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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.
This paper establishes the asymptotic properties of this method, which we call Virtual Historical Simulation (VHS). Numerical illustrations are provided.
