The Mathematics of Financial Modelingand Investment Management

19-EquityPort Page 552 Friday, March 12, 2004 12:40 PM

552 The Mathematics of Financial Modeling and Investment Management

This view that an investing process requires an integrated approach

to portfolio management is reinforced by Barra, a vendor of analytical

systems used by portfolio managers. Barra emphasizes that superior

investment performance is the product of careful attention paid by

equity managers to the following four elements:

■ Forming reasonable return expectations

■ Controlling portfolio risk to demonstrate investment prudence

■ Controlling trading costs

■ Monitoring total investment performance

Accordingly, the investing process that includes these four elements

are all equally important in realizing superior investment performance.

In Chapter 4, several quantitative models for general expected returns

were described. As for the second element, we will discuss the process of

controlling risk in this chapter and in more detail in Chapter 23. Trad-

ing costs were explained in Chapter 2.

ACTIVE VERSUS PASSIVE PORTFOLIO MANAGEMENT

In practice there are investors who pursue different degrees of active

management and different degrees of passive management. It would be

helpful to have some way of quantifying the degree of active or passive

management. John Loftus of Pacific Investment Management Company

(PIMCO) has suggested that one way of classifying the various types of

equity strategies is in terms of two measures—alpha and tracking error.^3

These measures begin with the calculation of the active return for a

period. The active return is the difference between the actual portfolio

return for a given period (say, a month) and the benchmark index return

for the same period. Alpha is defined as the average active return over

some time period. So, if there are 12 monthly active returns observed,

then the average of the 12 monthly active returns is the alpha. Tracking

error is the standard deviation of the active return. In the next section,

we discuss tracking error in more detail. Tracking error occurs because

the risk profile of a portfolio differs from that of the risk profile of the

benchmark index.

Based on these measures, Loftus proposes the classification scheme

shown in Exhibit 19.1. While there may be disagreements as to the values

(^3) John S. Loftus, “Enhanced Equity Indexing,” Chapter 4 in Frank J. Fabozzi (ed.),
Perspectives on Equity Indexing (New Hope, PA: Frank J. Fabozzi Associates,
2000).