Complete example

The complete model file folioloop_graph.mos with all the features discussed in this chapter looks as follows. Notice that the two modules mmxprs and mmive may be loaded with a single uses statement. The deviation data may either be added to the original data file or, as shown here, read from a second file foliodev.dat.

model "Portfolio optimization with LP"
 uses "mmxprs", "mmsvg"             ! Use Xpress Optimizer with SVG graphing

 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              ! Constraint declaration (optional)
 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))
   else
    writeln("No solution for high-risk values <= ", 100*r/20, "%")
   end-if
 end-do

! Drawing a graph to represent results (`GrS') and data (`GrL' & `GrH')
 svgaddgroup("GrS", "Solution values", SVG_GREY)
 svgaddgroup("GrL", "Low risk", SVG_GREEN)
 svgaddgroup("GrH", "High risk", SVG_RED)

 forall(r in 1..ct) svgaddpoint("GrS", SOLRET(r), SOLDEV(r))
 svgaddline("GrS", sum(r in 1..ct) [SOLRET(r), SOLDEV(r)])

 forall(s in SHARES - RISK) do
  svgaddpoint("GrL", RET(s), DEV(s))
  svgaddtext("GrL", RET(s)+1, 1.3*(DEV(s)-1), s)
 end-do

 forall(s in RISK) do
  svgaddpoint("GrH", RET(s), DEV(s))
  svgaddtext("GrH", RET(s)-2.5, DEV(s)-1, s)
 end-do

! Scale the size of the displayed graph
 svgsetgraphscale(10)
 svgsetgraphpointsize(2)

! Optionally save graphic to file
 svgsave("foliograph.svg")

! Display the graph and wait for window to be closed by the user
 svgrefresh
 svgwaitclose

end-model

The problem is not feasible for small limit values on the constraint Risk. This is shown in the following text output that we receive in addition to the graphs:

No solution for high-risk values <= 0%
No solution for high-risk values <= 5%
No solution for high-risk values <= 10%
No solution for high-risk values <= 15%