The premise of the paper titled The Arithmetic of Active Management by Sharpe is that active managers as a group have to necessarily underperform passive managers as a group because passive investors can freeride off of the active managers who spend resources on price discovery. Indeed many analysis such as SPIVA show, year after year, passive management outperforms active management. Retail and other investors learn to know this and consequently shift their assets from active to passive management - so much so that over half of the assets are now passively managed (looking at freefloat capital only).
The logical conclusion of this is that everyone in the future is a passive investor, prices don't reflect reality and billions of people are strip of their retirement.
The opposite argument is that once passive investing grows too large, the inefficiencies will allow active management to outperform the passive one, justifying their bigger fees. Hence, the market in the end is self-correcting.
But why would the Sharpes Arithmetic of Active Management cease to function in that hypothetical scenario?
