R: Decompose portfolio VaR into individual factor contributions

portVaRDecomp {facmodCS}

R Documentation

Decompose portfolio VaR into individual factor contributions

Description

Compute the factor contributions to Value-at-Risk (VaR) of portfolio returns based on Euler's theorem, given the fitted factor model. The partial derivative of VaR w.r.t. factor beta is computed as the expected factor return given portfolio return is equal to its VaR and approximated by a kernel estimator. Option to choose between non-parametric and Normal.

Usage

portVaRDecomp(object, ...)

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

Arguments

`object`	fit object of class `tsfm`, or `ffm`.
`...`	other optional arguments passed to `quantile` and optional arguments passed to `cov`
`weights`	a vector of weights of the assets in the portfolio. 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 VaR. Default is "np".
`invert`	a logical variable to choose if change VaR 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 VaR of the asset's return is given by:

VaR.fm = sum(cVaR_k) = sum(beta.star_k*mVaR_k)

where, summation is across the K factors and the residual, cVaR and mVaR are the component and marginal contributions to VaR respectively. The marginal contribution to VaR is defined as the expectation of F.star, conditional on the loss being equal to portVaR. This is approximated as described in Epperlein & Smillie (2006); a triangular smoothing kernel is used here.

Value

A list containing

`portVaR`	factor model VaR of portfolio return.
`n.exceed`	number of observations beyond VaR.
`idx.exceed`	a numeric vector of index values of exceedances.
`mVaR`	length-(K + 1) vector of marginal contributions to VaR.
`cVaR`	length-(K + 1) vector of component contributions to VaR.
`pcVaR`	length-(K + 1) vector of percentage component contributions to VaR.

Where, K is the number of factors.

Author(s)

Douglas Martin, Lingjie Yi