The Resource-Constrained Brain: A New Perspective on the Equity Premium Puzzle

Abstract

Findings from brain sciences show that the brain must first optimize on its own internal resources before seeking to optimize on the resources available in the external world. We show that this modest change in perspective, from resource-constrained humans to resource-constrained brains, provides a new perspective on how assets are priced in financial markets. We show that the brain-centric perspective potentially lowers the risk aversion needed to reconcile consumption data with asset prices and can contribute to countercyclical equity premia. We show that the brain-centric perspective can be easily integrated with several existing approaches on the equity premium puzzle.

Keywords:

• Equity premium
• Countercyclical equity premia
• Resource allocation in the brain
• Behavioral asset pricing
• Behavioral finance

JEL CLASSIFICATION:

• G40
• G41
• G00
• G12

Notes

1 Hence, gives rise to a low and stable risk-free rate.

2 A sample of this literature includes habits (Campbell and Cochrane 1999), recursive utility (Epstein and Zin 1989), long-run risks (Bansal and Yaron 2004; Bansal, Kiku, and Yaron 2012), idiosyncratic risk (Constantinides and Duffie 1996), heterogeneous preferences (Garleanu and Panageas 2015), rare disasters (Reitz 1988; Barro 2006), nonseparable utility across goods (Piazzesi, Schneider, and Tuzel 2007), institutional finance (Brunnermeir 2009; Krishnamurthy and He 2013), ambiguity aversion (Hansen and Sargent 2001), and behavioral finance (Shiller 1981, 2014), among others.

3 We demonstrate the improvement in the simplest 2-period discrete time framework (see Cochrane [2005], chapter 1). We show, in Extension to Alternative Preference Structure, how the brain-centric perspective can be integrated with other approaches.

4 Based on the counting method used, the number of neurons in the brain varies from 69 billion to 128 billion (Feldman 2020)

5 Expected reward is encoded in one particular area of the brain (the striatum) that includes the nucleus accumbens (Tobler et al. 2007), while other brain regions (such as the inferior frontal gyrus) are involved in risk encoding (Fukunaga Purcell, and Brown 2018).

6 See chapter 4 in Feldman (2020).

7 A sample of recent literature in neuroscience that explores the neural basis of schemas and their role in information absorption includes Tse et al. (2007), van Kesteren et al. (2010), Tse et al. (2011), van Kesteren et al. (2012), Ghosh and Gilboa (2014), Ghosh et al. (2014), Brod et al. (2015), Spalding et al. (2015), Sweegers et al. (2015), Gilboa and Marlatte (2017), and Ohki and Takei (2018). Although direct neurophysiological evidence of schemas in the brain has started appearing since a decade and a half, the notion of schemas has a long history (Bartlett 1932; Bransford and Johnson 1972; Anderson and Pearson 1984). See Hampson and Morris (1996), Anderson (2000), and Pankin (2013) for an overview of schema theory.

8 See Loth, Gomez, and Happe (2011).

9 McKenzie (2018) argued that a brain-focused approach could potentially lead to an integration of neoclassical and behaviural economics. Siddiqi and Murphy (2020) showed that adjusting the capital asset pricing model for optimal resource allocation in the brain provides a unified explanation for anomalies such as size, value, and momentum.

10 See footnote 2 for references to several prominent papers in the literature on these puzzles.

11 Henkel, Martin, and Nardari (2011) also showed that the expected reward becomes easier to predict in downturns.

12 A sample of large and growing literature that explores the neural basis of schemas and their role in information absorption includes Tse et al. (2007), van Kesteren et al. (2010), Tse et al. (2011), van Kesteren et al. (2012), Ghosh and Gilboa (2014), Ghosh et al. (2014), Brod et al. (2015), Spalding et al. (2015), Sweegers et al. (2015), Gilboa and Marlatte (2017), and Ohki and Takei (2018).

13 See Hampson and Morris (1996), Anderson (2000), and Pankin (2013) for an overview of schema theory in cognitive science literature. The concept of schemas goes back to the early history of cognitive science as a discipline of inquiry (Barlett 1932; Bransford and Johnson 1972; Anderson and Pearson 1984).

14 Because each individual has limited processing capacity and a finite amount of information, each human brain tends to utilize only “good enough” Bayesian sampling of the available knowledge to provide a satisficing analysis of the world (Sanborn and Chater 2016).

15 The adjustment is typically less than complete toward the correct value given all information (Epley and Gilovich 2006).

16 See chapter 1 in Cochrane (2005).

17 The relationship is exact in continuous time. The discrete time approximation as shown here is from Cochrane (2005) (chapter 1).

18 This point is exogenously chosen for the purpose of illustration. However, it can be easily shown that it follows from a parameterization of the brain’s internal resource allocation problem presented in Appendix 1.

19 Source: Bloomberg. Averages are calculated as at March 31, 2021, over a 52-week period. It is interesting to note that the daily trading volumes seem to follow a power-law distribution in which large-cap stocks dominate the trading volume. Power law distributions frequently arise in studies on human attention. For emergence of power laws in human attention in various contexts, see Grabowski (2009) and Wu et al. (2012). For power laws in the brain, see Tomasi, Shokri-Kojori, and Volkow (2017). For a discussion on power law distributions in economics, see Gabaix (2016).

20 Such a time variation in risk aversion is consistent with neuroscience research, which indicates that the biological chemical testosterone innately rises in human brains after successes or wealth increases, thus leading to declines in investor risk aversion in rising/bull markets, but testosterone levels have been found to fall after financial or other losses, thus naturally leading to greater risk aversion in declining markets (Coates, Gurnell, Sarnyai 2010).

21 As shown by Klibanoff, Marinacci, and Mukerji (2005), a rise in ambiguity/ambiguity aversion in recessions can also cause investor behavior to appear to reflect a rise in risk aversion. Recessions tend to be characterized by rising uncertainty and ambiguity/risk aversion, as well as investment portfolio losses and consumption levels falling near to minimally acceptable levels.

22 See Cochrane (2005) (chapter 1).

23 See Cochrane (2017) for a review of this literature.

24 Bidder and Dew-Becker (2016) showed that investors may have great difficulty in even determining what model actually characterizes consumption risk, as well as in estimating individual risk parameter values, especially with respect to the persistence of a recession, although they did show that expected returns are predictably higher when real consumption declines. Thus, it is reasonable to conclude that, in a downturn, the brain is able to fully estimate expected returns with an allocation of only a very small amount of resources to that task (therefore resulting in m1 approaching 1.0), while no amount of resources may be sufficient to fully evaluate the uncertain risks involved in a recession (therefore resulting in m2 being far less than both 1.0 and m1 in adverse economic environments). A changing covariance between consumption and dividend growth in recessions (Xu 2021) adds further difficulty to the process of evaluating relevant asset risks then.

25 The model can be further applied to enrich the recent modelling of regime changes related to risk of inflation/deflation (Campbell, Pflueger, and Viceira 2020; Katz, Lustig, and Nielsen 2017; Boons et al. 2020). Such uncertainty may at least partially stem from the unknown likelihood and effects of monetary/fiscal responses in such environments (Song 2017) that may excessively strain the capacity of the brain to analyze such risks of possible regime changes (even while such higher risk creates predictably higher expected returns as compensation for those unresolved risks/uncertainty, thus further contributing to $m_1>m_2$ in a downturn and hence countercyclical equity premiums).

26 Specifically, Alonso, Brocas, and Carrillo (2014) and Siddiqi and Murphy (2020) focus on the case when the CES does not know the resource needs of cognitive tasks and is only aware of the probability distribution of their needs. For simplicity and without any loss of generality regarding the results in the article, we have allowed the CES to be aware of the needs of each task.