After that day, the ETF is worth $60. If you sell $5 of it, you hold $55 of 2x exposure and $5 of cash, which is equivalent to what you would have if you had done no trading; on net you are long $110 of stocks and short $50 cash.
I think the mistake in your reasoning is saying that you ‘get rid of half equity and half debt’. You actually reduce your equity by 2x, your debt by 1x, and then receive 1x cash also.
Note that the paper you link to says several things that basically echo Paul:
“The above suggests that a leveraged ETF with a positive expected raw return but
negative expected growth, increasingly resembles a lottery ticket over time. As time
passes, the chances of the lottery player ending up with zero approach certainty, but the
payoff if he wins continues to increase to ensure that the lottery itself has favorable odds.”
“We find that
the expected raw return of the levered ETF is the highest simply because the investor
borrows at 2% to invest at 7.5%; however, the distribution of return outcomes is arguably
unattractive. The investor in a levered ETF achieves negative expected growth and also
has the lowest median portfolio return.”
As Paul pointed out, this is close to the opposite of the martingale strategy; in the martingale strategy you eliminate your losses with near-certainty (where how near depends on how much you can afford to keep doubling up) but your losses should you incur them get larger and larger, here you eliminate your gains with near-certainty but the gains get larger and larger.
Something that is explicitly ignored in that paper is the presence of fees and transaction costs. Daily leveraged ETFs do more trading than, say, one that rebalanced monthly would, because standard deviations scale with the square root of time. In the non-theoretical world, there are costs to this which should be considered, and they get bigger as the ETF(s) in question get bigger.
Finally, I would note that there is a surprising amount of nonsense written about ETFs online. I could point to much clearer-cut examples of incorrect or highly misleading statements.
After that day, the ETF is worth $60. If you sell $5 of it, you hold $55 of 2x exposure and $5 of cash, which is equivalent to what you would have if you had done no trading; on net you are long $110 of stocks and short $50 cash.
Thanks for this! Now I understand.
BTW, if you have time:
What’s your opinion on non-rebalancing leverage done manually?
What if you pay for the leverage interest using new income in a similar way as people pay off home loans? (This doc encourages such an approach.)
After that day, the ETF is worth $60. If you sell $5 of it, you hold $55 of 2x exposure and $5 of cash, which is equivalent to what you would have if you had done no trading; on net you are long $110 of stocks and short $50 cash.
I think the mistake in your reasoning is saying that you ‘get rid of half equity and half debt’. You actually reduce your equity by 2x, your debt by 1x, and then receive 1x cash also.
Note that the paper you link to says several things that basically echo Paul:
“The above suggests that a leveraged ETF with a positive expected raw return but negative expected growth, increasingly resembles a lottery ticket over time. As time passes, the chances of the lottery player ending up with zero approach certainty, but the payoff if he wins continues to increase to ensure that the lottery itself has favorable odds.”
“We find that the expected raw return of the levered ETF is the highest simply because the investor borrows at 2% to invest at 7.5%; however, the distribution of return outcomes is arguably unattractive. The investor in a levered ETF achieves negative expected growth and also has the lowest median portfolio return.”
As Paul pointed out, this is close to the opposite of the martingale strategy; in the martingale strategy you eliminate your losses with near-certainty (where how near depends on how much you can afford to keep doubling up) but your losses should you incur them get larger and larger, here you eliminate your gains with near-certainty but the gains get larger and larger.
Something that is explicitly ignored in that paper is the presence of fees and transaction costs. Daily leveraged ETFs do more trading than, say, one that rebalanced monthly would, because standard deviations scale with the square root of time. In the non-theoretical world, there are costs to this which should be considered, and they get bigger as the ETF(s) in question get bigger.
Finally, I would note that there is a surprising amount of nonsense written about ETFs online. I could point to much clearer-cut examples of incorrect or highly misleading statements.
Thanks for this! Now I understand.
BTW, if you have time:
What’s your opinion on non-rebalancing leverage done manually?
What if you pay for the leverage interest using new income in a similar way as people pay off home loans? (This doc encourages such an approach.)