The Mathematics of Financial Modelingand Investment Management

19-EquityPort Page 570 Friday, March 12, 2004 12:40 PM

570 The Mathematics of Financial Modeling and Investment Management

implemented (researched) in a timely and cost-efficient manner. This

trade-off is shown in Exhibit 19.4.

The exhibit displays the relationship between the depth of equity man-

ager insights (vertical axis) and the breadth of those insights (horizontal

axis). The depth of equity manager insights is measured in formal terms by

the information coefficient (IC, on the vertical axis), while the breadth

(BR) of manager insights can be measured by the potential number of

investment ideas or the number of securities in the manager’s acceptable

universe. When the breadth of equity manager insights is low—as in the

case of traditional equity management, according to Jacobs and Levy—

then the depth, or “goodness” of each insight needs to be high in order to

produce a constant level of active reward-to-active risk (information ratio,

IR). Exhibit 19.4 shows that this low breadth/high depth combination

produces the same level of active reward that would be associated with a

pair-wise high number of investable ideas (or securities) and a relatively

low level of equity manager “goodness” or depth per insight.

In a risk management context, one can say that the probability of fail-

ure to achieve a given level of active reward is quite high when the breadth

of investment ideas or securities to be analyzed is very low. If the market is

price efficient, that scenario is likely in the traditional fundamental analysis

approach to active equity management discussed earlier. On the other

hand, the risk of not achieving a given level of active reward is low when

EXHIBIT 19.4 Combination of Breadth (Number) of Insights and Depth, or

“Goodness,” of Insights Needed to Produce a Given Investment Return/Risk Ratio

Source: See Bruce I. Jacobs and Kenneth N. Levy, “Investment Management: An

Architecture for the Equity Market,” Chapter 1 in Frank J. Fabozzi (ed.), Active

Equity Portfolio Management (New Hope, PA: Frank J. Fabozzi Associates,

1998), p. 6.