The Mathematics of Financial Modelingand Investment Management

19-EquityPort Page 568 Friday, March 12, 2004 12:40 PM

568 The Mathematics of Financial Modeling and Investment Management

estimated intrinsic value, while “expensive” or overvalued stocks have a

market price that exceeds the calculated present worth of the stock.

Quantitative fundamental analysis seeks to assess the value of secu-

rities using a statistical model derived from historical information about

security returns. The most commonly used model is the fundamental

multifactor risk model that we will explain later in this chapter. In addi-

tion to identifying the expected return for a security, a fundamental fac-

tor model can be used to construct a portfolio or rebalance a portfolio

as demonstrated later in this chapter.

Bruce Jacobs and Kenneth Levy refer to strategies that employ quan-

titative methods to select stocks and to construct portfolios that have the

same risk profile as a benchmark index but provide the opportunity to

enhance returns relative to that benchmark index at appropriate incre-

mental level as an “engineered approach” to portfolio management.

Fundamental Law of Active Management

The information ratio is the ratio of alpha to the tracking error. It is a

reward (as measured by alpha) to risk (as measured by tracking error)

ratio. The higher the information ratio, the better the performance of

the manager. Two portfolio managers, Richard Grinold and Ronald

Kahn, have developed a framework—which they refer to as the “funda-

mental law of active management”—for explaining how the informa-

tion ratio changes as a function of:^9

1. The depth of an active manager’s skill


2. The breadth or number of independent insights or investment opportu-
   nities.

In formal terms, the information ratio can be expressed as

IR = IC × BR 0.5^

where:

IR = the information ratio

IC = the information coefficient

BR = the number of independent insights or opportunities available

to the active manager

In the above expression, the information ratio (IR) is the reward-to-

risk ratio for an active portfolio manager. In turn, the information coef-

(^9) For a practical discussion of this active management “law,” see Ronald N. Kahn,
“The Fundamental Law of Active Management,” BARRA Newsletter (Winter 1997).