/// <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>
/// 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));
}
