  We consider the mean field game of cross--holding introduced in
\citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity
value dynamics are affected by a common noise. In contrast with
\cite{DjeteTouzi}, the problem exhibits the standard paradigm of mean--variance
trade off. Our crucial observation is to search for equilibrium solutions of
our mean field game among those models which satisfy an appropriate notion of
no--arbitrage. Under this condition, it follows that the representative agent
optimization step is reduced to a standard portfolio optimization problem with
random endowment.
