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?

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    $\begingroup$ You can look up the Grossman-Stiglitz paradox. $\endgroup$ Aug 8 at 17:13
  • $\begingroup$ Thank you for your comment, I'm familiar with the Grossman-Stiglitz paradox - the idea that market can't ever be in an equilibrium because then no one would spend the resources for information. But I think it doesn't answer my original question that is - if passive investors necessarily do better as a group than active investors according to Sharpe, then how can there ever be any utility by spending resources for information. $\endgroup$ Aug 8 at 20:12
  • $\begingroup$ Even of prices don't reflect reflect reality, no one is striped of their retirement. As long as assets have value, you have money for retirement. $\endgroup$
    – AKdemy
    Aug 9 at 10:59
  • $\begingroup$ Also, SPIVA is very much simplified. The main screen just shows managers beating the SPX (for the US). However, there are plenty of funds who never claim the spx to be their benchmark, and many who have a lot less volatility. Lastly, people tend to think they are better then average. I believe there will always be enough people engaging in active investment. $\endgroup$
    – AKdemy
    Aug 9 at 11:02
  • $\begingroup$ There would be self correction even if everyone would just hold the market portfolio. Firms go bust and are created because of (lack) of demand and profitability reasons, not because there is a stock market. During an IPO, you still need to convince people of the value of your firm. $\endgroup$
    – AKdemy
    Aug 9 at 11:07


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