Compute sample lower partial moments of data
lpm(Data) lpm(Data,MAR) lpm(Data,MAR,Order) Moment = lpm(Data,MAR,Order)
(Optional) Scalar minimum acceptable return (default
(Optional) Either a scalar or a
NUMSERIES assets with
a scalar minimum acceptable return
MAR, and one
or more nonnegative moment orders in a
lower partial moments relative to
MAR for each
asset in a
NUMORDERS x NUMSERIES matrix
Moment is a
x NUMSERIES matrix of lower partial moments with
NUMSERIES series, that is, each row contains
lower partial moments for a given order.
To compute upper partial moments, reverse the signs of both
not reverse the sign of the output). This function computes sample
lower partial moments from data. To compute expected lower partial
moments for multivariate normal asset returns with a specified mean
and covariance, use
you can compute various investment ratios such as Omega ratio, Sortino
ratio, and Upside Potential ratio, where:
Omega = lpm(-Data, -MAR, 1) / lpm(Data, MAR,
Sortino = (mean(Data) - MAR) / sqrt(lpm(Data,
Upside = lpm(-Data, -MAR, 1) / sqrt(lpm(Data,
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.