19-EquityPort Page 560 Friday, March 12, 2004 12:40 PM
560 The Mathematics of Financial Modeling and Investment ManagementTaking square root on both sides and denoting |.|as absolute value, we
see the following relationship between tracking error and portfolio beta:σ(rp – rb)= w – 1 σ()rb = β– 1 σ()rbPortfolio tracking error with respect to the benchmark index
increases when both the beta falls below 1 and when the beta rises
above 1. The same is true of the weight of the portfolio in the bench-
mark index. So, as portfolio increases the proportion of cash held, even
though its absolute risk falls, its tracking error (i.e., relative risk) rises.
In the above example, we make the simplistic assumption that the
manager only chooses between holding the market portfolio and cash
when making changes to its beta. In the more general case, where the man-
ager can hold any number of stocks in any proportion, its beta can differ
from 1 due to other reasons. But, even in this general case, the tracking
error increases when the portfolio beta deviates from the market beta.EQUITY STYLE MANAGEMENT
Before we discuss the various types of active and passive strategies, let’s
discuss an important topic regarding what has come to be known as
equity investment styles. Several academic studies found that there were
categories of stocks that had similar characteristics and performance
patterns. Moreover, the returns of these stock categories performed dif-
ferently than other categories of stocks. That is, the returns of stocks
within a category were highly correlated and the returns between cate-
gories of stocks were relatively uncorrelated. As a result of these studies,
practitioners began to view these categories of stocks with similar per-
formance as a “style” of investing. Using size as a basis for categorizing
style, some managers became “large cap” investors while others “small
cap” investors. (“Cap” means market capitalization.) Moreover, there
was a commonly held belief that a manager could shift “styles” to
enhance performance return.
Today, the notion of an equity investment style is widely accepted in
the investment community. Next we look at the popular equity style
types and the difficulties of classifying stocks according to style.Types of Equity Styles
Stocks can be classified by style in many ways. The most common is in
terms of one or more measures of “growth” and “value.” Within a
growth and value style there is often a substyle based on some measure