\$title Standard QP Model - no Covariance Matrix (QP4,SEQ=174) \$onText Instead of using the covariances, but operate directly on the data. Additional information can be found at: http://www.gams.com/modlib/adddocs/qp4doc.htm Kalvelagen, E, Model Building with GAMS. forthcoming de Wetering, A V, private communication. Keywords: nonlinear programming, quadratic programming, finance \$offText \$include qpdata.inc Set d(days) 'selected days' s(stocks) 'selected stocks'; Alias (s,t); * select subset of stocks and periods d(days) = ord(days) > 1 and ord(days) < 31; s(stocks) = ord(stocks) < 51; Parameter mean(stocks) 'mean of daily return' dev(stocks,days) 'deviations' totmean 'total mean return'; mean(s) = sum(d, return(s,d))/card(d); dev(s,d) = return(s,d) - mean(s); totmean = sum(s, mean(s))/(card(s)); Variable z 'objective variable' x(stocks) 'investments' w(days) 'intermediate variables'; Positive Variable x; Equation obj 'objective' budget retcon 'return constraint' wdef(days); obj.. z =e= sum(d, sqr(w(d)))/(card(d) - 1); wdef(d).. w(d) =e= sum(s, x(s)*dev(s,d)); budget.. sum(s, x(s)) =e= 1.0; retcon.. sum(s, mean(s)*x(s)) =g= totmean*1.25; Model qp4 / all /; solve qp4 using nlp minimizing z; display x.l;