74 The Basics of financial economeTrics
Robert Jones analyzed the performance of the average large-cap mutual
fund adjusted for risk.^22 As noted earlier, tests of market efficiency are joint
tests of the assumed asset pricing model. Jones used a model similar to the
three-factor model proposed by Eugene Fama and Kenneth French that we
will describe later in this chapter. The variables in his regression model are
Yt=the difference between the returns on a composite mutual fund
index and the S&P 500 in month t
X1,t=the difference between the S&P 500 return and the 90-day Trea-
sury rate for month t
X2,t=the difference between the returns on the Russell 3000 Value
Index and the Russell 3000 Growth Index for month t
X3,t=the difference between the returns on the Russell 1000 Index
(large-cap stocks) and the Russell 2000 Index (small-cap stocks)
for month tThe dependent variable, (Yt), is obtained from indexes published by
Lipper, a firm that constructs performance indexes for mutual funds classi-
fied by investment category. Specifically, the dependent variable in the study
was the average of the return on the Lipper Growth Index and the Lipper
Growth and Income Index each month minus the return on the S&P 500.
Yt is the active return.
The first independent variable (X1,t) is a measure of the return of the
market over the risk-free rate and is therefore the excess return on the mar-
ket in general. The second independent variable (X2,t) is a proxy for the dif-
ference in performance of two “styles” that have been found to be important
in explaining stock returns: value and growth. (We describe this further later
in this chapter.) In the regression, the independent variable X2,t is the excess
return of value style over growth style. Market capitalization is another style
factor. The last independent variable (X3,t) is the difference in size between
large-cap and small-cap stocks and therefore reflects size.
The regression was run over 219 months from January 1979 through
March 1997. The results are reported below with the t-statistic for each
parameter shown in parentheses:
Yˆt= –0.007 – 0.083X1,t – 0.071X2,t – 0.244X3,t
(–0.192) (–8.771) (–3.628) (–17.380)(^22) Robert C. Jones, “The Active versus Passive Debate: Perspectives of an Active
Quant,” in Active Equity Portfolio Management, ed. Frank J. Fabozzi (New York:
John Wiley & Sons, 1998).