/// <summary>
/// Algorithm "beta" statistic - the covariance between the algorithm and benchmark performance, divided by benchmark's variance
/// </summary>
/// <param name="algoPerformance">Collection of double values for algorithm daily performance.</param>
/// <param name="benchmarkPerformance">Collection of double benchmark daily performance values.</param>
/// <remarks>Invokes the variance and covariance extensions in the MathNet Statistics class</remarks>
/// <returns>Value for beta</returns>
public static double Beta(List<double> algoPerformance, List<double> benchmarkPerformance)
{
return algoPerformance.Covariance(benchmarkPerformance) / benchmarkPerformance.Variance();
}
/// <summary>
/// Initializes a new instance of the <see cref="PortfolioStatistics"/> class
/// </summary>
/// <param name="profitLoss">Trade record of profits and losses</param>
/// <param name="equity">The list of daily equity values</param>
/// <param name="listPerformance">The list of algorithm performance values</param>
/// <param name="listBenchmark">The list of benchmark values</param>
/// <param name="startingCapital">The algorithm starting capital</param>
/// <param name="tradingDaysPerYear">The number of trading days per year</param>
public PortfolioStatistics(
SortedDictionary<DateTime, decimal> profitLoss,
SortedDictionary<DateTime, decimal> equity,
List<double> listPerformance,
List<double> listBenchmark,
decimal startingCapital,
int tradingDaysPerYear = 252)
{
if (startingCapital == 0) return;
var runningCapital = startingCapital;
var totalProfit = 0m;
var totalLoss = 0m;
var totalWins = 0;
var totalLosses = 0;
foreach (var pair in profitLoss)
{
var tradeProfitLoss = pair.Value;
if (tradeProfitLoss > 0)
{
totalProfit += tradeProfitLoss / runningCapital;
totalWins++;
}
else
{
totalLoss += tradeProfitLoss / runningCapital;
totalLosses++;
}
runningCapital += tradeProfitLoss;
}
AverageWinRate = totalWins == 0 ? 0 : totalProfit / totalWins;
AverageLossRate = totalLosses == 0 ? 0 : totalLoss / totalLosses;
ProfitLossRatio = AverageLossRate == 0 ? 0 : AverageWinRate / Math.Abs(AverageLossRate);
WinRate = profitLoss.Count == 0 ? 0 : (decimal)totalWins / profitLoss.Count;
LossRate = profitLoss.Count == 0 ? 0 : (decimal)totalLosses / profitLoss.Count;
Expectancy = WinRate * ProfitLossRatio - LossRate;
if (profitLoss.Count > 0)
{
TotalNetProfit = (equity.Values.LastOrDefault() / startingCapital) - 1;
}
var fractionOfYears = (decimal)(equity.Keys.LastOrDefault() - equity.Keys.FirstOrDefault()).TotalDays / 365;
CompoundingAnnualReturn = CompoundingAnnualPerformance(startingCapital, equity.Values.LastOrDefault(), fractionOfYears);
Drawdown = DrawdownPercent(equity, 3);
AnnualVariance = GetAnnualVariance(listPerformance, tradingDaysPerYear);
AnnualStandardDeviation = (decimal)Math.Sqrt((double)AnnualVariance);
var annualPerformance = GetAnnualPerformance(listPerformance, tradingDaysPerYear);
SharpeRatio = AnnualStandardDeviation == 0 ? 0 : (annualPerformance - RiskFreeRate) / AnnualStandardDeviation;
var benchmarkVariance = listBenchmark.Variance();
Beta = benchmarkVariance.IsNaNOrZero() ? 0 : (decimal)(listPerformance.Covariance(listBenchmark) / benchmarkVariance);
Alpha = Beta == 0 ? 0 : annualPerformance - (RiskFreeRate + Beta * (GetAnnualPerformance(listBenchmark, tradingDaysPerYear) - RiskFreeRate));
var correlation = Correlation.Pearson(listPerformance, listBenchmark);
var benchmarkAnnualVariance = benchmarkVariance * tradingDaysPerYear;
TrackingError = correlation.IsNaNOrZero() || benchmarkAnnualVariance.IsNaNOrZero() ? 0 :
(decimal)Math.Sqrt((double)AnnualVariance - 2 * correlation * (double)AnnualStandardDeviation * Math.Sqrt(benchmarkAnnualVariance) + benchmarkAnnualVariance);
InformationRatio = TrackingError == 0 ? 0 : (annualPerformance - GetAnnualPerformance(listBenchmark, tradingDaysPerYear)) / TrackingError;
TreynorRatio = Beta == 0 ? 0 : (annualPerformance - RiskFreeRate) / Beta;
}
