Estimates the percentiles of ES distribution for normally distributed geometric returns, for specified confidence level and holding period using the theory of order statistics.
The input arguments contain either return data or else mean and standard deviation data. Accordingly, number of input arguments is either 5 or 7. In case there 5 input arguments, the mean, standard deviation and number of samples is computed from return data. See examples for details.
returns Vector of daily geometric return data
mu Mean of daily geometric return data
sigma Standard deviation of daily geometric return data
n Sample size
investment Size of investment
perc Desired percentile
cl ES confidence level and must be a scalar
hp ES holding period and must be a a scalar
Percentiles of ES distribution function
Dowd, K. Measuring Market Risk, Wiley, 2007.
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# Estimates Percentiles of ES distribution data <- runif(5, min = 0, max = .2) LogNormalESDFPerc(returns = data, investment = 5, perc = .7, cl = .95, hp = 60) # Estimates Percentiles given mean, standard deviation and number of sambles of return data LogNormalESDFPerc(mu = .012, sigma = .03, n= 10, investment = 5, perc = .8, cl = .99, hp = 40)
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