We previously demonstrated that stock indices exhibit mean-reverting property in the short term and trending property in the long term. Reference  further explored the trending/mean-reverting properties in a longer timeframe and pointed out that in the very long term, the markets mean-revert,
We provide further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years). Our results bolster Black’s intuition that prices tend to be off roughly by a factor of 2, and take years to equilibrate. The story behind these results fits well with the existence of two types of behaviour in financial markets: “chartists”, who act as trend followers, and “fundamentalists”, who set in when the price is clearly out of line. Mean-reversion is a self-correcting mechanism, tempering (albeit only weakly) the exuberance of financial markets.
Such trending/mean-reverting properties exist not only in equity indices but also in bonds, FX, and commodity markets. The article concluded,
…we have provided some further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years). This dovetails with Black’s intuition that prices tend to be off by a factor of two: it takes roughly six years for the price of an asset with 20 % annual volatility to vary by 50 %.
As a result, the authors recommended diversifying investment strategies, i.e. mixing trending and mean-reverting strategies. This is indeed a common practice in the industry,
From a very practical point of view, our results suggest that universal trend following strategies should be supplemented by universal “value” strategies that mean-revert on long term returns. As is well known, trend following strategies offer a hedge against market drawdowns; value strategies offer a hedge against over-exploited trends. As a consequence, we find that mixing both strategies significantly improves the profitability of the resulting portfolios.
 J. P. Bouchaud, S. Ciliberti, Y. Lempérière, A. Majewski, P. Seager, K. Sin Ronia, Black was right: Price is within a factor 2 of Value, arXiv:1711.04717
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