I do not think your central claim, that riskiness declines with time horizon, is true outside of some special cases. If you have other arguments for this I would be happy to discuss them.
The obvious argument is the Central Limit Theorem. Unless you want to argue that the log-variance of stock movements is secretly infinite, which seems doubtful.
Yes your average return will mean revert but I do not think there is any reason to think total wealth will revert to trend. e.g. if SPY falls by 10% this year, there is little to no catch up growth in future, though obviously future positive returns will dilute the 10% drop.
The obvious argument is the Central Limit Theorem. Unless you want to argue that the log-variance of stock movements is secretly infinite, which seems doubtful.
Yes your average return will mean revert but I do not think there is any reason to think total wealth will revert to trend. e.g. if SPY falls by 10% this year, there is little to no catch up growth in future, though obviously future positive returns will dilute the 10% drop.
Oh, huh, you’re right—the relative log-variance of a product of iid lognormals shrinks, but the relative variance doesn’t. TIL, thanks!