/// <summary>
/// Calculates Spearman's Rho.
/// Correlation of ranks of array elements.
/// </summary>
public static double SpearmansRho(double[] array1, double[] array2)
{
if (array1.Length != array2.Length)
{
throw new ArgumentException("Arrays must be the same length");
}
double[] rank1 = RankArray(array1);
double[] rank2 = RankArray(array2);
return(Moments.Correlation(rank1, rank2));
}
/// <summary>
/// Assumes returns are normally distributed.
/// WARNING: Not very accurate. Intended for educational use and as a baseline for comparison to other models.
/// </summary>
/// <param name="returnArray">Historical returns from which VaR is to be calculated. The last value, with the highest index is assumed to be the most recent data point.</param>
/// <param name="windowLength">Length of the VaR window. The number of historical returns that will be used to calculate the VaR.</param>
/// <param name="confidenceLevel">VaR confidence level. 95% and 99% are typical values. If confidenceLevel is 95% then we expect 95% of days to be better (have a more positive return) than the VaR.</param>
public static double NormalValueAtRisk(double[] returnArray, int windowLength, double confidenceLevel)
{
double[] da = new double[windowLength];
for (int i = 0; i < windowLength; i++)
{
da[i] = returnArray[returnArray.Length - windowLength + i];
}
double mean = Moments.Mean(da);
double standardDeviation = Moments.StandardDeviation(da);
double var = Distributions.NormalCumulativeDistributionFunctionInverse(1 - confidenceLevel, mean, standardDeviation);
return(-var); //By convention VaR is quoted as a positive value, even though it corresponds to a loss.
}
/// <summary>
/// Hybrid VaR is based on historical data, but weights more recent data more heavily.
/// </summary>
/// <param name="returnArray">Historical returns from which VaR is to be calculated. The last value, with the highest index is assumed to be the most recent data point.</param>
/// <param name="windowLength">Length of the VaR window. The number of historical returns that will be used to calculate the VaR.</param>
/// <param name="confidenceLevel">VaR confidence level. 95% and 99% are typical values. If confidenceLevel is 95% then we expect 95% of days to be better (have a more positive return) than the VaR.</param>
/// <param name="decayFactor">For a decay factor d, the most recent data point has weight 1, the second d, the third d^2, ...</param>
/// <param name="correctSerialCorrelation">If true, correction is for infinite return length.</param>
public static double HybridValueAtRisk(double[] returnArray, int windowLength, double confidenceLevel, double decayFactor, bool correctSerialCorrelation)
{
double uncorrected = HybridValueAtRisk(returnArray, windowLength, confidenceLevel, decayFactor);
if (!correctSerialCorrelation)
{
return(uncorrected);
}
double[] subArray = Tools.MostRecentValues(returnArray, windowLength);
double serialCorrelation = Moments.SerialCorrelation(subArray, decayFactor);
double varianceCorrectionFactor = SerialCorrelationCorrection.SerialCorrelationVarianceCorrection(serialCorrelation); //don't use version w/ windowLength. windowLenght != length. Length is how far back we go to get data for the calculation. windowLenght is the return lenght that we are correcting to (infinite, by default).
return(uncorrected * Math.Sqrt(varianceCorrectionFactor));
}
/// <summary>
/// Returns the incremental incremental VaR for the subportfolio relative to the portfolio.
/// </summary>
/// <param name="portfolioArray">Return array of portfolio. The last element (index = n-1), is the most recent.</param>
/// <param name="subPortfolioArray">Return array of the sub-portfolio for which incremental VaR is being measured. The last element (index = n-1), is the most recent.</param>
/// <param name="decayFactor">In most applications, the decay factor is between 0 and 1. Weigth on the last element in arrays is 1.0, the 2nd to last element d, 3rd to last d^2, ...</param>
/// <param name="portfolioValutAtRisk">Value at risk of the portfolio.</param>
/// <param name="length">Window length. Method uses the most recent n points, n = length.</param>
public static double IncrementalValueAtRisk(double[] portfolioArray, double[] subPortfolioArray, double decayFactor, double portfolioValutAtRisk, int length)
{
double[] portfolioArrayLen = Tools.MostRecentValues(portfolioArray, length);
double[] subPortfolioArrayLen = Tools.MostRecentValues(subPortfolioArray, length);
double portfolioStandardDeviation = Moments.StandardDeviation(portfolioArray, decayFactor, length);
if (Tools.ArrayAllEqual(subPortfolioArray))
{
return(0.0);
}
double iStandardDeviation = Moments.IncrementalStandardDeviation(portfolioArrayLen, subPortfolioArrayLen, decayFactor);
return((portfolioValutAtRisk / portfolioStandardDeviation) * iStandardDeviation);
}
/// <summary>
/// Returns the slope of an OLS regression analysis.
/// </summary>
/// <param name="yData">Data for the dependent variable, or regressand.</param>
/// <param name="xData">Data for the independent variable, or regressor.</param>
/// <param name="length">Window length. Method uses the most recent n points, n = length.</param>
public static double Beta(double[] yData, double[] xData, int length)
{
double[] xDataSubSet = Tools.MostRecentValues(xData, length);
double[] yDataSubSet = Tools.MostRecentValues(yData, length);
double mX = Moments.Mean(xData);
double mY = Moments.Mean(yData);
double sumXY = 0, sumXX = 0;
for (int i = 0; i < length; i++)
{
sumXY += xDataSubSet[i] * yDataSubSet[i];
sumXX += xDataSubSet[i] * xDataSubSet[i];
}
return((sumXY - length * mY * mX) / (sumXX - length * mX * mX));
}
/// <summary>
/// Returns the incremental incremental VaR for the subportfolio relative to the portfolio.
/// </summary>
/// <param name="portfolioArray">Return array of portfolio. The last element (index = n-1), is the most recent.</param>
/// <param name="subPortfolioArray">Return array of the sub-portfolio for which incremental VaR is being measured. The last element (index = n-1), is the most recent.</param>
/// <param name="decayFactor">In most applications, the decay factor is between 0 and 1. Weigth on the last element in arrays is 1.0, the 2nd to last element d, 3rd to last d^2, ...</param>
/// <param name="portfolioValutAtRisk">Value at risk of the portfolio.</param>
/// <param name="length">Window length. Method uses the most recent n points, n = length.</param>
/// <param name="correctSerialCorrelation">If true, correction is for infinite return length.</param>
public static double IncrementalValueAtRisk(double[] portfolioArray, double[] subPortfolioArray, double decayFactor, double portfolioValutAtRisk, int length, bool correctSerialCorrelation)
{
double uncorrected = IncrementalValueAtRisk(portfolioArray, subPortfolioArray, decayFactor, portfolioValutAtRisk, length);
if (!correctSerialCorrelation || uncorrected == 0.0)
{
return(uncorrected);
}
int len = portfolioArray.Length;
double[] otherArray = new double[len];
for (int i = 0; i < len; i++)
{
otherArray[i] = portfolioArray[i] - subPortfolioArray[i];
}
Matrix CStar = Moments.CovarianceMatrixSerialCorrelationCorrected(portfolioArray, otherArray, decayFactor, length);
double sdPort = Math.Sqrt(CStar[0, 0] + CStar[1, 1] + 2 * CStar[0, 1]);
double iStandardDeviation = (CStar[0, 0] + CStar[0, 1]) / sdPort;
return((portfolioValutAtRisk / sdPort) * iStandardDeviation);
}
