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

   file folioloop.mos
   ``````````````````
   Modeling a small LP problem 
   to perform portfolio optimization.
   -- Re-solving with varied parameter settings --
   
  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Aug. 2003
*******************************************************!)

model "Portfolio optimization with LP"
 uses "mmxprs"

 parameters
  DATAFILE= "folio.dat"              ! File with problem data
  DEVDATA= "foliodev.dat"            ! File with deviation data
  MAXVAL = 0.3                       ! Max. investment per share
  MINAM = 0.5                        ! Min. investment into N.-American values
 end-parameters

 declarations
  SHARES: set of string              ! Set of shares
  RISK: set of string                ! Set of high-risk values among shares
  NA: set of string                  ! Set of shares issued in N.-America
  RET: array(SHARES) of real         ! Estimated return in investment
  DEV: array(SHARES) of real         ! Standard deviation
  SOLRET: array(range) of real       ! Solution values (total return)
  SOLDEV: array(range) of real       ! Solution values (average deviation)
 end-declarations

 initializations from DATAFILE
  RISK RET NA
 end-initializations

 initializations from DEVDATA
  DEV
 end-initializations

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

! Objective: total return
 Return:= sum(s in SHARES) RET(s)*frac(s) 

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

! Spend all the capital
 sum(s in SHARES) frac(s) = 1
 
! Upper bounds on the investment per share
 forall(s in SHARES) frac(s) <= MAXVAL

! Solve the problem for different limits on high-risk shares
 ct:=0
 forall(r in 0..20) do
  ! Limit the percentage of high-risk values
   Risk:= sum(s in RISK) frac(s) <= r/20

   maximize(Return)                  ! Solve the problem
   
   if (getprobstat = XPRS_OPT) then  ! Save the optimal solution value
    ct+=1
    SOLRET(ct):= getobjval
    SOLDEV(ct):= getsol(sum(s in SHARES) DEV(s)*frac(s))
    writeln(r/20, "%: ret ", SOLRET(ct), " dev ", SOLDEV(ct))
   else
    writeln("No solution for high-risk values <= ", 100*r/20, "%")
   end-if
 end-do

! Print the data 
 writeln("Low risk shares:")
 forall (s in SHARES - RISK) writeln(s, ": ret ", RET(s), " dev ", DEV(s))
 
 writeln("High risk shares:")
 forall (s in RISK) writeln(s, ": ret ", RET(s), " dev ", DEV(s))
  
end-model