19-EquityPort Page 565 Friday, March 12, 2004 12:40 PM
Equity Portfolio Management 565rized. A typical risk factor is the industry in which a company operates.
Other factors might include risk characteristics such as beta or capitali-
zation. The use of two characteristics would add a second dimension to
the stratification. In the case of the industry categorization, each com-
pany in the benchmark index is assigned to an industry. This means that
the companies in the benchmark have been stratified by industry. The
objective of this method is then to reduce residual risk by diversifying
across all industries in the same proportion as the benchmark index.
Stock issues within each cell or stratum, or in this case industry, can
then be selected randomly or by some other criterion such as capitaliza-
tion ranking.
The second method is using a multifactor risk model to construct a
portfolio that matches the risk profile of the benchmark index. By doing
so, a predicted tracking error close to zero can be obtained. In the case
of smaller portfolios, this approach is ideal since the manager can assess
the tradeoff of including more stock issues versus the higher transaction
costs for constructing the indexed portfolio. This can be measured in
terms of the effect on predicted tracking error.Index Tracking and Cointegration
As seen earlier in this chapter, using tools such as multifactor models,
index trackers try to replicate the returns of the index. This methodology
has the advantage of being in line with classical methods of portfolio
management. In fact, it can be easily cast in the mean-variance frame-
work. However, it has the disadvantage that errors grow in time. In fact,
tracking error is assumed to grow with the square root of time. However,
if the tracking portfolio is cointegrated with the index, errors are station-
ary. In this case, a time dependent tracking error is suboptimal.
The techniques of cointegration are clearly important for index
tracking. Its use in index tracking was pioneered by Carol Alexander at
the ISMA Centre in Reading, United Kingdom. In fact, because cointe-
gration allows a manager to specify a stationary tracking error and,
therefore, an optimal global index tracking methodology, the techniques
of cointegration can be applied to any portfolio that is strongly cointe-
grated with an index.
The key challenge of cointegration methods is to find the right coin-
tegrating portfolio. This is a difficult task when working with large port-
folios. As mentioned above, standard cointegration tests do not work for
large portfolios. One possible solution is the use economic consider-
ations that might suggest the choice of particular market segments which
can be tested for cointegration in aggregate. A more abstract approach is
to use state-space models to find meaningful common factors.