A Time-Series Analysis and Forecast of CAPE

Abstract

Expanding stock market valuation multiples add to expected returns, and contracting multiples subtract from them. But how to forecast valuation measures such as the cyclically adjusted price-to-earnings (CAPE) ratio? Using Robert Shiller’s CAPE, the author first shows that forecasts based on mean reversion are almost certainly wrong—CAPE appears to be nonstationary, indicating no tendency toward mean reversion. The author then provides forecasts of CAPE using time-series analysis—an approach that requires no theory and accommodates a range of views about factors that influence valuation. The author suggests that practitioners use these time-series forecasts to help inform capital market assumptions.

TOPICS: Security analysis and valuation, fundamental equity analysis, quantitative methods, statistical methods, financial crises and financial market history

Key Findings

• ▪ CAPE may be nonstationary and as such have no tendency to revert to its long-term or any other mean—forecasts of CAPE based on mean regression may be wrong.

• ▪ Considering the range of outcomes for CAPE values suggested by time-series models reduces the chances of a big surprise in either direction.

• ▪ Practitioners factoring valuation changes into their capital market assumptions may wish to assume no or small changes as a base case, rather than reversion to a long-term mean value.