Single-index and portfolio models for forecasting value-at-risk thresholds

The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value-at-risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single-index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single-index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations, Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations.