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Equity Portfolio Management 561of size. The motivation for the value/growth style categories can be
explained in terms of the most common measure for classifying stocks
as growth or value—the price-to-book value per share (P/B) ratio. Earn-
ings growth will increase the book value per share. Assuming no change
in the P/B ratio, a stock’s price will increase if earnings grow—as higher
book value times a constant P/B ratio leads to higher stock price. A
manager who is growth oriented is concerned with earnings growth and
seeks those stocks from a universe of stocks that have higher relative
earnings growth. The growth manager’s risks are that growth in earn-
ings will not materialize and/or that the P/B ratio will decline.
For a value manager, concern is with the price component rather
than with the future earnings growth. Stocks would be classified as
value stocks within a universe of stocks if they are viewed as cheap in
terms of their P/B ratio. By cheap it is meant that the P/B ratio is low rel-
ative to the universe of stocks. The expectation of the manager who fol-
lows a value style is that the P/B ratio will return to some normal level
and thus even with book value per share constant, the price will rise.
The risk is that the P/B ratio will not increase.
Within the value and growth categories there are substyles. With the
notion of style investing came stock market indexes that could be used
to represent different styles. There are three major services that provide
popular style indexes based on capitalization. Standard & Poor’s
together with Barra publishes cap-based growth and value indexes
based on three S&P indexes: the S&P 500 Index (also called the S&P
Composite Index), the Mid Cap 400 Index, and the Small Cap 600
indexes. Based on its Russell 1000, Russell 3000, and Russell Top 200,
Frank Russell publishes three large cap style indexes. It also produces a
mid-cap index and a small cap based on both the Russell 2000 and Rus-
sell 2500 indexes. A large, mid-, and small cap set of indexes is also pro-
duced by Wilshire Associates.
From the statistical point of view identifying styles means classify-
ing stocks. Classification is a broad topic in statistics. Classification
used for style analysis is typically unsupervised insofar as no given
example is needed. The simplest unsupervised technique is linear dis-
criminant analysis. If stocks are characterized by a number of attributes,
linear discriminant analysis tries to find a hyperplane that discriminates
between two groups. Consider, for instance “value” and “growth.”
Each stock is characterized by a pair of value and growth numbers.
Therefore, all stocks can be visualized as a set of points in the value-
growth plane. Discriminant analysis tries to find the straight line that
cuts that set in two subsets in some optimal way. Criteria for optimal
cutting are needed. Nonlinear discriminant analysis might use nonlinear
functions as discriminant.