qp4.gms : Standard QP Model - no covariance matrix
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
Reference:
- Kalvelagen, E, Model Building with GAMS. forthcoming
Small Model of Type: NLP Includes: qpdata.inc
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$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.
$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));
variables z objective variable
x(stocks) investments
w(days) intermediate variables
;
positive variables x;
equations 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 minizing z;
display x.l;
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