R: Decompose portfolio ES into individual factor contributions

portEsDecomp {facmodCS}

R Documentation

Decompose portfolio ES into individual factor contributions

Description

Compute the factor contributions to Expected Tail Loss or Expected Shortfall (ES) of portfolio returns based on Euler's theorem, given the fitted factor model. The partial derivative of ES with respect to factor beta is computed as the expected factor return given portfolio return is less than or equal to its value-at-risk (VaR). Option to choose between non-parametric and Normal.

Usage

portEsDecomp(object, ...)

## S3 method for class 'ffm'
portEsDecomp(
  object,
  weights = NULL,
  factor.cov,
  p = 0.05,
  type = c("np", "normal"),
  invert = FALSE,
  ...
)

Arguments

`object`	fit object of class `ffm`.
`...`	other optional arguments passed to `quantile` and optional arguments passed to `cov`
`weights`	a vector of weights of the assets in the portfolio, names of the vector should match with asset names. Default is NULL, in which case an equal weights will be used.
`factor.cov`	optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix.
`p`	tail probability for calculation. Default is 0.05.
`type`	one of "np" (non-parametric) or "normal" for calculating Es. Default is "np".
`invert`	a logical variable to choose if change ES to positive number, default is False

Details

The factor model for a portfolio's return at time t has the form

R(t) = beta'f(t) + e(t) = beta.star'f.star(t)

where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'. By Euler's theorem, the ES of the portfolio's return is given by:

ES.fm = sum(cES_k) = sum(beta.star_k*mES_k)

where, summation is across the K factors and the residual, cES and mES are the component and marginal contributions to ES respectively. The marginal contribution to ES is defined as the expected value of F.star, conditional on the loss being less than or equal to portVaR. This is estimated as a sample average of the observations in that data window.

Value

A list containing

`portES`	factor model ES of portfolio returns.
`mES`	length-(K + 1) vector of marginal contributions to Es.
`cES`	length-(K + 1) vector of component contributions to Es.
`pcES`	length-(K + 1) vector of percentage component contributions to Es.

Where, K is the number of factors.

Author(s)

Douglas Martin, Lingjie Yi