21-Bond Portfolio Man Page 677 Wednesday, February 4, 2004 1:12 PM
Bond Portfolio Management 677bs m = 0rs = hs
mαi, γi ≥ 0; i ∈ UThe first condition is the initial budget constraint, which tells us
that the initial investment (which has a negative sign) plus the initial
borrowing plus the initial budget B is equal to the first surplus. The sec-
ond condition is the liability-matching condition. The third condition is
the self-financing condition. Note that as interest rates are known in
each scenario, bond prices are also known in each scenario. The fifth
and sixth conditions are the statements that there is no borrowing at the
final stage and that the objective is the final cash. The seventh condition
is the constraint that weights are nonnegative at each stage
This formulation illustrates all the basic ingredients. The problem is
formulated as a deterministic equivalent problem, setting as its objective
the maximization of final expected cash. The final stage is certain and
the process is backward. With this objective, the stochastic optimization
problem is recast as an LP problem.
This formulation can be extended to an arbitrary number of stages.
Formulating in full generality a multistage stochastic optimization prob-
lem is beyond the scope of this book. In fact, there are many technical
points that need a careful handling.^20SUMMARY
■ Bond market indexes can be classified as broad-based bond market
indexes and specialized bond market indexes.
■ Bond management strategies range from pure bond index matching to
active management.
■ Pure bond index matching strategy involves the least risk of underper-
forming a bond market index.
■ Enhanced indexing strategies involve constructing portfolios to match
the primary risk factors associated with a bond market index without
acquiring each issue in the index.(^20) See, for example, Peter Kall and Stein W. Wallace, Stochastic Programming
(Chichester, U.K.: John Wiley & Sons, 1994).