The results are very similar at each tenor, which strongly suggests that there is no significant active mean reversion. Moreover, we see that there is no significant risk reduction from holding equities for longer periods.
So we see good reasons to believe that returns are independent and very little grounds for believing that any form of active mean reversion happens4
. This leads us to the seemingly perverse view that the reason equities have mean-reverted historically is precisely because they are random. Or, in plain English, our somewhat less spectacular conclusion is that recent equity returns are no guide either way to equity returns in the future.
This highlights a significant flaw in the conventional wisdom, namely that equities are safer over the long-term. The idea, called “time diversification”, is that over sufficiently long periods (typically 20-30 years), your returns will revert to a long-term mean. This is contradicted by our findings.
Moreover, without any form of active mean reversion the whole argument collapses: if your portfolio falls in value, and has active mean reversion, then you can “ride out the storm”; if returns are independent, then there is no storm to ride out, and a large loss might well be followed by another large loss. Any other view is akin to the gambler’s fallacy. In reality, without active mean reversion, holding equities for longer periods may be trading the apparent security of a seemingly lower probability of loss for the more sinister increase in the risk of much larger losses.
If holding equities for longer makes them riskier5
, then how should investors think about earning a risk premium from equities? The obvious answer is by thinking in terms of risk; in particular, by thinking about risk limits over a shorter period. If you’re not prepared to take a gamble once, you shouldn’t take it 30 times; so if you’re not prepared to take more than a certain level of risk in one year (however you choose to measure your risk), then you shouldn’t take more risk every year for 30 years. If equities always bounce straight back, then time diversification makes sense; our research suggests they don’t, and that it doesn’t. Since equity returns do not seem to revert to a mean, having a disciplined risk management framework for the equity part of a portfolio is really the only viable approach - it is certainly far superior to blindly trusting the flawed logic of time diversification.
 “Mean Reversion
”- (Exley, Mehta, Smith) gives a good outline of the difficulties with the definition
 From Professor Shiller’s website, http://www.econ.yale.edu/~shiller/
 We also looked at autocorrelation, and reached the same conclusions