$title Standard QP Model- linear Approximation (QP5,SEQ=175)
$onText
Linear approximation of qp4 operate directly on the data.
Additional information can be found at:
http://www.gams.com/modlib/adddocs/qp5doc.htm
Kalvelagen, E, Model Building with GAMS. forthcoming
de Wetering, A V, private communication.
Keywords: linear programming, quadratic programming, linear approximation, finance
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$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'
wplus(days) 'intermediate variables'
wmin(days) 'intermediate variables';
Positive Variable x, wplus, wmin;
Equation
obj 'objective'
budget
retcon 'return constraint'
wdef(days);
obj.. z =e= sum(d, wplus(d) + wmin(d));
wdef(d).. wplus(d) - wmin(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 qp5 / all /;
solve qp5 using lp minimizing z;
display x.l;