Description
Optimization model to pick a small subset of the stocks together with some weights, such that this portfolio has a similar behavior to our overall Dow Jones index.
Category : GAMS Data Utilities library
Main file : pickstock.gms includes : pickstock.gms dowjones2016.csv
$title Stock Selection Optimization
* Optimization model to pick a small subset of the stocks together with
* some weights, such that this portfolio has a similar behavior to our
* overall Dow Jones index.
Set date 'date'
symbol 'stock symbol';
$onExternalInput
Parameter price(date<,symbol<) 'Price';
Scalar maxstock 'maximum number of stocks to select' / 2 /
trainingdays 'number of days for training' / 99 /;
$setNames "%gams.input%" fp fn fe
$if not set fileName $set fileName %fp%dowjones2016.csv
$call.checkErrorLevel gamstool csvread "%fileName%" gdxout=stockdata.gdx id=price Index=1,2 Values=3 UseHeader=y > %system.nullfile% 2>&1
$gdxIn stockdata
$load price
$offExternalInput
Alias (d,date), (s,symbol);
Parameter
avgprice(symbol) 'average price of stock'
weight(symbol) 'weight of stock'
contribution(date,symbol) 'contribution of stock on date'
index(date) 'Dow Jones index';
Parameter
fund(date) 'Index fund report parameter'
error(date) 'Absolute error';
Set td(date) 'training days'
ntd(date) 'none-training days';
* input validataion
set error01(date, symbol);
error01(date, symbol) = price(date, symbol) < 0;
file log / miro.log /;
put log '------------------------------------'/;
put log ' Data validation'/;
put log '------------------------------------'/;
if(card(error01),
put log 'price:: No negative prices allowed!'/;
loop(error01(date, symbol),
put log / ' Symbol ' symbol.tl:4 ' has negative price at the date: ' date.tl:0;
);
abort "Data errors detected."
);
putclose log;
avgprice(s) = sum(d, price(d,s))/card(d);
weight(symbol) = avgprice(symbol)/sum(s, avgprice(s));
contribution(d,s) = weight(s)*price(d,s);
index(d) = sum(s, contribution(d,s));
Variable
p(symbol) 'is stock included?'
w(symbol) 'what part of the portfolio'
slpos(date) 'positive slack'
slneg(date) 'negative slack'
obj 'objective';
Positive variables w, slpos, slneg;
Binary variable p;
Equation
deffit(date) 'fit to Dow Jones index'
defpick(symbol) 'can only use stock if picked'
defnumstock 'few stocks allowed'
defobj 'absolute violation (L1 norm) from index';
deffit(td).. sum(s, price(td,s)*w(s)) =e= index(td) + slpos(td) - slneg(td);
defpick(s).. w(s) =l= p(s);
defnumstock.. sum(s, p(s)) =l= maxstock;
defobj.. obj =e= sum(td, slpos(td) + slneg(td));
Model pickStock /all/;
option optCR=0.01;
td(d) = ord(d)<=trainingdays;
ntd(d) = not td(d);
solve pickStock min obj using mip;
fund(d) = sum(s, price(d, s)*w.l(s));
error(d) = abs(index(d)-fund(d));
Set fHdr 'fund header' / dj 'dow jones','index fund' /
errHdr 'stock symbol header' / 'absolute error train', 'absolute error test' /;
$onExternalOutput
Scalar error_train 'Absolute error in entire training phase'
error_test 'Absolute error in entire testing phase'
error_ratio 'Ratio between error test and error train'
Parameter
stock_weight(symbol) 'weight'
dowVSindex(date,fHdr) 'dow jones vs. index fund'
abserror(date,errHdr) 'absolute error'
table dowVSindex;
table abserror;
Singleton Set
firstDayTraining(date) 'first date of training period'
lastDayTraining(date) 'last date of training period' ;
$offExternalOutput
stock_weight(s) = w.l(s);
dowVSindex(d,'dj') = index(d);
dowVSindex(d,'index fund') = fund(d);
abserror(td, 'absolute error train') = error(td);
abserror(ntd,'absolute error test') = error(ntd);
lastDayTraining(td) = td.pos=card(td);
firstDayTraining(td) = td.pos=1;
error_train = obj.l;
error_test = sum(ntd, error(ntd));
if(error_train > 0,
error_ratio = error_test/error_train;
else
error_ratio = inf;);
* parameter including all stocks and dow jones index
$onExternalOutput
Parameter priceMerge(date,*) 'Price (stocks & dow jones)';
$offExternalOutput
priceMerge(d,symbol) = price(d,symbol);
priceMerge(d,'DowJones') = index(d);