Traditional VaR models require risk estimates for the portfolio holdings, i.e. variance
and correlations. Historical volatilities are ill-behaved measures of risk because they
presume that the statistical moments of the security returns remain constant over
different time periods. Conditional multivariate time series techniques are more
appropriate since they use past information in a more efficient way to compute
current variances and covariances. One such model which fits well with financial
data is the multivariate GARCH. Its use, however, is restricted to few assets at a
time.
A simple procedure to overcome the difficulties of inferring current portfolio volatility
from past data, is to utilize the knowledge of current portfolio weights and
historical returns of the portfolio components in order to construct a hypothetical
series of the returns that the portfolio would have earned if its current weights had
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