\$title Standard QCP Model (QCP1,SEQ=283) \$onText This is the gamslib model QP1 expressed as a QCP. Also note that the full sized data set is used and the handling of the Q matrix is simplified. The first in a series of variations on the standard QP formulation. The subsequent models exploit data and problem structures to arrive at formulations that have sensational computational advantages. Additional information can be found at: http://www.gams.com/modlib/adddocs/qp1doc.htm Kalvelagen, E, Model Building with GAMS. forthcoming de Wetering, A V, private communication. Keywords: quadratic constraint programming, finance, portfolio optimization, investment planning \$offText \$eolCom // \$include qpdata.inc Set d(days) 'selected days' s(stocks) 'selected stocks'; Alias (s,t); * note that we have to drop the first day because of the definition of * return(stocks,days-1) = val(stocks,days) - val(stocks,days-1); d(days+1) = yes; // this will drop the first day s(stocks) = yes; Parameter mean(stocks) 'mean of daily return' dev(stocks,days) 'deviations' covar(stocks,sstocks) 'covariance matrix of returns (upper)' totmean 'total mean return'; mean(s) = sum(d, return(s,d))/card(d); dev(s,d) = return(s,d) - mean(s); covar(s,t) = sum(d, dev(s,d)*dev(t,d))/(card(d)-1); totmean = sum(s, mean(s))/(card(s)); Variable z 'objective variable' x(stocks) 'investments'; Positive Variable x; Equation obj 'objective' budget retcon 'return constraint'; obj.. z =e= sum((s,t), x(s)*covar(s,t)*x(t)); budget.. sum(s, x(s)) =e= 1.0; retcon.. sum(s, mean(s)*x(s)) =g= totmean*1.25; Model qcp1 / all /; option limCol = 0, limRow = 0; qcp1.workFactor = 20; solve qcp1 using qcp minimizing z;