Also note that this continuous-time model doesn’t allow margin accounts to go bankrupt. Because a continuous-time margin account maintains constant leverage, if its assets fall, it rebalances immediately by selling some securities. In the real world, margin accounts can go bankrupt. This could, with low probability, even happen if the account rebalances daily. For instance, a 5X-leveraged margin account that rebalanced once per day might have been wiped out by 1987′s Black Monday. By not allowing for bankruptcy (and by ignoring black swans in general), continuous-time equations like those above may slightly overstate the expected value of leverage. In the extreme case, taking t = ∞, a margin investor who doesn’t rebalance continuously would go bankrupt with probability 1 (since eventually there would be a huge, near-instantaneous market downturn that destroys the account), while the leveraged mean equation concludes that the margin investor ends up with infinite expected wealth.
One might think that rebalancing more frequently than daily would help (perhaps with the help of an algorithm), but you can’t rebalance when markets are closed, e.g., during weekends. I haven’t figured out the best way to mitigate this risk yet (which isn’t really so much about bankruptcy as being over-leveraged when asset values fall too much before you’re able to rebalance), but two ideas are (1) keep some put options in one’s portfolio, and (2) have some assets that are protected during bankruptcy (e.g., retirement accounts, spendthrift trusts).
Bankruptcy risk for a leveraged portfolio
From Brian Tomasik’s Should Altruists Leverage Investments?
One might think that rebalancing more frequently than daily would help (perhaps with the help of an algorithm), but you can’t rebalance when markets are closed, e.g., during weekends. I haven’t figured out the best way to mitigate this risk yet (which isn’t really so much about bankruptcy as being over-leveraged when asset values fall too much before you’re able to rebalance), but two ideas are (1) keep some put options in one’s portfolio, and (2) have some assets that are protected during bankruptcy (e.g., retirement accounts, spendthrift trusts).
And being careful about instruments with unlimited downside.