However these assumptions are inappropriate as during periods of high volatility and market turbulence, historical correlations tend to break down.
Intuitively, this is evident during a financial crisis where all industry sectors experience a significant increase in correlations, as opposed to an upward trending market.
For example, to improve the estimation of the variance-covariance matrix, one can generate a forecast of asset distributions via Monte-Carlo simulation based upon the Gaussian copula and well-specified marginals.
Not accounting for these attributes lead to severe estimation error in the correlation and variance-covariance that have negative biases (as much as 70% of the true values).
[5] Estimation of VaR or CVaR for large portfolios of assets using the variance-covariance matrix may be inappropriate if the underlying returns distributions exhibit asymmetric dependence.
In such scenarios, vine copulas that allow for asymmetric dependence (e.g., Clayton, Rotated Gumbel) across portfolios of assets are most appropriate in the calculation of tail risk using VaR or CVaR.
[7] These revisions, the "Fundamental Review of the Trading Book", address deficiencies relating to the existing Internal models and Standardised approach for the calculation of market-risk capital, and in particular discuss the following: In the United States, a section on market risk is mandated by the SEC[8] in all annual reports submitted on Form 10-K.