  We consider the hedging problem where a futures position can be automatically
liquidated by the exchange without notice. We derive a semi-closed form for an
optimal hedging strategy with dual objectives - to minimise both the variance
of the hedged portfolio and the probability of liquidations due to insufficient
collateral. The optimal solution depends on the statistical characteristics of
the spot and futures extreme returns and parameters that characterise the
hedger by loss aversion, choice of leverage and collateral management. An
empirical analysis of bitcoin shows that the optimal strategy combines superior
hedge effectiveness with a reduction in the probability of liquidation. We
compare the performance of seven major direct and inverse hedging instruments
traded on five different exchanges, based on minute-level data. We also link
this performance to novel speculative trading metrics, which differ markedly
between venues.
