/// <summary>
/// Calculates the residual risk (annualised standard deviation of the error term from the CAPM linear regession)
/// </summary>
/// <param name="asset">Asset time series</param>
/// <param name="benchmark">Benchmark time series</param>
/// <param name="riskfree">Risk-free rate of return specified as a fractional value, e.g. 0.05 for 5%</param>
/// <returns>Returns the standard deviation</returns>
public static double ResidualRisk(ITimeSeries <double> asset, ITimeSeries <double> benchmark, double riskfree = 0)
{
var Ra = asset.AsTimeSeries() - riskfree;
var Rb = benchmark.AsTimeSeries() - riskfree;
return(Math.Round(Statistics.StandardDeviation(Model.LinearRegression(Ra.Data, Rb.Data).Residuals) * Math.Sqrt(asset.PeriodsInYear()), DecimalDigits));
}
/// <summary>
/// Calculates the regression coefficients of the linear CAPM regresion model
/// </summary>
/// <param name="asset"></param>
/// <param name="benchmark"></param>
/// <param name="riskfree">Risk-free rate of return specified as a fractional value, e.g. 0.05 for 5%</param>
/// <returns>The CAPM coefficients - Alpha and Beta</returns>
public static CAPMCoefficients CAPModel(ITimeSeries <double> asset, ITimeSeries <double> benchmark, double riskfree = 0)
{
var Ra = asset.AsTimeSeries() - riskfree;
var Rb = benchmark.AsTimeSeries() - riskfree;
var capm = Model.LinearRegression(Ra.Data, Rb.Data);
return(new CAPMCoefficients(Math.Round(capm.Intercept, DecimalDigits), Math.Round(capm.Coefficients.First(), DecimalDigits)));
}
public void Result()
{
TimeSeriesFactory <double> .SampleData.RandomSeed = 8;
ITimeSeries <double> asset = TimeSeriesFactory <double> .SampleData.Gaussian(mu_a, sigma_a, numperiods : elements, freq : DataFrequency.Daily);
var res = PortfolioAnalytics.TrackingError(asset, benchmark);
var te = (asset.AsTimeSeries() - benchmark.AsTimeSeries()).AnnualisedStdDev();
Assert.AreEqual(te, res, 0.001);
}
/// <summary>
/// Calculates the portfolio tracking error, i.e. the annualised standard deviation of the difference in returns between the portfolio and the benchmark
/// </summary>
/// <param name="portfolio">Portfolio time series</param>
/// <param name="benchmark">Benchmark time series</param>
/// <returns></returns>
public static double TrackingError(ITimeSeries <double> portfolio, ITimeSeries <double> benchmark)
{
return(Math.Round((portfolio.AsTimeSeries() - benchmark.AsTimeSeries()).AnnualisedStdDev(), DecimalDigits));
}
