomalies form two clusters:

Authors construct factors based on equally-weighted averages of stocks' anomaly rankings, in the perspective of having a less noisy mispricing measure for each stock across anomalies. In particular, stock's rankings are averaged with respect to the available anomaly measures within each of the two clusters. Thus, each month a stock has two composite mispricing measures, P1 and P2.

Mispricing factors are then constructed by applying a 2x3 sorting procedure, similarly to Fama-French (2015):

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


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 Stambaugh-Yuan (2017) constructed differs from the homonymous factor constructed by means of the standard Fama-French (1993, 2015) methodology widely adopted.

First of all, stocks used to form the size factor in a given month are the stocks not used in forming either of the mispricing factors.

Moreover, in Stambaugh-Yuan (2017) the return on the small-cap leg is the value-weighted portfolio of stocks present in the intersection of both small-cap middle groups when sorting on the P1 and P2 mispricing composite measures. The large-cap leg is the value-weighted portfolio of stocks in the intersection of the large-cap middle groups in the sorts on the two measures. Thus the value of SMB in a given month is the return on the small-cap leg minus the large-cap return.

Computing SMB using stocks only from the middle of their mispricing sorts is meant to reduce the "arbitrage asymmetry bias" while neutralizing mispricing effects.

MGMT factor

The MGMT factor is the arithmetic average of the returns on the two low-P1 portfolios (underpriced stocks) minus the arithmetic average of the returns on the two high-P1 portfolios (overpriced stocks).

PERF factor

The PERF factor is the arithmetic average of the returns on the two low-P2 portfolios (underpriced stocks) minus the arithmetic average of the returns on the two high-P2 portfolios (overpriced stocks).



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.

Stambaugh, R. F. and Yuan, Y. (2017). Mispricing Factors. The Review of Financial Studies.



JustinMShea/ExpectedReturns documentation built on Sept. 27, 2020, 5:41 p.m.