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Return predictability and social dynamics

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Abstract

The ability to predict stock returns from financial ratios is a long-standing but still controversial topic. There is ongoing debate about the empirical evidence as well as about appropriate theoretical explanations. We provide evidence from a simulated economy that local, social interaction among agents is remarkably successful in matching several established empirical facts. We find significant return predictability at various forecast horizons, absence of dividend growth predictability, high persistence in dividend yields, and absence of significant return autocorrelations. Our results suggest that social dynamics are a simple, intuitively appealing and successful way to explain predictability.

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Notes

  1. See e.g. Cochrane (2008), Lettau and Van Nieuwerburgh (2008), or Koijen and Van Binsbergen (2010) for recent contributions that support the evidence of predictability, while Ang and Bekaert (2007), or Goyal and Welch (2003, 2008) are examples that question the evidence.

  2. Early contributions that make a case for social dynamics include Shiller (1984) and Gali (1994).

  3. See e.g. Hong et al. (2004), Baker and Wurgler (2007), Brown et al. (2008), Grinblatt et al. (2008), Kaustia and Knüpfer (2012).

  4. Collard et al. (2006) stress the role of persistence in explaining predictability.

  5. See e.g. Menzly et al. (2004) for time-varying preference, Campbell and Cochrane (1999) for habit formation. For an overview, see e.g. Cochrane (2005), or Koijen and Van Nieuwerburgh (2009).

  6. Examples include Calvet and Fisher (2007), who consider a dividend process with state dependent volatility, or Bansal and Yaron (2004) who assume a dividend process whose growth rate follows an AR(1) process.

  7. Cecchetti et al. (2000) address the well-known equity premium puzzle, while Whitelaw (2000) shows that regime-switching models can explain the non-linear relationship between expected returns and volatility. Empirically, Lettau and Van Nieuwerburgh (2008) argue that taking account of regime-switches substantially strengthens the evidence for return predictability.

  8. Predictability can be traced back to the persistence in the updated estimates. However, Timmermann (1993) considers the case where a representative agent has incomplete information with respect to constant drift and diffusion parameters. In such a set-up, the predictability effect fades out quickly, since a constant can be estimated with high accuracy after only few observations.

  9. In the following, we will use the terms ‘social dynamics’ and ‘local interaction’ synonymously.

  10. “Investing in speculative assets is a social activity. Investors spend a substantial part of their leisure time discussing investments, reading about investments, or gossiping about others’ successes or failures in investing. It is thus plausible that investors’ behavior (and hence prices of speculative assets) would be influenced by social movements.” Shiller (1984), p. 457.

  11. In this sense, Kirman (1992) argues: “The sum of the behavior of simple economically plausible individuals may generate complicated dynamics, whereas constructing one individual whose behavior has these dynamics may lead to that individual having very unnatural characteristics.” (Kirman 1992, p. 118). In Kirman (1993), he puts forward a model that replicates the dynamics of opinions in a social context and explains apparent abrupt changes in aggregate behavior.

  12. Thereby, Orlean (1995) generalizes the herding results to a non-sequential setting. See e.g. Bikhchandani et al. (1992) for the classical sequential herding model.

  13. A stable network is characterized by links between nodes in the network which are fixed over time. See Goyal (2007) for a general reference on networks, and Wolfram (2002) as a general reference on cellular automatons.

  14. In general, the agents opportunity set is frequently assumed to additionally contain a riskless asset which is in zero net supply. However, note that in this endowment economy, equilibrium requires that aggregate consumption equals aggregate dividends, so that all agents only hold the risky asset, and the rate of return on the riskless asset is only to be interpreted as the economy’s shadow risk-free interest rate.

  15. The interpretation can be justified by results in Carroll (2003), who shows that unlike households, professional forecasters are able to form close to rational expectations.

  16. In more formal terms, we may define the neighborhood of agent i as \( \mathbb{N}_{i} = \{ j;(i - 1){\text{mod}}\,N \le {\text{j}} \le ({\text{i + 1}}){\text{mod}}\,N\} \), where the modulo operator makes sure that the neighborhood of agent N includes agent 1, since 501 mod 500 = 1. Note further that the neighborhood definition does not imply that agent i is her own neighbor, which would violate the condition of irreflexivity, but that the neighborhood \({{\mathbb{N}}_i}\) characterizes the group of agents to which agent i belongs. Including the element of the network in his own neighborhood is common in the construction of cellular automata.

  17. An extension to finitely many different states would be straightforward.

  18. Considering the impact of the mood of investors on asset returns is by no means an exotic issue, but has already been discussed in the behavioral finance literature. Saunders (1993) and Hirshleifer and Shumway (2003) for example find evidence that the weather has a significant influence on stock returns, the channel being the mood of investors.

  19. Note that we do not consider the influence of market prices. There are basically two reasons: On the one hand, it is far from clear what agents can infer from market prices in such an environment, and on the other hand, in the pure exchange economy, prices have no speculative role.

  20. They are identical in each time step except for the initial random distribution of states in t 0. Initial states of agents are iid from a uniform distribution.

  21. This is also the reason why we ourselves were cautious in writing above that agents try to maximize their life-time utility.

  22. The necessary condition that the infinite sum in (8) converges is (2 μ(s) − γ σ 2 D ) > 0, which will be always satisfied by the numerical simulations.

  23. Note that the functional form of the value function V (s) t+1 (i.e. utility of a share of current dividend times a constant) is also obtained if the optimization horizon is extended to arbitrary finite time horizons. See Hillebrand and Wenzelburger (2007).

  24. By taking this example to the extreme, we would obtain a dp t series which is piece-wise constant at two levels, such as e.g. in Cecchetti et al. (1990).

  25. Such as e.g. with Shiller (1984), Summers (1986).

  26. Early contributions pointing towards this interpretation include Fama and French (1989) and Ferson and Harvey (1993).

  27. For an overview, see e.g. Cochrane (2005) or Koijen and Van Nieuwerburgh (2009).

  28. It is common to regress on the log dividend-price ratio dp t  =  − pd t .

  29. We set the initial growth rate to μ 0 = μ h , the initial estimate \(\hat{\mu}_0=0.5\), and the initial dividend yield to dp 0 =  −3. We drop initial values from the final sample.

  30. The transition probabilities correspond roughly to estimates in Cecchetti et al. (1990, 2000) and Ozoguz (2009). However, they find that there is a substantial asymmetry, in that the probability to stay in an expansion is much higher than to stay in a recession.

  31. See also Cochrane (2005), p. 455 et seq. for a discussion.

  32. Note that the standard OLS coefficient would be 0.0363 with a standard error of 0.0147, implying a t-stat of 2.679, which confirms the upward bias in both the coefficient and t values. Note further that the Newey-West corrected standard errors are 0.0133, implying an even larger t-statistic of 2.972.

  33. \(\bar{pd}=3.359\) implies a price-dividend ratio of 28.76 or a dividend yield of 3.47 %.

  34. See Cochrane (2008), p.1540 for a more detailed discussion.

  35. Cochrane (2008) calls this finding the “dog that did not bark”-effect, following the famous Sherlock Holmes case.

  36. See in particular Goyal and Welch (2003, 2008), who document a surprising lack of out-of sample predictive performance.

  37. This finding is consistent with the results in Cecchetti et al. (1990).

  38. Indeed, from unreported results, we find that the partial autocorrelation function at higher lags goes down to zero.

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Acknowledgments

We thank Matthias Bank, Christian Flor, Arie Gozluklu, Jörn van Halteren, Stefan Hirth, Wolfgang Kürsten (the editor), Maik Schmeling, Lorne Switzer, Martin Wallmeier, an anonymous referee that provided a very detailed and helpful report, and seminar participants at the German Finance Association Annual Meeting 2010 Hamburg, the European Financial Management Association Annual Meeting 2010 Aarhus, the Financial Management Association European Annual Meeting 2010 Hamburg, and the Financial Management Association Annual Meeting 2010 New York. As always, all remaining errors are our own.

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  1. Department of Economics, Innsbruck University, 6020, Innsbruck, Austria

    Richard Hule

  2. Department of Banking and Finance, Innsbruck University, 6020, Innsbruck, Austria

    Jochen Lawrenz

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Hule, R., Lawrenz, J. Return predictability and social dynamics. Rev Manag Sci 7, 159–189 (2013). https://doi.org/10.1007/s11846-013-0099-z

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