The Partial Moments package
The Partial Moments package provides methods, both analytical and sample based, for calculating the partial moments of a distribution or dataset. Additionally, it provides for the calculation of symmetric multivariate couterparts and portfolio optimizer methods based on those.
For multivariate datasets, the user should start by calling the
pmExpectation, followed by
and finally the
pmSolver for portfolio optimization (subject to constraints : see
There is a relative amount of flexibility as to how the main function
pmExpectation is called and with what combination
of inputs. The user should go through the detailed examples. Additionally, the function
psRisk implements the family
of risk measures described in Pedersen and Satchell (1998), which among other interesting measures also subsumes partial moments.
Stone, B. (1973), A General Class of Three-Parameter Risk Measures, Journal of Finance, 28, 675-685
Fishburn, P.C., Decision and Value Theory, 1964, Wiley, New York
Fishburn, P.C., Mean-Risk Analysis with Risk Associated with Below-Target Returns, 1977, American Economic Review, 67, 116-126
Nawrocki, David N. (1991), Optimal algorithms and lower partial moment: ex post results, Applied Economics, 23 (3), 465-70.
Farinelli, S. and Tibiletti, L. , Sharpe thinking in asset ranking with one-sided measures, European Journal of Operational Research Volume 185, Issue 3, 16 March 2008, Pages 1542-1547.
Pedersen,C.S and Satchell,S.E (1998), An Extended Family of Financial-Risk Measures, The Geneva Papers on Risk and Insurance Theory, 23, 89<96>-117
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