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Economics and finance Description
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 13: Economics and finance problems
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
Data Files
h7qportf.mos (!****************************************************** Mosel Example Problems ====================== file h7qportf.mos ````````````````` Mean-variance portfolio selection An investor considers 4 different securities to invest capital. The mean yield on each invested dollar in each of the securities is known. The investor gets estimates of the variance/covariance matrix of estimated returns on the securities. What fraction of the total capital should be invested in each security? Two problem variants are proposed. Problem 1: Which investment strategy should the investor adopt to minimize the variance subject to getting some specified minimum target yield? Problem 2: Which is the least variance investment strategy if the investor wants to choose at most two different securities (again subject to getting some specified minimum target yield)? For problem 1, a quadratic program (quadratic objective function subject to linear constraints and continuous variables) is presented. For problem 2, the model is extended by introducing binary decision variables leading to a Mixed Integer Quadratic Program. The module 'mmnl' is used in both cases to handle such a quadratic (non- linear) feature. (c) 2008 Fair Isaac Corporation author: S. Heipcke, Aug. 2002, rev. Sep. 2017 *******************************************************!) model "H-7 QP Portfolio" uses "mmxprs", "mmnl" parameters TARGET = 7.0 ! Minimum target yield MAXASSETS = 4 ! Maximum number of assets in portfolio end-parameters declarations SECS = 1..4 ! Set of securities RET: array(SECS) of real ! Expected yield of securities VAR: array(SECS,SECS) of real ! Variance/covariance matrix of ! estimated returns frac: array(SECS) of mpvar ! Fraction of capital used per security end-declarations initializations from 'h7qportf.dat' RET VAR end-initializations ! **** First problem: unlimited number of assets **** ! Objective: mean variance Variance:= sum(s,t in SECS) VAR(s,t)*frac(s)*frac(t) ! Spend all the capital sum(s in SECS) frac(s) = 1 ! Target yield sum(s in SECS) RET(s)*frac(s) >= TARGET ! Solve the problem minimize(Variance) ! Solution printing declarations NAMES: array(SECS) of string end-declarations initializations from 'h7qportf.dat' ! Get the names of the assets NAMES end-initializations writeln("With a target of ", TARGET, " minimum variance is ", getobjval) forall(s in SECS) writeln(NAMES(s), ": ", getsol(frac(s))*100, "%") ! **** Second problem: limit total number of assets **** declarations buy: array(SECS) of mpvar ! 1 if asset is in portfolio, 0 otherwise end-declarations ! Limit the total number of assets sum(s in SECS) buy(s) <= MAXASSETS forall(s in SECS) do buy(s) is_binary frac(s) <= buy(s) end-do ! Solve the problem minimize(Variance) writeln("With a target of ", TARGET," and at most ", MAXASSETS, " assets, minimum variance is ", getobjval) forall(s in SECS) writeln(NAMES(s), ": ", getsol(frac(s))*100, "%") end-model | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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