Partial Moment Two. Expected  squared Linear Loss in access of of some fixed threshold.

 

Syntax

pm2_pen(w,matrix)

short call

pm2_pen_name(w,matrix)

call with optional name

 

Parameters

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.

is a threshold value.

 

Mathematical Definition

Partial Moment Two 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 Two

Portfolio Optimization with Exponential, Logarithmic, and Linear-Quadratic Utilities

 

See also

Partial Moment Group, Partial Moment Two for Gain.