A simple model of market valuation and trend reversion for U.S. equities: 100 Years of bubbles, non-bubbles, and inverse-bubbles

•A suggested measure of equity market valuation is based on Ornstein-Uhlenbeck trend reversion.•Trend reversion and market efficiency are reconciled by weakness of trend's gravitational pull.•The approach provides an operational measure of over- or under-valuation of equity markets.•The approach indicates that “bubbles” and “inverse bubbles” are both common.

Appraising the current valuation of equity markets is a popular pastime for academics, investors, and pundits alike. Here I consider a measure of valuation based on a century-long trend of U.S. equity returns and the tendency of returns to revert (eventually) to that trend. The approach here is to incorporate a simple trend into an Ornstein-Uhlenbeck process. The empirical results offer some support for the theoretical description, though not to an extent that would cause harm to the concept of efficient markets. The reconciliation of trend reversion with market efficiency lies in the weakness of the trend's “gravitational pull.” The results do, however, provide an operational measure for describing markets as over- or under-valued, which indicates that “bubbles” and “inverse bubbles” are both common.