By Soren S Nielson, Andrea Consiglio, Stavros A. Zenios
In Practical monetary Optimization: A Library of GAMS Models, the authors offer a various set of types for portfolio optimization, in response to the final Algebraic Modelling procedure. ‘GAMS’ includes a language which permits a high-level, algebraic illustration of mathematical types and a collection of solvers – numerical algorithms – to resolve them. The procedure used to be constructed in line with the necessity for strong and versatile front-end instruments to control huge, real-life models.
The paintings starts with an outline of the constitution of the GAMS language, and discusses matters with regards to the administration of knowledge in GAMS versions. The authors offer versions for mean-variance portfolio optimization which deal with the query of buying and selling off the portfolio anticipated go back opposed to its danger. mounted source of revenue portfolio optimization versions practice regular calculations and make allowance the consumer to bootstrap a yield curve from bond costs. commitment types enable for normal portfolio commitment with borrowing and re-investment judgements, and are prolonged to house maximisation of horizon go back and to include numerous sensible issues at the portfolio tradeability. Immunization types offer for the issue immunization of portfolios of treasury and company bonds.
The scenario-based portfolio optimization challenge is addressed with suggest absolute deviation types, monitoring types, remorse versions, conditional VaR types, anticipated application maximization types and put/call effective frontier types. The authors hire stochastic programming for dynamic portfolio optimization, constructing stochastic commitment types as stochastic extensions of the mounted source of revenue types mentioned in bankruptcy four. Two-stage and multi-stage stochastic courses expand the state of affairs types analysed in bankruptcy five to permit dynamic rebalancing of portfolios as time evolves and new details turns into recognized. versions for structuring index cash and hedging rate of interest danger on overseas portfolios also are provided.
The ultimate bankruptcy presents a suite of ‘case studies’: versions for large-scale purposes of portfolio optimization, which might be used because the foundation for the advance of commercial help platforms to fit any particular standards, together with versions for the administration of partaking policies and private asset allocation.
The name could be a worthwhile consultant for quantitative builders and analysts, portfolio and asset managers, funding strategists and complicated scholars of finance.
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Extra resources for Practical Financial Optimization: A Library of GAMS Models
VarDef .. PortReturn PortVariance and the portfolio variance =E= SUM(i, ExpectedReturns(i)*x(i)); =E= SUM((i,j), x(i)*VarCov(i,j)*x(j)); The variables x(i) measure the fraction of capital to be invested in each asset. By normalizing to one, the set of feasible portfolios – those whose weights add up to one – is identiﬁed by the following constraint: NormalCon .. SUM(i, x(i)) =E= 1; The objective value z is a weighted sum of the portfolio’s expected return, PortReturn, and its risk, PortVariance, where the parameter λ varies between zero and one.
2 Basics of Data Handling 29 GAMS communicates with Excel via GDX (GAMS Data Exchange) ﬁles. A GDX ﬁle is a ﬁle that stores the values of one or more GAMS symbols such as sets, parameters, variables, and equations. GDX ﬁles can be used to prepare data for a GAMS model, present results of a GAMS model, store results of the same model using different parameters, etc. A GDX ﬁle does not store a model formulation or executable statements. GDX ﬁles are portable between different platforms. In order to write data from GAMS to Excel, the user writes a GDX ﬁle and then reads the Excel ﬁle from the GDX ﬁle: GAMS → GDX → Excel.
TABLES A TABLE declaration is just a syntactically convenient way to declare a multidimensional parameter. 05 ; The elements speciﬁed in a table must be positioned on the same row and column as the corresponding indices. Omitted entries correspond to zeroes. 06 and CashFlow("2004","GOVT_1") = 0. All of the CashFlow entries for 2006 are 0. The elements speciﬁed must be numerical constants and cannot be expressions. 4 28 Data Management Chap. 2; Tables with three or more dimensions can have set elements corresponding to any number of indices speciﬁed vertically (down along the ﬁrst column) or horizontally (along the top line), separated by periods.