/// <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 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);
}
