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Value matters: Predictability of Stock Index Returns

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  • Natascia Angelini
  • Giacomo Bormetti
  • Stefano Marmi
  • Franco Nardini

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.

Suggested Citation

  • Natascia Angelini & Giacomo Bormetti & Stefano Marmi & Franco Nardini, 2012. "Value matters: Predictability of Stock Index Returns," Papers 1204.5055, arXiv.org, revised Jul 2013.
  • Handle: RePEc:arx:papers:1204.5055
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    1. James M. Poterba & Andrew A. Samwick, 1995. "Stock Ownership Patterns, Stock Market Fluctuations, and Consumption," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 26(2), pages 295-372.
    2. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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