*Minimum variance portfolio * Minimum variance portfolio selection from Bera, A.K. and Park, S.Y. paper set i Portfolios /health, utility, other/ k # of observations /1*1/ ; alias (j,i); parameter return(i) Return on asset cov(i,i) Covarianve matrix muhat ; return("health") = 1.551 ; return("utility") = 1.156 ; return("other") = 1.215 ; **** Priors *q(i) = 1/card(i); *** Cov matrix table cov(i,i) covariance matrix health utility other health 57.298 12.221 33.026 utility 12.221 13.168 11.814 other 33.026 11.814 27.952 ; positive variables pi(i) shares from minimum variance ; variables obj1 objective function ; equations MV ME objective function Ereturn Expected return equation sumi Proper prob for MV ; **** We need the MV to use as priors MV.. obj1 =e= sum(i,sum(j,pi(i)*pi(j)*cov(i,j))) ; Ereturn.. 1.37 =e= sum(i, pi(i)*return(i)); sumi.. 1 =e= sum(i, pi(i)); model M_v /MV Ereturn sumi /; solve M_v minimizing obj1 using nlp; muhat = sum(i, pi.l(i)*return(i)); display pi.l, muhat, obj1.l;