  In order to estimate the conditional risk of a portfolio's return, two
strategies can be advocated. A multivariate strategy requires estimating a
dynamic model for the vector of risk factors, which is often challenging, when
at all possible, for large portfolios. A univariate approach based on a dynamic
model for the portfolio's return seems more attractive. However, when the
combination of the individual returns is time varying, the portfolio's return
series is typically non stationary which may invalidate statistical inference.
An alternative approach consists in reconstituting a "virtual portfolio", whose
returns are built using the current composition of the portfolio and for which
a stationary dynamic model can be estimated.
  This paper establishes the asymptotic properties of this method, that we call
Virtual Historical Simulation. Numerical illustrations on simulated and real
data are provided.
