Address:
Abstract
A MIP implementation of a disjunctive model for optimal assignments of financial items and derivatives in hedge accounting is presented. Item and derivative sensitivity to risk factors is used to determine if certain hedges are permitted; disallowed hedges lead to elimination of rows and columns of the mixed integer program during preprocessing. Two "large" submatrices of the coefficient matrix for the MIP implementation, which have nonzero entries for the binary variables, are shown to be totally unimodular. Results from computer trials are reported: most of the large programs in the trials solved quickly, and in many the optimal MIP objective function value was equal to the optimal objective function value for its linear relaxation. Background information on the standards for hedge accounting is presented.
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Talk at INFORMS Spring 2000 Meeting, Salt Lake City, May 7-10, 2000
Financial institutions optimize portfolios in reference to risk management goals, accounting standards, and financial analysts' expectations. We present MIP formulations of portfolio optimization that take market and pricing model results as input and that express specific accounting standards and risk management goals in disjunctive constraints. Experimental results are presented.
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Katherine Wyatt
Logic Based Systems Lab
Brooklyn College, CUNY
Brooklyn, NY 11210
wyatt@sci.brooklyn.cuny.edu
ABSTRACT:
New accounting standards for financial derivatives mandate
on-balance sheet reporting and the designation of hedged
item - hedging derivative pairs for reporting offsetting
gain or loss on financial statements. A program that uses
disjunctive constraints to model the criteria for hedge
accounting across all types of financial instruments and
against allowable risks is presented. The program has a
piecewise linear objective function, and uses standard risk
management reports as input. A linear relaxation of the
disjunctive program models compliance for most hedges
against market risk.
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Katherine Wyatt
Logic Based Systems Lab
Brooklyn College, CUNY
Brooklyn, NY 11210
wyatt@sci.brooklyn.cuny.edu
ABSTRACT:
Financial institutions often use derivatives to protect the earnings
of their portfolios from changes in market factors. Companies take
positions in derivatives that are expected to move opposite in
value to items in their portfolio; these derivatives are hedges. If a
hedge relationship qualifies for hedge accounting, then an institution
only reports in earnings the amount of gain or loss on the derivative
(over the financial period) that remains after netting the gain or loss
of the hedged item/hedging derivative pair. New Financial Accounting Standards
Board rules for hedge accounting were recently released and will go
into effect after June 15, 2000. A suite of programs that uses
disjunctive, or logical, constraints to model many of the criteria
for hedge accounting is presented. The programs use standard risk
management reports as input, and a linear program models compliance
for many hedges against market risk.
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Katherine Wyatt
Logic Based Systems Lab
Brooklyn College, CUNY
Brooklyn, NY 11210
wyatt@sci.brooklyn.cuny.edu
ABSTRACT:
Selecting an optimal portfolio is often complicated by structural requirements, for example, trade amount limits, restrictions on industry sector, or regulatory requirements. Solutions to these portfolio problems can be found with disjunctive programs, where the structural requirements are expressed as logical disjunctions that describe allowable choices. The complexity of quadratic programs makes adding disjunctions to a traditional mean-variance model computationally prohibitive. However, if absolute deviation is used to measure dispersion of returns instead of variance, then structural requirements can be added to a portfolio selection model with linear constraints and a linear objective function. Absolute deviation models produce step-shaped programs that can be decomposed into smaller linear programs that share a set of constraints. When logical (disjunctive) constraints are added to an absolute deviation model, the resulting programs are disjunctive linear programs that inherit the step shape of the model. We show that these programs can be solved by combining Benders decomposition and branch-and-bound search. We present an algorithm that combines search among the disjunctive sets with solution of the relaxed problems that result from decomposition; objective function values on disjunctive sets feasible for relaxed problems are used to prune the search tree.
Last modified: 15 December 2000