21-Bond Portfolio Man Page 678 Wednesday, February 4, 2004 1:12 PM
678 The Mathematics of Financial Modeling and Investment Management■ Active bond strategies attempt to outperform the bond market index
by intentionally constructing a portfolio that will have a greater index
mismatch than in the case of enhanced indexing.
■ Tracking error, or active risk, is the standard deviation of a portfolio’s
return relative to the return of the benchmark index.
■ Systematic risk factors are the common factors that affect all securities
in a certain category in the benchmark bond market index.
■ Nonsystematic factor risk is the risk that is not attributable to the sys-
tematic risk factors.
■ Systematic risk factors are divided into term structure risk factors and
nonterm structure risk factors.
■ Given the risk factors associated with a benchmark index, forward-
looking tracking error can be estimated.
■ A multifactor risk model can be used by the portfolio manager in com-
bination with optimization in constructing and rebalancing a portfolio
to reduce tracking error.
■ Optimization is generally done step-by-step based on marginal contri-
butions of each security.
■ Liability-funding strategies are strategies whose objective is to match a
given set of liabilities due at future times.
■ Cash flow matching in a deterministic environment is the problem of
matching a predetermined set of liabilities with an investment portfolio
that produces a deterministic stream of cash flows.
■ Cash flow matching problems can be solved with linear programming
or mixed-integer programming algorithms.
■ The objective of an immunization strategy is to construct a portfolio
that is insensitive to small parallel shifts of interest rates.
■ A given stream of liabilities can be matched with a portfolio whose
duration is equal to the duration of the liabilities and whose present
value is equal to the present value of the liabilities.
■ Matching duration and present value makes portfolios insensitive only
to small parallel shifts of interest rates; in order to minimize the effects
of nonparallel shifts, optimization procedures are needed.
■ Scenario optimization optimizes on a number of representative scenar-
ios.
■ Multistage stochastic optimization deals with the problem of optimiza-
tion when there is recourse, that is, when decisions are made at each
stage.
■ Taking expectations at each stage, stochastic optimization becomes a
problem of deterministic optimization.