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
of expected lower partial moments with
NUMSERIES series, that is, each row contains
expected lower partial moments for a given order.
To compute upper partial moments, reverse the signs of both
MAR (do not
reverse the signs of either
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
Vijay S. Bawa. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice." Journal of Financial and Quantitative Analysis. Vol. 13, No. 2, June 1978, pp. 255–271.
W. V. Harlow. "Asset Allocation in a Downside-Risk Framework." Financial Analysts Journal. Vol. 47, No. 5, September/October 1991, pp. 28–40.
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.