$title Standard QP Model- linear Approximation (QP5,SEQ=175)

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Linear approximation of qp4 operate directly on the data.
Additional information can be found at:

/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;