PROGRAM TestStockPorts
! ----------------------------------------------------------------------------
! This program is designed to test if portfolio theory is worth anything.
! The Matt Factor is defined as M(i)=SQRT((R-Ri)^2+(S-Si)^2), where R is 
! the optimal return I want, Ri, is the return that is calculated from the 
! "stock" data, S is risk that I optimized for, and Si, is the actual 
! calculated risk.
! ----------------------------------------------------------------------------
! Created by Matthew S. Norton
! Last Updated
! February 21, 2008
! ----------------------------------------------------------------------------
! NOTE: This is in FORTRAN 90 and you will need a FORTRAN 90 complier to run this code
! ----------------------------------------------------------------------------

!  IMPLICIT NONE
INTEGER, PARAMETER :: NMAT = 3, NumTrials = 10000
REAL*8, DIMENSION(NMAT) :: Weights, Returns, PerR
REAL*8, DIMENSION(NMAT, NMAT) :: QMat, PerQ
REAL*8 :: QOUT(NMAT,NMAT),ROUT(NMAT), RETURNI = 0.0d0, Riski = 0.0d0, Risks = 0.0d0
REAL*8 :: Returnss(2) = 0.0d0, Risk(2) = 0.0d0, Mattian = 0.0d0, Com1 = 0.0d0 
REAL*8 :: Com2 = 0.0d0, Mattians = 0.0d0, Coms1 = 0.0d0, Coms2 = 0.0d0, Comz1 = 0.0d0, Comz2 = 0.0d0
INTEGER :: I, J, Count = 1, Now(8), L

OPEN(UNIT = 10, FILE = "RiskRet.txt", STATUS = "UNKNOWN")
OPEN(UNIT = 20, FILE = "Mattian.txt", STATUS = "UNKNOWN")

!DO I = 1, NMAT
!     PRINT *, "Please input value for return for stock", I
!     READ *, Returns(I)
!END DO
Returns(1) = 0.01d0   *100.
Returns(2) = 0.02d0   *100.
Returns(3) = 0.04d0   *100.
DO I = 1, NMAT
     PerR(I) = Returns(I)
END DO
!PRINT *, (Returns(I), I = 1, NMAT)
!DO I = 1, NMAT
!     DO J = 1, NMAT
!          WRITE(*, 100) "Please input value of covarience matrix Q(",I,",",J,")"
!          READ*, QMAT(I,J)
!     END DO
!END DO
QMAT(1,1)=0.1**2   *100.**2
QMAT(2,2)=0.2**2   *100.**2
QMAT(3,3)=0.4**2   *100.**2
 
QMAT(1,2)=SQRT(QMAT(1,1))*SQRT(QMAT(2,2)) * 0.1   
QMAT(2,1)=QMAT(1,2)

QMAT(1,3)=SQRT(QMAT(1,1))*SQRT(QMAT(3,3)) * (-0.1)   
QMAT(3,1)=QMAT(1,3)

QMAT(2,3)=SQRT(QMAT(2,2))*SQRT(QMAT(3,3)) * (0.0)   
QMAT(3,2)=QMAT(2,3)

DO I = 1, NMAT
     DO J = 1, NMAT
          PerQ(I,J) = QMAT(I,J)
     END DO
END DO
!PRINT *, "Covarience matrix is:"
!DO I = 1, NMAT
!     DO J = 1, NMAT
!          WRITE(*,105, ADVANCE = 'NO') QMat(I,J)
!     END DO
!     WRITE(*,*)
!END DO

!DO I = 1, NMAT
!     WRITE(*, 110) "Please input value for weight ", I
!     READ *, Weights(I)
!END DO
Weights(1) = 0.4425659182603772d0
Weights(2) = 0.33267029746624077d0
Weights(3) = 0.2247637842733821d0
!PRINT *, (Weights(I), I = 1, NMAT)

DO I = 1, NMAT
     Returnss(1) = Weights(I) * PerR(I)
END DO
DO I = 1, NMAT
     DO J = 1, NMAT
          Risk(1) = Risk(1) + QMAT(I,J) * Weights(I) * Weights(J) 
     END DO
END DO
 Risks = DSQRT(Risk(1))
 CALL date_and_time(values=now)
 CALL random_seed(put=now(5:8))
 DO L = 1, NumTrials
      !PRINT *, L
!      CALL ResetValues()
      CALL AdjustValues(RETURNS,QMAT,ROUT,QOUT)
!      CALL AdjustValues()
           RETURNSS=0.0d0
           RETURNI=0.0d0
      DO I = 1, NMAT
           RETURNI = RETURNI+Weights(I) * ROUT(I)
      END DO

           RISKI=0.
      DO I = 1, NMAT
      DO J = 1, NMAT
           RiskI = RiskI + Weights(I)*QOUT(I,J)*Weights(J)
      END DO
      END DO
            RISKI=SQRT(RISKI)  

      IF (MOD(L,500) == 0) THEN
         WRITE(*,*) L, RETURNI,RISKI
      ENDIF 

        WRITE(10,*) L, RETURNI,RISKI

      Mattian = Matt(Returni, returnss(1), Riski, Risks)
      Com1 = Compare(Returni, Returnss(1))
      Com2 = Compare(Riski, Risks)
      Mattians = Mattians + Mattian
      Coms1 = Coms1 + RETURNI
      Coms2 = Coms2 + RISKI
      Comz1 = Comz1 + Com1
      Comz2 = Comz2 + Com2
      WRITE(20,*) L, Mattian, Com1, Com2
      !PRINT *, Mattian, Com1, Com2
!      IF (MOD(L,500) == 0) PRINT *, L
END DO

Mattians = Mattians / REAL(NumTrials)
 Coms1 = Coms1 / REAL(NumTrials)
 Coms2 = Coms2 / REAL(NumTrials)
 Comz1 = Comz1 / REAL(NumTrials)
 Comz2 = Comz2 / REAL(NumTrials)
 
 PRINT *, "Mattian = ", Mattians, "Return = ", Coms1, "Risks = ", Coms2 
 PRINT *, "Comparison of Returns = ", Comz1, "Comparison of Risks = ", Comz2
      
 

100 FORMAT(1X, A42, I1, A1, I1, A1) 
105 FORMAT(1X, F7.5)
110 FORMAT(1X, A30, I1)

! ----------------------------------------------------------------------------
 CONTAINS
! ----------------------------------------------------------------------------

SUBROUTINE AdjustValues(RIN,QIN,ROUT,QOUT)
REAL*8 :: X, Signs, RIN(NMAT), Y, QIN(NMAT, NMAT)
REAL*8 :: ROUT(NMAT), QOUT(NMAT, NMAT)
REAL*8 :: R(NMAT,2), Q(NMAT, NMAT,2)
REAL*8, PARAMETER :: Ad = 0.01d0
INTEGER :: I, J

  DO I=1,NMAT
       CALL Random_Number(X)
       ROUT(I)=RIN(I)+ (2.*X-1.) * 1.
  END DO  
  DO I=1,NMAT
       DO J=I,NMAT
            CALL Random_Number(X)
            QOUT(I,J)=QIN(I,J)+  (2.*X-1.) * ( 10. )**2
            QOUT(J,I)=QOUT(I,J)
       END DO  
  END DO  

END SUBROUTINE

! ----------------------------------------------------------------------------

FUNCTION Signed(Y)
REAL*8, INTENT(IN) :: Y
REAL*8 :: Signed
 Signed = NINT(ABS(Y) / Y)

END FUNCTION Signed
     
! ----------------------------------------------------------------------------
 
 FUNCTION Matt(ReId, ReMe, RiId, RiMe)
 REAL*8 :: Matt
 REAL*8 :: ReId, ReMe, RiId, RiMe
 
 Matt = DSQRT((ReId - ReMe) ** 2 + (RiId - RiMe) ** 2)
 
 END FUNCTION
 
! ----------------------------------------------------------------------------
 
FUNCTION Compare(Idiot, Me)
REAL*8 :: Compare
REAL*8 :: Idiot, Me

 Compare = Idiot - Me
 
 END FUNCTION
 
 ! ----------------------------------------------------------------------------
   
END PROGRAM