  In this paper, we obtain a property of the expectation of the inverse of
compound Wishart matrices which results from their orthogonal invariance. Using
this property as well as results from random matrix theory (RMT), we derive the
asymptotic effect of the noise induced by estimating the covariance matrix on
computing the risk of the optimal portfolio. This in turn enables us to get an
asymptotically unbiased estimator of the risk of the optimal portfolio not only
for the case of independent observations but also in the case of correlated
observations. This improvement provides a new approach to estimate the risk of
a portfolio based on covariance matrices estimated from exponentially weighted
moving averages of stock returns.
