/// <summary>
/// Calculate the efficient frontier for a given covariance matrix and mean vector
/// </summary>
/// <param name="covariance">Covariance Matrix of assets included in portfolio</param>
/// <param name="mean">Expected return of assets in portfolio</param>
public IPortfolio Calculate()
{
// MVO using quadratic programming
// Optimal portfolio is:
// min(-dvec'bvec+1/2x'Dmat*x) - where ' is the transpose of vector/matrix
// Dmat - Covariance Matrix - quadratic terms
// dvec - [0..nAssets] - linear terms
// Amat - variable weigths in constraints equation
// bvec - constraint equalities
// with constraints
// A'x >= b
// meq = eqsumW
// Get mean returns of all instruments in portfolio
var meanReturns = from sp in _samplePortfolio
select sp.Mean;
// Get covariance matrix for all instruments in portfolio
var cov = from sp in _samplePortfolio
select new KeyValuePair <string, Dictionary <string, double> >(sp.ID, sp.Covariance);
var covariance = CovarianceMatrix.Create(cov.ToDictionary(a => a.Key, b => b.Value));
var portfConf = new ConfigurationManager(_samplePortfolio);
OptimizationResult result;
double[] dvec = new double[_samplePortfolio.Count].Zeros(_samplePortfolio.Count);
try
{
result = QuadProg.Solve(covariance, dvec, portfConf.Amat, portfConf.Bvec, portfConf.NumEquals);
}
catch (Exception e)
{
// Solution not found - create NaN Portfolio
result = new OptimizationResult(new double[] { double.NaN }, double.NaN);
// Log error
Console.WriteLine(e.Message);
}
int q = 0;
double sum = 0;
foreach (var m in meanReturns)
{
sum = sum + m * result.Solution[q];
q++;
}
var portf = PortfolioFactory.Create(_samplePortfolio, _samplePortfolio.Name, sum, result.Value);
for (int c = 0; c < result.Solution.Length; c++)
{
portf[_samplePortfolio[c].ID].Weight = result.Solution[c];
}
return(portf);
}
/// <summary>
/// Calculate the efficient frontier for a given covariance matrix and mean vector
/// </summary>
/// <param name="covariance">Covariance Matrix of assets included in portfolio</param>
/// <param name="mean">Expected return of assets in portfolio</param>
public IEnumerable <IPortfolio> Calculate(int digits = 4)
{
// MVO using quadratic programming
// Optimal portfolio is:
// min(-dvec'bvec+1/2x'Dmat*x) - where ' is the transpose of vector/matrix
// Dmat - Covariance Matrix - quadratic terms
// dvec - [0..nAssets] - linear terms
// Amat - variable weigths in constraints equation
// bvec - constraint equalities
// with constraints
// A'x >= b
// meq = eqsumW
var meanReturns = from sp in _samplePortfolio
select sp.Mean;
var cov = from ins in _samplePortfolio
select new KeyValuePair <string, Dictionary <string, double> >(ins.ID, ins.Covariance);
var covariance = CovarianceMatrix.Create(cov.ToDictionary(a => a.Key, b => b.Value));
List <IPortfolio> portfolios = new List <IPortfolio>();
// generate sequence of target returns for the efficient frontier and minimum variance locus
var targetReturns = new double[_numPortfolios].Seq(meanReturns.Min(), meanReturns.Max(), (int)_numPortfolios, digits);
double[] dvec = new double[_samplePortfolio.Count].Zeros(_samplePortfolio.Count);
// For every target return find the minimum variance portfolio
for (int i = 0; i < _numPortfolios; i++)
{
var portfConf = new ConfigurationManager(_samplePortfolio, targetReturns[i]);
OptimizationResult result;
try
{
result = QuadProg.Solve(covariance, dvec, portfConf.Amat, portfConf.Bvec, portfConf.NumEquals);
}
catch (Exception e)
{
// Solution not found - create NaN Portfolio
result = new OptimizationResult(new double[] { double.NaN }, double.NaN);
// Log error
Console.WriteLine(e.Message);
}
var portf = PortfolioFactory.Create(_samplePortfolio, i.ToString(), targetReturns[i], result.Value);
for (int c = 0; c < result.Solution.Length; c++)
{
portf[_samplePortfolio[c].ID].Weight = result.Solution[c];
}
portfolios.Add(portf);
}
return(portfolios);
}