Revision 8e8882847d428a8f6e4080507e95b42acc6674ad authored by Rene Brun on 26 September 2006, 13:44:50 UTC, committed by Rene Brun on 26 September 2006, 13:44:50 UTC
When loading the geometry from a file, the element table is recreated (never streamed) so the attribute flags (defined/used) of elements are lost. The patch loops over all defined materials/mixtures in this case and restores the flags. Affected: TFluka when geometry was loaded from the file. git-svn-id: http://root.cern.ch/svn/root/trunk@16348 27541ba8-7e3a-0410-8455-c3a389f83636
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portfolio.C
#include "Riostream.h"
#include "TCanvas.h"
#include "TFile.h"
#include "TTree.h"
#include "TArrayF.h"
#include "TH1.h"
#include "TF1.h"
#include "TLegend.h"
#include "TSystem.h"
#include "TMatrixD.h"
#include "TMatrixDSym.h"
#include "TVectorD.h"
#include "TQpProbDens.h"
#include "TGondzioSolver.h"
// Running this macro :
// .x portfolio.C+
// or gSystem->Load("libQuadp"); .L portFolio.C+; portfolio()
//
// This macro shows in detail the use of the quadratic programming package quadp .
// Let's first review what we exactly mean by "quadratic programming" :
//
// We want to minimize the following objective function :
//
// c^T x + ( 1/2 ) x^T Q x wrt. the vector x
//
// c is a vector and Q a symmetric positive definite matrix
//
// You might wonder what is so special about this objective which is quadratic in
// the unknowns, that can not be done by Minuit/Fumili . Well, we have in addition
// the following boundary conditions on x:
//
// A x = b
// clo <= C x <= cup
// xlo <= x <= xup , where A and C are arbitray matrices and the rest are vectors
//
// Not all these constraints have to be defined . Our example will only use xlo, A and b
// Still, this could be handled by a general non-linear minimizer like Minuit by introducing
// so-called "slack" variables . However, quadp is tailored to objective functions not more
// complex than being quadratic . This allows usage of solving techniques which are even
// stable for problems involving for instance 500 variables, 100 inequality conditions
// and 50 equality conditions .
//
// Enough said about quadratic programming, let's return to our example .
// Suppose, after a long day of doing physics, you have a look at your investments and
// realize that an early retirement is not possible, given the returns of your stocks .
// So what now ? ROOT to the rescue ......
//
// In 1990 Harry Markowitz was awarded the Noble prize for economics : " his work provided new tools
// for weighing the risks and rewards of different investments and for valuing corporate stocks and bonds" .
// In plain English, he developed the tools to balance greed and fear, we want the maximum return
// with the minimum amount of risk. Our stock portfolio should be at the "Efficient Frontier",
// see http://www.riskglossary.com/articles/efficient_frontier.htm .
// To quantify better the risk we are willing to take, we define a utility function U(x) . It describes
// as a function of our total assets x, our "satisfaction" . A common choice is 1-exp(-k*x) (the reason for
// the exponent will be clear later) . The parameter k is the risk-aversion factor . For small values of k
// the satisfaction is small for small values of x; by increasing x the satisfaction can still be increased
// significantly . For large values of k, U(x) increases rapidly to 1, there is no increase in satisfaction
// for additional dollars earned .
//
// In summary : small k ==> risk-loving investor
// large k ==> risk-averse investor
//
// Suppose we have for nrStocks the historical daily returns r = closing_price(n) - closing_price(n-1) .
// Define a vector x of length of nrStocks, which contains the fraction of our money invested in
// each stock . We can calculate the average daily return z of our portfolio and its variance using
// the portfolio covariance Covar :
//
// z = r^T x and var = x^T Covar x
//
// Assuming that the daily returns have a Normal distribution, N(x), so will z with mean r^T x
// and variance x^T Covar x
//
// The expected value of the utility function is : E(u(x)) = Int (1-exp(-k*x) N(x) dx
// = 1-exp(-k (r^T x - 0.5 k x^T Covar x) )
//
// Its value is maximized by maximizing r^T x -0.5 k x^T Covar x
// under the condition sum (x_i) = 1, meaning we want all our money invested and
// x_i >= 0 , we can not "short" a stock
//
// For 10 stocks we got the historical daily data for Sep-2000 to Jun-2004:
//
// GE : General Electric Co
// SUNW : Sun Microsystems Inc
// QCOM : Qualcomm Inc
// BRCM : Broadcom Corp
// TYC : Tyco International Ltd
// IBM : International Business Machines Corp
// AMAT : Applied Materials Inc
// C : Citigroup Inc
// PFE : Pfizer Inc
// HD : Home Depot Inc
//
// We calculate the optimal portfolio for 2.0 and 10.0 .
//
// Food for thought :
// - We assumed that the stock returns have a Normal distribution . Check this assumption by
// histogramming the stock returns !
// - We used for the expected return in the objective function, the flat average over a time
// period . Investment firms will put significant resources in improving the return predicton .
// - If you want to trade significant number of shares, several other considerations have
// to be taken into account :
// + If you are going to buy, you will drive the price up (so-called "slippage") .
// This can be taken into account by adding terms to the objective
// (Google for "slippage optimization")
// + FTC regulations might have to be added to the inequality constraints
// - Investment firms do not want to be exposed to the "market" as defined by a broad
// index like the S&P and "hedge" this exposure away . A perfect hedge this can be added
// as an equality constrain, otherwise add an inequality constrain .
const Int_t nrStocks = 10;
static const Char_t *stocks[] =
{"GE","SUNW","QCOM","BRCM","TYC","IBM","AMAT","C","PFE","HD"};
class TStockDaily {
public:
Int_t fDate;
Int_t fOpen; // 100*open_price
Int_t fHigh; // 100*high_price
Int_t fLow; // 100*low_price
Int_t fClose; // 100*close_price
Int_t fVol;
Int_t fCloseAdj; // 100*close_price adjusted for splits and dividend
TStockDaily() {
fDate = fVol = fOpen = fHigh = fLow = fClose = fCloseAdj = 0;
}
virtual ~TStockDaily() {}
ClassDef(TStockDaily,1)
};
//---------------------------------------------------------------------------
Double_t RiskProfile(Double_t *x, Double_t *par) {
Double_t riskFactor = par[0];
return 1-TMath::Exp(-riskFactor*x[0]);
}
//---------------------------------------------------------------------------
TArrayF &StockReturn(TFile *f,const TString &name,Int_t sDay,Int_t eDay)
{
TTree *tDaily = (TTree*)f->Get(name);
TStockDaily *data = 0;
tDaily->SetBranchAddress("daily",&data);
TBranch *b_closeAdj = tDaily->GetBranch("fCloseAdj");
TBranch *b_date = tDaily->GetBranch("fDate");
//read only the "adjusted close" branch for all entries
const Int_t nrEntries = (Int_t)tDaily->GetEntries();
TArrayF closeAdj(nrEntries);
for (Int_t i = 0; i < nrEntries; i++) {
b_date->GetEntry(i);
b_closeAdj->GetEntry(i);
if (data->fDate >= sDay && data->fDate <= eDay)
#ifdef __CINT__
closeAdj.AddAt(data->fCloseAdj/100. , i );
#else
closeAdj[i] = data->fCloseAdj/100.;
#endif
}
TArrayF *r = new TArrayF(nrEntries-1);
for (Int_t i = 1; i < nrEntries; i++)
// (*r)[i-1] = closeAdj[i]-closeAdj[i-1];
#ifdef __CINT__
r->AddAt(closeAdj[i]/closeAdj[i-1],1);
#else
(*r)[i-1] = closeAdj[i]/closeAdj[i-1];
#endif
return *r;
}
#ifndef __MAKECINT__
//---------------------------------------------------------------------------
TVectorD OptimalInvest(Double_t riskFactor,TVectorD r,TMatrixDSym Covar)
{
// what the quadratic programming package will do:
//
// minimize c^T x + ( 1/2 ) x^T Q x
// subject to A x = b
// clo <= C x <= cup
// xlo <= x <= xup
// what we want :
//
// maximize c^T x - k ( 1/2 ) x^T Q x
// subject to sum_x x_i = 1
// 0 <= x_i
// We have nrStocks weights to determine,
// 1 equality- and 0 inequality- equations (the simple square boundary
// condition (xlo <= x <= xup) does not count)
const Int_t nrVar = nrStocks;
const Int_t nrEqual = 1;
const Int_t nrInEqual = 0;
// flip the sign of the objective function because we want to maximize
TVectorD c = -1.*r;
TMatrixDSym Q = riskFactor*Covar;
// equality equation
TMatrixD A(nrEqual,nrVar); A = 1;
TVectorD b(nrEqual); b = 1;
// inequality equation
//
// - although not applicable in the current situatio since nrInEqual = 0, one
// has to specify not only clo and cup but also an index vector iclo and icup,
// whose values are either 0 or 1 . If iclo[j] = 1, the lower boundary condition
// is active on x[j], etc. ...
TMatrixD C (nrInEqual,nrVar);
TVectorD clo (nrInEqual);
TVectorD cup (nrInEqual);
TVectorD iclo(nrInEqual);
TVectorD icup(nrInEqual);
// simple square boundary condition : 0 <= x_i, so only xlo is relevant .
// Like for clo and cup above, we have to define an index vector ixlo and ixup .
// Since each variable has the lower boundary, we can set the whole vector
// ixlo = 1
TVectorD xlo (nrVar); xlo = 0;
TVectorD xup (nrVar); xup = 0;
TVectorD ixlo(nrVar); ixlo = 1;
TVectorD ixup(nrVar); ixup = 0;
// setup the quadratic programming problem . Since a small number of variables are
// involved and "Q" has everywhere entries, we chose the dense version "TQpProbDens" .
// In case of a sparse formulation, simply replace all "Dens" by "Sparse" below and
// use TMatrixDSparse instead of TMatrixDSym and TMatrixD
TQpProbDens *qp = new TQpProbDens(nrVar,nrEqual,nrInEqual);
// stuff all the matrices/vectors defined above in the proper places
TQpDataDens *prob = (TQpDataDens *)qp->MakeData(c,Q,xlo,ixlo,xup,ixup,A,b,C,clo,iclo,cup,icup);
// setup the nrStock variables, vars->fX will contain the final solution
TQpVar *vars = qp->MakeVariables(prob);
TQpResidual *resid = qp->MakeResiduals(prob);
// Now we have to choose the method of solving, either TGondzioSolver or TMehrotraSolver
// The Gondzio method is more sophisticated and therefore numerically more involved
// If one want the Mehrotra method, simply replace "Gondzio" by "Mehrotra" .
TGondzioSolver *s = new TGondzioSolver(qp,prob);
const Int_t status = s->Solve(prob,vars,resid);
const TVectorD weight = vars->fX;
delete qp; delete prob; delete vars; delete resid; delete s;
if (status != 0) {
cout << "Could not solve this problem." <<endl;
return TVectorD(nrStocks);
}
return weight;
}
#endif
//---------------------------------------------------------------------------
void portfolio()
{
const Int_t sDay = 20000809;
const Int_t eDay = 20040602;
const char *fname = "stock.root";
TFile *f = 0;
if (!gSystem->AccessPathName(fname)) {
f = TFile::Open(fname);
} else {
printf("accessing %s file from http://root.cern.ch/files\n",fname);
f = TFile::Open(Form("http://root.cern.ch/files/%s",fname));
}
if (!f) return;
TArrayF *data = new TArrayF[nrStocks];
for (Int_t i = 0; i < nrStocks; i++) {
const TString symbol = stocks[i];
data[i] = StockReturn(f,symbol,sDay,eDay);
}
const Int_t nrData = data[0].GetSize();
TVectorD r(nrStocks);
for (Int_t i = 0; i < nrStocks; i++)
r[i] = data[i].GetSum()/nrData;
TMatrixDSym Covar(nrStocks);
for (Int_t i = 0; i < nrStocks; i++) {
for (Int_t j = 0; j <= i; j++) {
Double_t sum = 0.;
for (Int_t k = 0; k < nrData; k++)
sum += (data[i][k]-r[i])*(data[j][k]-r[j]);
Covar(i,j) = Covar(j,i) = sum/nrData;
}
}
const TVectorD weight1 = OptimalInvest(2.0,r,Covar);
const TVectorD weight2 = OptimalInvest(10.,r,Covar);
cout << "stock daily daily w1 w2" <<endl;
cout << "symb return sdv " <<endl;
for (Int_t i = 0; i < nrStocks; i++)
printf("%s\t: %.3f %.3f %.3f %.3f\n",stocks[i],r[i],TMath::Sqrt(Covar[i][i]),weight1[i],weight2[i]);
TCanvas *c1 = new TCanvas("c1","Portfolio Optimizations",10,10,800,900);
c1->Divide(1,2);
// utility function / risk profile
c1->cd(1);
gPad->SetGridx();
gPad->SetGridy();
TF1 *f1 = new TF1("f1",RiskProfile,0,2.5,1);
f1->SetParameter(0,2.0);
f1->SetLineColor(49);
f1->Draw("AC");
f1->GetHistogram()->SetXTitle("dollar");
f1->GetHistogram()->SetYTitle("utility");
f1->GetHistogram()->SetMinimum(0.0);
f1->GetHistogram()->SetMaximum(1.0);
TF1 *f2 = new TF1("f2",RiskProfile,0,2.5,1);
f2->SetParameter(0,10.);
f2->SetLineColor(50);
f2->Draw("CSAME");
TLegend *legend1 = new TLegend(0.50,0.65,0.70,0.82);
legend1->AddEntry(f1,"1-exp(-2.0*x)","l");
legend1->AddEntry(f2,"1-exp(-10.*x)","l");
legend1->Draw();
// vertical bar chart of portfolio distribution
c1->cd(2);
TH1F *h1 = new TH1F("h1","Portfolio Distribution",nrStocks,0,0);
TH1F *h2 = new TH1F("h2","Portfolio Distribution",nrStocks,0,0);
h1->SetStats(0);
h1->SetFillColor(49);
h2->SetFillColor(50);
h1->SetBarWidth(0.45);
h1->SetBarOffset(0.1);
h2->SetBarWidth(0.4);
h2->SetBarOffset(0.55);
for (Int_t i = 0; i < nrStocks; i++) {
h1->Fill(stocks[i],weight1[i]);
h2->Fill(stocks[i],weight2[i]);
}
h1->Draw("BAR2");
h2->Draw("BAR2SAME");
TLegend *legend2 = new TLegend(0.50,0.65,0.70,0.82);
legend2->AddEntry(h1,"high risk","f");
legend2->AddEntry(h2,"low risk","f");
legend2->Draw();
}
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