Value Matters: Predictability of Stock Index Returns

27 Pages Posted: 2 Apr 2012 Last revised: 15 Jul 2013

See all articles by Natascia Angelini

Natascia Angelini

University of Bologna - School of Economics, Management, and Statistics; Mediterranean University of Reggio Calabria

Giacomo Bormetti

University of Bologna - Department of Mathematics

Stefano Marmi

Scuola Normale Superiore

Franco Nardini

University of Bologna - Department of Mathematics

Date Written: March 30, 2012

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.

Keywords: Valuation Ratios, Long Run Stock Market Returns

JEL Classification: G12, G17

Suggested Citation

Angelini, Natascia and Bormetti, Giacomo and Marmi, Stefano and Nardini, Franco, Value Matters: Predictability of Stock Index Returns (March 30, 2012). Available at SSRN: https://ssrn.com/abstract=2031406 or http://dx.doi.org/10.2139/ssrn.2031406

Natascia Angelini

University of Bologna - School of Economics, Management, and Statistics

Italy

Mediterranean University of Reggio Calabria ( email )

Via dei Bianchi, 2
Reggio Calabria, Reggio Calabria 89127
Italy

Giacomo Bormetti (Contact Author)

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Stefano Marmi

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy
+39050509064 (Phone)
+39050563513 (Fax)

HOME PAGE: http://homepage.sns.it/marmi/

Franco Nardini

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

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