FICO
FICO Xpress Optimization Examples Repository
FICO Optimization Community FICO Xpress Optimization Home
Back to examples browserPrevious exampleNext example

Folio - Modelling examples from 'Getting started'

Description
  • Chapter 3 Inputting and Solving a Linear Programming problem
    • foliolp.mos: modeling and solving a small LP problem
    • foliolperr.mos: LP model with syntax errors
    • foliolps.mos: LP model using string indices
  • Chapter 4 Working with data
    • foliodata.mos (data file: folio.dat): data input from file, result output to a file, model parameters
    • folioodbc.mos (data files: folio.xls, folio.mdb, folio.sqlite): data input from a spreadsheet or database, result output to a spreadsheet or database, model parameters
    • folioexcel.mos (data file: folio.xls): same as folioodbc.mos but with Excel-specific data input and output (Windows only)
    • foliosheet.mos (data file: folio.xls): same as folioodbc.mos but with data input and output through generic spreadsheet access
    • foliocsv.mos (data file: folio.csv): same as folioodbc.mos but with data input and output through generic spreadsheet access in CSV format
  • Chapter 5 Drawing user graphs
    • folioloop.mos (data files: folio.dat, foliodev.dat): re-solving with varied parameter settings
    • folioloop_graph.mos (data files: folio.dat, foliodev.dat): re-solving with varied parameter settings, graphical solution display
    • foliolps_graph.mos: same as foliolps, adding graphical solution display
  • Chapter 6 Mixed Integer Programming
    • foliomip1.mos (data file: folio.dat): modeling and solving a small MIP problem (binary variables)
    • foliomip2.mos (data file: folio.dat): modeling and solving a small MIP problem (semi-continuous variables)
  • Chapter 7 Quadratic Programming
    • folioqp.mos (data file: folioqp.dat): modeling and solving a QP and a MIQP problem
    • folioqp_graph.mos (data files: folioqp.dat, folioqpgraph.dat): re-solving a QP problem with varied parameter settings, graphical solution display
    • folioqc.mos (data file: folioqp.dat): modeling and solving a QCQP and
    • foliomiqc.mos (data file: folioqp.dat): modeling and solving a MIQCQP
  • Chapter 8 Heuristics
    • folioheur.mos (data file: folio.dat): heuristic solution of a MIP problem


Source Files

Data Files





folioqpr.mos

(!******************************************************
   Mosel Example Problems
   ======================

   file folioqpr.mos
   `````````````````
   Modeling a small QP problem 
   to perform portfolio optimization.
   -- 1. QP: minimize variance
      2. MIQP: limited number of assets --
   -- Using R to calculate covariance matrix --
  
   !!! This example requires an installation of R, see the
   !!! chapter 'R' of the 'Mosel Language Reference' for
   !!! compatible versions and setup instructions
   
  (c) 2015 Fair Isaac Corporation
      author: S.Lannez, Jul. 2015, rev. Sep. 2017
*******************************************************!)

model "Portfolio optimization with QP/MIQP"
 uses "mmxprs", "mmnl"
 uses "r"                            ! Use R functions

 parameters
  MAXVAL = 0.3                       ! Max. investment per share
  MINAM = 0.5                        ! Min. investment into N.-American values
  MAXNUM = 4                         ! Max. number of different assets
  TARGET = 9.0                       ! Minimum target yield
 end-parameters

 declarations
  SHARES = 1..10                     ! Set of shares
  RISK: set of integer               ! Set of high-risk values among shares
  NA: set of integer                 ! Set of shares issued in N.-America
  DATES: set of string               ! Historical dates
  RET: array(SHARES) of real         ! Estimated return in investment
  VAR: array(SHARES,SHARES) of real  ! Variance/covariance matrix of
                                     ! estimated returns
  OPEN: array(SHARES,DATES) of real  ! Historical share value at market opening
  CLOSE: array(SHARES,DATES) of real ! Historical share value at market closing
 end-declarations

 initializations from "folioqp.dat"
  RISK RET NA
 end-initializations

! Load historical values to compute the covariance
 initializations from "folioqphist.dat"
  OPEN CLOSE
 end-initializations

! **** Perform some statistics using R ****

! Copy array to R environments
 Rset('open',OPEN) 
 Rset('close',CLOSE)
! Print covariance of share value at market openings
 writeln("Covariances at market openings:")
 Rprint('cov(t(open))')
! Calculate and retrieve covariance of mean value
 Rgetarr('cov(t((open+close)/2))',VAR)

 declarations
  frac: array(SHARES) of mpvar      ! Fraction of capital used per share
 end-declarations

! **** First problem: unlimited number of assets ****

! Objective: mean variance
 Variance:= sum(s,t in SHARES) VAR(s,t)*frac(s)*frac(t) 

! Minimum amount of North-American values
 sum(s in NA) frac(s) >= MINAM

! Spend all the capital
 sum(s in SHARES) frac(s) = 1
 
! Target yield
 sum(s in SHARES) RET(s)*frac(s) >=  TARGET

! Upper bounds on the investment per share
 forall(s in SHARES) frac(s) <= MAXVAL

! Solve the problem
 minimize(Variance)

! Solution printing
 writeln("With a target of ", TARGET, " minimum variance is ", getobjval)
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%")  

! **** Second problem: limit total number of assets ****

 declarations
  buy: array(SHARES) of mpvar       ! 1 if asset is in portfolio, 0 otherwise
 end-declarations

! Limit the total number of assets
 sum(s in SHARES) buy(s) <= MAXNUM

 forall(s in SHARES) 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 ", MAXNUM,
          " assets,\n minimum variance is ", getobjval)
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%") 

! Round integer values and resolve
 fixglobal(true)
 minimize(Variance)
 writeln("With all binary variables rounded to the nearest integer:")
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%") 
 
end-model 

Back to examples browserPrevious exampleNext example