ࡱ> J): V( I, J) * X( I) * X( J)); ! Must be fully invested; [FULL] @SUM( ASSET: X) = 1; ! Upper bounds on each; @FOR( ASSET: @BND( 0, X, UB)); ! Desired value or return after 1 period; [RET] @SUM( ASSET: RATE * X) >= GROWTH; END MODEL: ! GENPRT: Generic Markowitz portfolio; SETS: ASSET/1..3/: RATE, UB, X; COVMAT( ASSET, ASSET): V; ENDSETS DATA: ! The data; ! Expected growth rate of each asset; RATE = 1.3 1.2 1.08; ! Upper bound on investment in each; UB = .75 .75 .75; ! Covariance matrix; V = 3 1 -.5 1 2 -.4 -.5 -.4 1; ! Desired growth rate of portfolio; GROWTH = 1.12; ENDDATA ! The model; ! Min the variance; [VAR] MIN = @SUM( COVMAT( I, Root EntryCONTENTS Root Entry*0_^8e ContentsI  f3 ! Must be fully invested;\cf2 \par [FULL] \cf1 @SUM\cf2 ( ASSET: X) = 1; \par \cf3 ! Upper bounds on each;\cf2 \par \cf1 @FOR\cf2 ( ASSET: \cf1 @BND\cf2 ( 0, X, UB)); \par \cf3 ! Desired value or return after 1 period;\cf2 \par [RET] \cf1 @SUM\cf2 ( ASSET: RATE * X) >= GROWTH; \par \cf1 END\cf2 \par \par } {\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset0 Courier New;}} {\colortbl ;\red0\green0\blue255;\red0\green0\blue0;\red0\green175\blue0;} \viewkind4\uc1\pard\cf1\f0\fs20 MODEL\cf2 : \par \cf3 ! GENPRT: Generic Markowitz portfolio;\cf2 \par \cf1 SETS\cf2 : \par ASSET/1..3/: RATE, UB, X; \par COVMAT( ASSET, ASSET): V; \par \cf1 ENDSETS\cf2 \par \cf1 DATA\cf2 : \par \cf3 ! The data;\cf2 \par \cf3 ! Expected growth rate of each asset;\cf2 \par RATE = 1.3 1.2 1.08; \par \cf3 ! Upper bound on investment in each;\cf2 \par UB = .75 .75 .75; \par \cf3 ! Covariance matrix;\cf2 \par V = 3 1 -.5 \par 1 2 -.4 \par -.5 -.4 1; \par \cf3 ! Desired growth rate of portfolio;\cf2 \par GROWTH = 1.12; \par \cf1 ENDDATA\cf2 \par \par \cf3 ! The model;\cf2 \par \cf3 ! Min the variance;\cf2 \par [VAR] \cf1 MIN\cf2 = \cf1 @SUM\cf2 ( COVMAT( I, J): \par V( I, J) * X( I) * X( J)); \par \c