CDaR for Gain Multiple (cdarmulti_dev_g)
Contents
CDaR for Gain Multiple. Suppose we have k=1,..., K portfolio return sample-paths. For every sample-path k, and every time moment, j=1,...J , portfolio -drawdown = -d(k,j) = maxn (-(uncompounded cumulative portfolio return at time moment n on sample-path k ) + (uncompounded cumulative portfolio return at time moment j on sample-path k )). CDaR for Gain Multiple = CVaR Component Positive of the vector (-d(1,1), ..., -d(K,J)) = average of the largest (1-α)% components of the vector (-d(1,1), ..., -d(K,J)), where 0≤α≤1 .
Syntax
cdarmulti_dev_g(α, matrix_1,matrix_2,...,matrix_K) |
short call |
cdarmulti_dev_g_name(α, matrix_1,matrix_2,...,matrix_K) |
call with optional name |
Parameters
matrix_k 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 confidence level.
Mathematical Definition
CDaR for Gain Multiple function is calculated as follows
,
where:
is CVaR Risk for Loss function,
is a function with scenarious:
,
are scenarios for Loss Function (See section Loss and Gain Functions)
is an argument of CDaR Deviation for Gain Multiple function.
Example
See also
CDaR, CDaR for Gain, Drawdown Maximum, Drawdown Maximum for Gain, Drawdown Average, Drawdown Average for Gain, CDaR Multiple, Drawdown Maximum Multiple, Drawdown Maximum for Gain Multiple, Drawdown Average Multiple, Drawdown Average for Gain Multiple