NAGJavaExamples/QCQP/portfolioOptimizationQCQP.java at main · vedsgit/NAGJavaExamples · GitHub

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import com.nag.routines.G02.G02BX;

import com.nag.routines.E04.E04RA;

import com.nag.routines.E04.E04RS;

import com.nag.routines.E04.E04RJ;

import com.nag.routines.E04.E04RH;

import com.nag.routines.E04.E04ZM;

import com.nag.routines.E04.E04PT;

import com.nag.routines.E04.E04PTU;

import com.nag.routines.E04.E04RZ;

import java.io.BufferedReader;

import java.io.File;

import java.io.FileReader;

import java.io.FileNotFoundException;

import java.io.IOException;

import java.util.Map;

import java.util.LinkedHashMap;

import java.util.Arrays;

import java.util.ArrayList;

import java.io.FileWriter;

public class portfolioOptimizationQCQP {

public final static String dataFolder = "data";

public static String dataFile = "data" + File.separator + "djia_close_price.csv";

public static void main(String[] args) {

int i, j;

E04RA e04ra = new E04RA();

E04RS e04rs = new E04RS();

E04RJ e04rj = new E04RJ();

E04RH e04rh = new E04RH();

E04ZM e04zm = new E04ZM();

E04PT e04pt = new E04PT();

MONIT monit = new MONIT();

E04RZ e04rz = new E04RZ();

// Data Preparation

// Load stock price data from djia_close_price.csv

String[] dateIndex = new String[0];

Map<String, double[]> closePrice = new LinkedHashMap<>();

try {

BufferedReader reader = new BufferedReader(new FileReader(dataFile));

String line = reader.readLine().substring(1);

dateIndex = line.split(",");

String[] data;

String key;

double[] values;

while ((line = reader.readLine()) != null) {

data = line.split(",");

key = data[0];

values = parseDoubleArr(Arrays.copyOfRange(data, 1, data.length));

closePrice.put(key, values);

}

reader.close();

} catch (FileNotFoundException e) {

System.err.println("***FATAL: Can't find " + dataFile);

System.exit(-2);

} catch (IOException e) {

System.err.println("***FATAL: Can't read " + dataFile + "\n" + e.getMessage());

}

int m = dateIndex.length;

int n = closePrice.size();

double[][] data = new double[m][n];

i = 0;

for (Map.Entry<String, double[]> entry : closePrice.entrySet()) {

double[] tempA = entry.getValue();

for (j = 0; j < m; j++) {

data[j][i] = tempA[j];

}

i++;

}

// Relative return

double[][] relRtn = new double[m - 1][n];

for (j = 0; j < m - 1; j++) {

for (i = 0; i < n; i++) {

relRtn[j][i] = (data[j + 1][i] - data[j][i]) / data[j][i];

}

printMatrixToFile(relRtn, "relRtn.d");

// Mean return

double[] r = new double[n];

for (j = 0; j < n; j++) {

double sum = 0;

for (i = 0; i < m - 1; i++) {

sum += relRtn[i][j];

}

r[j] = sum;

r[j] /= m - 1;

}

// Covariance matrix

G02BX g02bx = new G02BX();

String weight = "U";

n = relRtn.length;

m = relRtn[0].length;

int ldx = n;

double[] x1d = convert2DTo1D(relRtn);

double[] wt = new double[0];

double[] xbar = new double[m];

double[] std = new double[m];

int ldv = m;

double[] v1d = new double[ldv * m];

double[] r1d = new double[ldv * m];

int ifail = 0;

g02bx.eval(weight, n, m, x1d, ldx, wt, xbar, std, v1d, ldv, r1d, ifail);

double[][] V = convert1DTo2D(v1d, m);

// Classic Mean-Variance Model

// Efficient Frontier

int itemsDiagLength = V.length;

int itemsAboveDiagLength = (int) (Math.pow(itemsDiagLength, 2) - itemsDiagLength) / 2 + itemsDiagLength;

int[] irowq = new int[itemsAboveDiagLength];

int[] icolq = new int[itemsAboveDiagLength];

double[] vVal = new double[itemsAboveDiagLength];

int c = 0;

// Input for quadratic objective

// Sparsity pattern of upper triangular V

for (i = 0; i < V.length; i++) {

for (j = i; j < V[0].length; j++) {

vVal[c] = V[i][j];

irowq[c] = i + 1;

icolq[c] = j + 1;

c++;

}

n = closePrice.size();

// Sparsity pattern of r, which is actually dense in this application

int[] idxr = new int[n];

for (i = 0; i < n; i++) {

idxr[i] = i + 1;

}

// Input for linear constraint: e'x = 1

int[] irowa = new int[n];

int[] icola = new int[n];

double[] a = new double[n];

double[] bl = new double[1];

double[] bu = new double[1];

double[] blx = new double[n];

double[] bux = new double[n];

Arrays.fill(irowa, 1);

for (i = 0; i < n; i++) {

icola[i] = i + 1;

}

Arrays.fill(a, 1.0);

bl[0] = 1.0;

bu[0] = 1.0;

// Input for bound constraint: x >= 0

Arrays.fill(blx, 0.0);

Arrays.fill(bux, 1.0e20);

// Set step for mu

int step = 2001;

// Initialize output data: absolute risk and return

ArrayList<Double> abRisk = new ArrayList<>();

ArrayList<Double> abRtn = new ArrayList<>();

int mu;

long handle = 0;

double[] q = new double[vVal.length];

int idqc;

double[] invertSignR = invertSignVector(r);

double[] x = new double[n];

double[] u = new double[0];

double[] uc = new double[0];

double[] rinfo = new double[100];

double[] stats = new double[100];

int[] iuser = new int[2];

double[] ruser = new double[1];

long cpuser = 0;

double[][] x2d;

double[][] VX;

double[][] XVX;

double[][] r2d;

double[][] RX;

for (mu = 0; mu < step; mu++) {

ifail = 0;

// Create problem handle

e04ra.eval(handle, n, ifail);

handle = e04ra.getHANDLE();

// Set quadratic objective function

// In qcqp standard form q should be 2*mu*V

for (i = 0; i < q.length; i++) {

q[i] = 2.0 * mu * vVal[i];

}

idqc = -1;

e04rs.eval(handle, 0.0, nonZeroLength(invertSignR), idxr, invertSignR, nonZeroLength(q), irowq, icolq, q,

idqc, ifail);

// Set linear constraint e'x = 1

e04rj.eval(handle, bl.length, bl, bu, nonZeroLength(a), irowa, icola, a, 0, ifail);

// Set bound constraint

e04rh.eval(handle, n, blx, bux, ifail);

// set options

e04zm.eval(handle, "Print Options = NO", ifail);

e04zm.eval(handle, "Print Level = 1", ifail);

e04zm.eval(handle, "Print File = -1", ifail);

e04zm.eval(handle, "SOCP Scaling = A", ifail);

// Call socp interior point solver

ifail = 1;

e04pt.eval(handle, n, x, 0, u, 0, uc, rinfo, stats, monit, iuser, ruser, cpuser, ifail);

ifail = e04pt.getIFAIL();

if (ifail == 0) {

// Compute risk and return from the portfolio

x2d = convert1DTo2D(x, x.length);

VX = multiplyMatrices(V, x2d);

XVX = multiplyMatrices(invertRowColMatrix(x2d), VX);

abRisk.add(Math.sqrt(XVX[0][0]));

r2d = convert1DTo2D(r, r.length);

RX = multiplyMatrices(invertRowColMatrix(r2d), x2d);

abRtn.add(RX[0][0]);

}

// Destroy the handle:

e04rz.eval(handle, ifail);

handle = e04rz.getHANDLE();

}

printVectorToFile(toArray(abRisk), "abRisk.d");

printVectorToFile(toArray(abRtn), "abRtn.d");

// Maximizing the Sharpe ratio

// Input for linear constraint: e'y = lambda

irowa = new int[(n + 1) + n];

icola = new int[(n + 1) + n];

a = new double[(n + 1) + n];

bl = new double[2];

bu = new double[2];

blx = new double[n + 1];

bux = new double[n + 1];

Arrays.fill(irowa, 0, n + 1, 1);

for (i = 0; i <= n; i++) {

icola[i] = i + 1;

}

Arrays.fill(a, 0, n, 1.0);

a[n] = -1.0;

bl[0] = 0.0;

bu[0] = 0.0;

// Input for linear constraint: r'y = 1

Arrays.fill(irowa, n + 1, irowa.length, 2);

for (i = 0; i < n; i++) {

icola[(n + 1) + i] = i + 1;

}

for (i = 0; i < n; i++) {

a[(n + 1) + i] = r[i];

}

bl[1] = 1.0;

bu[1] = 1.0;

// Input for bound constraint: x >= 0

Arrays.fill(blx, 0.0);

Arrays.fill(bux, 1.0e20);

ifail = 0;

// Create problem handle

e04ra.eval(handle, n + 1, ifail);

handle = e04ra.getHANDLE();

// Set quadratic objective function

// In qcqp standard form q should be 2*V

for (i = 0; i < q.length; i++) {

q[i] = 2.0 * vVal[i];

}

idqc = -1;

e04rs.eval(handle, 0.0, 0, idxr, r, nonZeroLength(q), irowq, icolq, q, idqc, ifail);

// Set linear constraints

e04rj.eval(handle, bl.length, bl, bu, nonZeroLength(a), irowa, icola, a, 0, ifail);

// Set bound constraint

e04rh.eval(handle, blx.length, blx, bux, ifail);

// Set options

e04zm.eval(handle, "Print Options = NO", ifail);

e04zm.eval(handle, "Print Level = 1", ifail);

e04zm.eval(handle, "Print File = -1", ifail);

e04zm.eval(handle, "SOCP Scaling = A", ifail);

// Call socp interior point solver

x = new double[n + 1];

e04pt.eval(handle, n + 1, x, 0, u, 0, uc, rinfo, stats, monit, iuser, ruser, cpuser, ifail);

x2d = convert1DTo2D(x, n);

VX = multiplyMatrices(V, x2d);

XVX = multiplyMatrices(invertRowColMatrix(x2d), VX);

double srRisk = Math.sqrt(XVX[0][0]) / x[n];

r2d = convert1DTo2D(r, n);

RX = multiplyMatrices(invertRowColMatrix(r2d), x2d);

double srRtn = RX[0][0] / x[n];

double[] srX = new double[n];

for (i = 0; i < srX.length; i++) {

srX[i] = x[i] / x[n];

}

// Destroy the handle:

e04rz.eval(handle, ifail);

handle = e04rz.getHANDLE();

printVectorToFile(new double[]{srRisk, srRtn}, "sr.d");

// Portfolio optimization with tracking-error constraint

// Generate a benchmark portfolio from efficient portfolio that maximize the

// Sharpe ratio

// Perturb x

double[] b = new double[n];

double sumB = 0;

for (i = 0; i < b.length; i++) {

b[i] = srX[i] + 1.0e-1;

sumB += b[i];

}

// Normalize b

for (i = 0; i < b.length; i++) {

b[i] /= sumB;

}

// Set limit on tracking-error

double tev = 0.000002;

// Compute risk and return at the benchmark

double[][] b2d = convert1DTo2D(b, n);

double[][] VB = multiplyMatrices(V, b2d);

double[][] BVB = multiplyMatrices(invertRowColMatrix(b2d), VB);

double bRisk = Math.sqrt(BVB[0][0]);

r2d = convert1DTo2D(r, n);

double[][] RB = multiplyMatrices(invertRowColMatrix(r2d), b2d);

double bRtn = RB[0][0];

irowa = new int[n];

icola = new int[n];

a = new double[n];

bl = new double[1];

bu = new double[1];

// Input for linear constraint: e'x = 0

Arrays.fill(irowa, 1);

for (i = 0; i < icola.length; i++) {

icola[i] = i + 1;

}

Arrays.fill(a, 1.0);

bl[0] = 0;

bu[0] = 0;

// Input for bound constraint: x >= -b

blx = invertSignVector(b);

Arrays.fill(bux, 1.0e20);

// Initialize output data: TEV risk and return

ArrayList<Double> tevRisk = new ArrayList<>();

ArrayList<Double> tevRtn = new ArrayList<>();

double[] rMu = new double[n];

double[][] Vb;

double[] Vb1d;

x = new double[n];

double[] xb;

double[][] xb2d;

double[][] xbVxb;

for (mu = 0; mu < step; mu++) {

ifail = 0;

// Create problem handle

e04ra.eval(handle, n, ifail);

handle = e04ra.getHANDLE();

// Set quadratic objective function

// In qcqp standard form q should be 2*mu*V

for (i = 0; i < q.length; i++) {

q[i] = 2.0 * mu * vVal[i];

}

Vb = multiplyMatrices(V, b2d);

Vb1d = convert2DTo1D(Vb);

for (i = 0; i < rMu.length; i++) {

rMu[i] = 2.0 * mu * Vb1d[i] - r[i];

}

idqc = -1;

e04rs.eval(handle, 0.0, nonZeroLength(rMu), idxr, rMu, nonZeroLength(q), irowq, icolq, q, idqc, ifail);

// Set quadratic constraint

// In qcqp standard form q should be 2*V

for (i = 0; i < q.length; i++) {

q[i] = 2.0 * vVal[i];

}

idqc = 0;

e04rs.eval(handle, -tev, 0, idxr, rMu, nonZeroLength(q), irowq, icolq, q, idqc, ifail);

// Set linear constraint e'x = 1

e04rj.eval(handle, bl.length, bl, bu, nonZeroLength(a), irowa, icola, a, 0, ifail);

// Set bound constraint

e04rh.eval(handle, blx.length, blx, bux, ifail);

// Set options

e04zm.eval(handle, "Print Options = NO", ifail);

e04zm.eval(handle, "Print Level = 1", ifail);

e04zm.eval(handle, "Print File = -1", ifail);

e04zm.eval(handle, "SOCP Scaling = A", ifail);

// Call socp interior point solver

// Mute warnings and do not count results from warnings

ifail = -1;

e04pt.eval(handle, n, x, 0, u, 0, uc, rinfo, stats, monit, iuser, ruser, cpuser, ifail);

ifail = e04pt.getIFAIL();

if (ifail == 0) {

// Compute risk and return from the portfolio

xb = addVectors(x, b);

xb2d = convert1DTo2D(xb, xb.length);

xbVxb = multiplyMatrices(invertRowColMatrix(xb2d), multiplyMatrices(V, xb2d));

tevRisk.add(Math.sqrt(xbVxb[0][0]));

tevRtn.add(multiplyMatrices(invertRowColMatrix(r2d), xb2d)[0][0]);

}

// Destroy the handle:

e04rz.eval(handle, ifail);

handle = e04rz.getHANDLE();

}

printVectorToFile(new double[]{bRisk, bRtn}, "b.d");

printVectorToFile(toArray(tevRisk), "tevRisk.d");

printVectorToFile(toArray(tevRtn), "tevRtn.d");

}

public static class MONIT extends E04PT.Abstract_E04PT_MONIT {

public void eval() {

E04PTU e04ptu = new E04PTU();

e04ptu.eval(this.HANDLE, this.RINFO, this.STATS, this.IUSER, this.RUSER, this.CPUSER, this.INFORM);

this.INFORM = e04ptu.getINFORM();

}

public static double[][] invertRowColMatrix(double[][] a) {

double[][] t = new double[a[0].length][a.length];

for (int i = 0; i < a.length; i++) {

for (int j = 0; j < a[0].length; j++) {

t[j][i] = a[i][j];

}

return t;

}

public static double[] invertSignVector(double[] a) {

double[] t = new double[a.length];

for (int i = 0; i < t.length; i++) {

t[i] = -a[i];

}

return t;

}

public static int nonZeroLength(double[] a) {

int c = 0;

for (int i = 0; i < a.length; i++) {

if (a[i] != 0) {

c++;

}

return c;

}

public static double[] parseDoubleArr(String[] a) {

double[] t = new double[a.length];

for (int i = 0; i < t.length; i++) {

t[i] = Double.parseDouble(a[i]);

}

return t;

}

public static double[] convert2DTo1D(double[][] a) {

double[] b = new double[a.length * a[0].length];

int n = a.length;

for (int i = 0; i < a.length; i++) {

for (int j = 0; j < a[0].length; j++) {

b[i + j * n] = a[i][j];

}

return b;

}

public static double[][] convert1DTo2D(double[] a, int n) {

double[][] b = new double[n][a.length / n];

for (int i = 0; i < b.length; i++) {

for (int j = 0; j < b[0].length; j++) {

b[i][j] = a[i + j * n];

}

return b;

}

public static double[] addVectors(double[] a, double[] b) {

double[] t = new double[a.length];

for (int i = 0; i < t.length; i++) {

t[i] = a[i] + b[i];

}

return t;

}

public static double[][] multiplyMatrices(double[][] firstMatrix, double[][] secondMatrix) {

double[][] result = new double[firstMatrix.length][secondMatrix[0].length];

for (int row = 0; row < result.length; row++) {

for (int col = 0; col < result[row].length; col++) {

result[row][col] = multiplyMatricesCell(firstMatrix, secondMatrix, row, col);

}

return result;

}

private static double multiplyMatricesCell(double[][] firstMatrix, double[][] secondMatrix, int row, int col) {

double cell = 0;

for (int i = 0; i < secondMatrix.length; i++) {

cell += firstMatrix[row][i] * secondMatrix[i][col];

}

return cell;

}

public static double[] toArray(ArrayList<Double> list) {

double[] t = new double[list.size()];

for (int i = 0; i < t.length; i++) {

t[i] = (double) list.get(i);

}

return t;

}

public static void printVectorToFile(double[] a, String fileName) {

try {

FileWriter writer = new FileWriter(new File(dataFolder + File.separator + fileName));

for (int i = 0; i < a.length; i++) {

writer.write(a[i] + "\n");

}

writer.close();

} catch (IOException e) {

System.out.println(e.getMessage());

e.printStackTrace();

}

public static void printMatrixToFile(double[][] a, String fileName) {

try {

FileWriter writer = new FileWriter(new File(dataFolder + File.separator + fileName));

for (int i = 0; i < a.length; i++) {

for (int j = 0; j < a[0].length; j++) {

writer.write(a[i][j] + " ");

}

writer.write("\n");

}

writer.close();

} catch (IOException e) {

System.out.println(e.getMessage());

e.printStackTrace();

}

NAGJavaExamples/QCQP/portfolioOptimizationQCQP.java at main · vedsgit/NAGJavaExamples · GitHub

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