A CAPE-Based Model of Long-Horizon Stock Index Return Predictability

Summary

The document presents a discrete-time model of stock index returns built around the cyclically adjusted price-earnings ratio, or CAPE. Return growth combines momentum, a fundamental component tied to the logarithm of the initial CAPE, and a random driving component that produces diffusive price behavior. In the model, initial valuation sets a reference level for growth, while disturbances can move prices away from it.

The authors prove that, at sufficiently long horizons, expected return and expected gross return vary linearly with initial log CAPE, while return variance declines at a rate consistent with diffusion. Momentum can still produce bubbles or crashes over shorter and medium horizons, so valuation is presented as a long-run reference rather than a guide to near-term price moves. These conclusions follow from the stated model assumptions; the document does not provide empirical validation, parameter estimates, or a trading rule for using CAPE in practice.

Key ideas

• The model links stock index return growth to momentum, initial log CAPE, and random disturbances.
• Initial CAPE establishes a reference growth level, while prices may deviate from it.
• At long horizons, the model makes expected returns linear in initial log CAPE.
• The model allows momentum to generate shorter-term bubbles and crashes.
• The stated results are theoretical and depend on the model assumptions.

Tags

# Value matters: Predictability of Stock Index Returns


# Value matters: Predictability of Stock Index Returns









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.