21-Bond Portfolio Man Page 660 Wednesday, February 4, 2004 1:12 PM
660 The Mathematics of Financial Modeling and Investment ManagementNonsystematic Risk Exposure
Now let’s look at nonsystematic risk. The nonsystematic tracking error is
divided into those that are issuer specific and those that are issue specific.
As indicated in Exhibit 21.3, the tracking error associated with the 57-
bond portfolio is 52 basis points per annum and there is 26 basis points
per annum of nonsystematic risk. The latter risk arises from the concen-
tration of the portfolio in individual securities or issuers. The last column
of Exhibit 21.2 shows this risk. The column reports the percentage of the
portfolio’s market value invested in each issue. Because there are only 57
issues in the portfolio, the portfolio is relatively small in terms of issues.
Consequently, each issue makes up a nontrivial fraction of the portfolio.
Specifically, look at the exposure to two corporate issuers, GTE Corp.
and Coca-Cola. Each is more than 8% of the portfolio. If there is a
downgrade of either firm, this would cause large losses in the 57-bond
portfolio, but it would not have a significant effect on the benchmark
which includes 6,932 issues. Consequently, a large exposure in a portfo-
lio to a specific corporate issuer represents a material mismatch between
the exposure of the portfolio and a benchmark that must be taken into
account in assessing a portfolio’s risk relative to a benchmark.Optimization Application
The multifactor risk model can be used by the portfolio manager in
combination with optimization in constructing and rebalancing a port-
folio to reduce tracking error. A portfolio manager using optimization,
for example, can determine the single largest transaction that can be
used to reduce tracking error. Or, a portfolio manager can determine
using optimization a series of transactions (i.e., bond swaps) that would
be necessary to alter the target tracking error at minimum cost.^9
Suppose that the portfolio manager’s objective is to minimize track-
ing error. From the universe of bonds selected by the portfolio manager,(^9) According to Lev Dynkin of Lehman Brothers, the optimization procedure is as fol-
lows. Instead of finding a complete portfolio that optimizes tracking error in the
model, a step-by-step optimization algorithm is chosen based on marginal contribu-
tions of each security already in a portfolio or any buy-candidate to the portfolio risk
versus the benchmark. Current portfolio holdings are then sorted in a descending or-
der of their marginal contribution to tracking error, offering the manager an oppor-
tunity to pick a sell candidate with the most impact on tracking error, but not forcing
the portfolio manager into any one choice. Once the sell candidate is selected, it is
paired with any eligible buy candidate to find the highest possible tracking error im-
provement. Buy candidates are ranked on the tracking error that would result from
having picked each specific security. This step-by-step optimization mechanism al-
lows the portfolio manager to intervene with every transaction.