78 The Basics of financial economeTrics
- Beta is not the only factor priced by the market. Several studies have dis-
covered other factors that explain stock returns. These include a price-
earnings factor, a dividend factor, a firm-size factor, and both a firm-size
factor and a book-market factor.
It is the last of these findings that has fostered the empirical search for other
factors using the financial econometric models.^23
Evidence for Multifactor Models
Regression-based tests seeking to dispute the CAPM have helped iden-
tify factors that have been found to be statistically significant in explain-
ing the variation in asset returns. Employing regression analysis, Robert
Jones of Goldman Sachs Asset Management at the time reported fac-
tors he found in the U.S. stock market.^24 For the period 1979 through
1996, he regressed monthly stock returns against the following factors:
“value” factors, “momentum” factors, and risk factors. The value factors
included four ratios: book/market ratio, earnings/price ratio, sales/price
ratio, and cash flow/price ratio. The three momentum factors included
estimate revisions for earnings, revisions ratio, and price momentum.
Three risk factors were used. The first is the systematic risk or beta from
the CAPM.^25 The second is the residual risk from the CAPM; this is the
risk not explained by the CAPM. The third risk is an uncertainty estimate
measure. The factors are beginning-of-month values that are properly
lagged where necessary.^26
Jones calculated the average monthly regression coefficient and t-statistic
for the series. Table 3.9 shows the estimated coefficient for each factor and
the t-statistic. All of the factors are highly significant. The lowest t-statistic is
(^23) It should be noted that in 1977 Richard Roll criticized the published tests of the
CAPM. He argued that while the CAPM is testable in principle, no correct test of
the theory had yet been presented. He also argued that there was practically no pos-
sibility that a correct empirical test would ever be accomplished in the future. See
Richard R. Roll, “A Critique of the Asset Pricing Theory: Part I. On the Past and
Potential Testability of the Theory,” Journal of Financial Economics 5 (March 1977):
129–176.
(^24) Jones, “The Active versus Passive Debate: Perspectives on an Active Quant.”
(^25) In the calculation of the CAPM a proxy for the market portfolio is needed. Jones
used the Russell 1000 Index. This index includes large-cap stocks.
(^26) Lagging is required because certain financial information is reported with lag. For
example, year-end income and balance sheet information for a given year is not
reported until three months after the corporation’s year-end.