Value matters: Predictability of Stock Index Returns

TL;DR

This paper introduces a dynamical model linking stock index returns to the CAPE ratio, showing that long-term returns are predictable from valuation metrics despite short-term volatility and bubbles.

Contribution

It develops a simple discrete-time model connecting CAPE to long-term returns, incorporating momentum, fundamental valuation, and stochastic price movements.

Findings

Expected long-term returns are linear in initial CAPE.

Variance of returns diminishes over time, indicating predictability.

Short-term bubbles and crashes can occur despite long-term valuation relevance.

Abstract

We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More precisely, we discuss a discrete time dynamics in which the return growth depends on three components: i) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones, ii) a fundamental component proportional to the logarithmic CAPE at time zero. The initial value of the ratio determines the reference growth level, from which the actual stock price may deviate as an effect of random external disturbances, and iii) a driving component which ensures the diffusive behaviour of stock prices. Under these assumptions, we prove that for a sufficiently large horizon the expected rate of return and the expected gross return are linear in the initial logarithmic CAPE, and their variance goes to zero with a rate of convergence consistent with the diffusive behaviour. Eventually this means that the momentum component may generate bubbles and crashes in the short and medium run, nevertheless the valuation ratio remains a good reference point of future long-run returns.