If the market cap of a market is constant, do stock prices necessarily follow the principle of reversion to the mean? How would one prove this? (I'm pretty sure this is trivial, but I don't know how to express the necessary ideas).
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Identically: $$ Market\_Cap \equiv Number\_of\_Shares \cdot Price\_per\_Share$$ If a market cap is constant than stock prices only fluctuate because of changes in the number of shares. Therefore, this would imply mean reversion in share prices only if the fluctuations in the number of shares were also mean reverting.
As a general matter in the United States over the last hundred or so years, the average price per share has mostly been \$20-\$40 while market capitalization has increased substantially, implying a large increase in the number of shares. This has mostly been achieved by stock splits, stock based acquisitions, and secondary equity offerings.
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$\begingroup$ Thanks, this is exactly what I wanted. Now, since cryptocurrencies are (at least in the beginning) inflationary, would this mean that tokens like bitcoin and ether probably do not satisfy reversion to the mean? (Since number of shares is constantly increasing, in some sense). $\endgroup$ Commented Oct 20, 2016 at 0:18
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$\begingroup$ It would be best to ask this as a separate question. $\endgroup$– BKayCommented Oct 20, 2016 at 0:21