Hedging with Automatic Liquidation and Leverage Selection on Bitcoin Futures
Bitcoin derivatives positions are maintained with a self-selected margin, often too low to avoid liquidation by the exchange, without notice, during periods of excessive volatility. Recently, the size and scale of such liquidations precipitated extreme discontent among traders and numerous lawsuits against exchanges. Clearly, hedgers of bitcoin should account for the possibility of automatic liquidation. That is the mathematical and operational problem that we address, deriving a semi-closed form for an optimal hedging strategy with dual objectives – to minimize both the variance of the hedged portfolio and the probability of liquidation due to insufficient collateral. An empirical analysis based on minute-level data compares the performance of major direct and inverse bitcoin hedging instruments traded on five major exchanges. The products have markedly different speculative trading scores according to new metrics introduced here. Instruments having similar hedging effectiveness can exhibit marked differences in speculative activity. Inverse perpetuals offer greater effectiveness than direct perpetuals, which also exhibit more speculation. We model hedgers with different levels of loss aversion that select their own level of leverage and collateral in the margin account. By following the optimal strategy, the hedger can reduce the liquidation probability to less than 1% and control leverage to a reasonable level, mostly below 5X.