Reversion to the Mean, Taken to the Extreme

Abstract

Mean reversion in stock prices has been associated with noise or ‘noise traders’ and on an aggregate level with the value effect. The mean reverting process has not only been observed in stock prices but also in reported earnings. A new cross-sectional equilibrium model is developed based on the observation that market aggregate price developments are positively related to earnings yield and market aggregate earnings developments are negatively related to earnings yield. As the two dependencies are close to linear, two coupled differential equations can be formulated and solved. The model shows that on average, portfolios with ‘value’ or ‘growth’ stocks will drift towards a mean valuation ratio. The time-dependent calibration shows that the speed with which portfolios have drifted towards earnings yield equilibrium has increased by almost a factor of 3 over the last 20 years. Market participants are doing an increasingly good job at predicting earnings developments, but the pricing of these earnings fluctuates over time. Data suggests that participation of ‘noise traders’ is strongly reduced after a market crash or strong bear market and builds up in the years after a crash. The model can be used by value investors as guidance for sector allocation and to optimize holding period.