Levered ETFs exhibit path dependency, or “volatility drag”, because they reset their leverage daily, which means you can’t calculate the return without knowing what the interest rate does in between the 3% rise
The entire section is based on a first-order approximation, as explicitly noted in the post (which is also why we set aside e.g. the important issue of convexity). This point is of course correct!
A related point: The US stock market has averaged 10% annual returns over a century. If your style of reasoning worked, we should instead buy a 3x levered S&P 500 ETF, get 30% return per year, compounding to 1278% return over a decade, handily beating out 162%.
This calculation, like that of many other commenters, estimates the total return. What matters is risk-adjusted return (a la Sharpe ratio). If you think the market is literally wrong with certainty, then the bet could be literally risk-free (“infinite Sharpe”, speaking loosely). If you aren’t 100% certain, then you have a finite risk-adjusted return, but still high—how high depends on your confidence level (etc).
Equities, on the other hand, have risk!
We welcome other criticisms to discuss, but comments like your first line are not helpful!
The point of my comment was that even if you’re 100% sure about the eventual interest rate move (which of course nobody can be), you still have major risk from path dependency (as shown by the concrete example). You haven’t even given a back-of-the-envelope calculation for the risk-adjusted return, and the “first-order approximation” you did give (which both uses leverage and ignores all risk) may be arbitrarily misleading, even for the purpose of “gives an idea of how large the possibilities are”. (Because if you apply enough leverage and ignore risk, there’s no limit to how large the possibilities are of any given trade.)
We welcome other criticisms to discuss, but comments like your first line are not helpful!
I thought about not writing that sentence, but figured that other readers can benefit from knowing my overall evaluation of the post (especially given that many others have upvoted it and/or written comments indicating overall approval). Would be interested to know if you still think I should not have said it, or should have said it in a different way.
The entire section is based on a first-order approximation, as explicitly noted in the post (which is also why we set aside e.g. the important issue of convexity). This point is of course correct!
This calculation, like that of many other commenters, estimates the total return. What matters is risk-adjusted return (a la Sharpe ratio). If you think the market is literally wrong with certainty, then the bet could be literally risk-free (“infinite Sharpe”, speaking loosely). If you aren’t 100% certain, then you have a finite risk-adjusted return, but still high—how high depends on your confidence level (etc).
Equities, on the other hand, have risk!
We welcome other criticisms to discuss, but comments like your first line are not helpful!
The point of my comment was that even if you’re 100% sure about the eventual interest rate move (which of course nobody can be), you still have major risk from path dependency (as shown by the concrete example). You haven’t even given a back-of-the-envelope calculation for the risk-adjusted return, and the “first-order approximation” you did give (which both uses leverage and ignores all risk) may be arbitrarily misleading, even for the purpose of “gives an idea of how large the possibilities are”. (Because if you apply enough leverage and ignore risk, there’s no limit to how large the possibilities are of any given trade.)
I thought about not writing that sentence, but figured that other readers can benefit from knowing my overall evaluation of the post (especially given that many others have upvoted it and/or written comments indicating overall approval). Would be interested to know if you still think I should not have said it, or should have said it in a different way.