Partial Moment. Expected access of  Linear Loss over some fixed threshold.

Syntax

pm_pen(w,matrix)

short call

pm_pen_name(w,matrix)

call with optional name

 

Parameters

is a threshold value.

 

matrix        is a Matrix of Scenarios:

       

where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.

 

Mathematical Definition

Partial Moment function is calculated as follows

,

where:

is Loss Function (See section Loss and Gain Functions),

is an argument of function.

 

Example

•Calculation in Run-File Environment
•Calculation in MATLAB Environment

 

Case Studies with Partial Moment

•Omega Portfolio Rebalancing
•Portfolio Optimization with Second Orders Stochastic Dominance Constraints
•Style Classification with Quantile Regression
•Mixed Quantile Regression: Estimation of CVaR with Explanatory Factors
•Quantile Regression: Style Classification of Portfolio

 

See also

Partial Moment Group, Partial Moment for Gain.

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