Compute expected lower partial moments for normal asset returns
elpm(Mean,Sigma) elpm(Mean,Sigma,MAR) elpm(Mean,Sigma,MAR,Order) Moment = elpm(Mean,Sigma,MAR,Order)
(Optional) Scalar minimum acceptable return (default
(Optional) Either a scalar or a
NUMSERIES asset returns with a vector
of mean returns in a
a vector of standard deviations of returns in a
a scalar minimum acceptable return
MAR, and one
or more nonnegative integer moment orders in a
compute expected lower partial moments (
MAR for each asset in a
Moment, is a
NUMSERIES matrix of expected
lower partial moments with
NUMSERIES series, that is, each row
contains expected lower partial moments for a given order. The output
Moment for the lower partial moment represents the moments of
asset returns that fall below a minimum acceptable level of return.
To compute upper partial moments, reverse the signs of both the input
MAR (do not reverse the signs
Sigma or the output). This function computes
expected lower partial moments with the mean and standard deviation of normally
distributed asset returns. To compute sample lower partial moments from asset
returns which have no distributional assumptions, use
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W. V. Harlow and K. S. Rao. "Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence." Journal of Financial and Quantitative Analysis. Vol. 24, No. 3, September 1989, pp. 285–311.
Frank A. Sortino and Robert van der Meer. "Downside Risk." Journal of Portfolio Management. Vol. 17, No. 5, Spring 1991, pp. 27–31.