19-EquityPort Page 564 Friday, March 12, 2004 12:40 PM
564 The Mathematics of Financial Modeling and Investment Managementered is first calculated. The cutoff between large and small is the stock
that will give an equal market capitalization. Even here though, one
might worry about “size jitter.”PASSIVE STRATEGIES
There are two types of passive strategies: a buy-and-hold strategy and
an indexing strategy. In a buy-and-hold strategy, a portfolio of stocks
based on some criterion is purchased and held to the end of some invest-
ment horizon. There is no active buying and selling of stocks once the
portfolio is created. While referred to as a passive strategy, there are ele-
ments of active management. Specifically, the investor who pursues this
strategy must determine which stock issues to buy.
An indexing strategy is the more commonly followed passive strat-
egy. With this strategy, the manager does not attempt to identify under-
valued or overvalued stock issues based on fundamental security
analysis. Nor does the manager attempt to forecast general movements
in the stock market and then structure the portfolio so as to take advan-
tage of those movements. Instead, an indexing strategy involves design-
ing a portfolio to track the total return performance of a benchmark
index. Next we explain how that is done.Constructing an Indexed Portfolio
In constructing a portfolio to replicate the performance of the bench-
mark index, sometimes referred to as the indexed portfolio or the track-
ing portfolio, there are several approaches that can be used. One
approach is to purchase all stock issues included in the benchmark
index in proportion to their weightings. A second approach, referred to
as the capitalization approach, is one in which the manager purchases a
number of the largest capitalized names in the benchmark index and
equally distributes the residual stock weighting across the other issues in
the benchmark index. For example, if the top 150 highest-capitalization
stock issues are selected for the replicating portfolio and these issues
account for 70% of the total capitalization of the benchmark index, the
remaining 30% is evenly proportioned among the other stock issues.
Another approach is to construct an indexed portfolio with fewer
stock issues than the benchmark index. Two methods used to implement
this approach are the cellular (or stratified sampling) method and the
multifactor risk model method.
In the cellular method, the manager begins by defining risk factors
by which the stocks that make up a benchmark index can be catego-