Optimal Resource Allocation in the Brain and the Capital Asset Pricing Model

Hammad, Siddiqi and Austin, Murphy (2020): Optimal Resource Allocation in the Brain and the Capital Asset Pricing Model.

Abstract

Using recent findings from brain sciences, we relax the implicit CAPM assumption of sufficient brain resources, and model human brain as solving two optimization problems instead of one, which are: 1) Optimal resource allocation in the brain. 2) Mean-variance optimization. A security market line with varying slopes (flat, upwards, and downwards) arises depending on the resource allocation decisions in the brain. Size, value, and momentum effects also emerge in this enriched framework. This suggests that the classical CAPM is not misspecified. Rather, what appears as misspecification may be the result of ignoring the optimal resource allocation problem in the brain.

• Item Type: MPRA Paper
• Language: English
• Keywords: CAPM, SML Slope, Resource Allocation, Size, Value, Momentum, High-Alpha-of-Low-Beta
• Subjects: G - Financial Economics > G1 - General Financial Markets > G10 - General; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Alonso, Brocas, and Carrillo (2014), “Resource allocation in the brain”, Review of Economic Studies, Vol. 81, pp. 501-534.

Anderson RC, Pearson PD. (1984), “A schema-theoretic view of basic processes in reading comprehension”, In Handbook of reading research (ed. PD Pearson, R Barr, ML Kamil).

Lawrence Erlbaum, Mahwah, NJ. American Psychiatric Association (2013). Diagnostic and statistical manual of mental disorders. 5th. Washington, DC.

Anderson, J. R. (2000). Cognitive Psychology and Its Implications (5th ed.). New York, NY. Worth Publishers.

Andreoni, J., and Sprenger, C. (2012), “Risk preferences are not time preferences”, American Economic Review, 102(7), 3357-3376.

Antoniou, C., Doukas, J., and Subrahmanyam, A. (2015), “Investor Sentiment, Beta, and the Cost of Equity Capital”, Management Science, Vol. 62, No. 2.

Bartlett FC. (1932), “Remembering: a study in experimental and social psychology”, Cambridge University Press, Cambridge.

Black, F. (1972), “Capital market equilibrium with restricted borrowing”, Journal of Business, Vol. 45, Issue 3, pp.444-455.

Blitz, D. (2020), “Factor Performance 2010-2019: A Lost Decade?”, Available at SSRN: https://ssrn.com/abstract=3562242

Bossaerts, P. (2009), “What decision neuroscience teaches us about financial decision making”, Annual Review of Financial Economics, pp. 383-404.

Bransford JD, Johnson MK. (1972), “Contextual prerequisites for understanding—some investigations of comprehension and recall”, Journal of Verbal Learning and Verbal Behavior, Vol. 11, pp. 717–726

Basu, Duong, Markov and Tan (2013), “How Important are Earnings Announcements as an Information Source”, European Accounting Review, Vol. 22, pp. 221-256.

Brod G, Lindenberger U, Werkle-Bergner M, Shing YL. (2015), “Differences in the neural signature of remembering schema-congruent and schema-incongruent events”, Neuroimage, Vol. 117, pp. 358–366

Cohen, R. B., C. Polk, and T. Vuolteenaho (2005), “Money illusion in the stock market: The Modigliani Cohn hypothesis”, Quarterly Journal of Economics, Vol. 120, Issue 2, pp. 639 – 668.

Fang and Peress (2009), “Media coverage and the cross section of stock returns”, Journal of Finance, Vol. 64, pp. 2023-2052.

Fama, E., and French, K. (2016), “Dissecting anomalies with a five-factor model”, The Review of Financial Studies, Vol. 29, Issue 1, pp. 69-103.

Fama, E., and French, K. (2011), “Size, Value, and Momentum in International Stock Returns.” Journal of Financial Economics 105 (2011), 457-472

Fama, E. F. and K. R. French (2004), “The capital asset pricing model: Theory and evidence”, The Journal of Economic Perspectives, Vol. 18, pp. 25–46.

Fama, E., and French. K. (1993), “Common risk factors in the returns on stocks and bonds”, Journal of Financial Economics, Vol. 33, Issue 1, pp. 3-56.

Frazzini and Pedersen (2014), “Betting against beta”, Journal of Financial Economics, Vol. 114, pp. 1-25.

Fu, L., Murphy, A., and Benzschawel, T. (2015), “Systematic Risk and Yield Premiums in the Bond Market.” Journal of Credit Risk 11, 1-40

Fukunaga, R., Purcell, J., and Brown, J. (2018), “Discriminating formal representations of risk in anterior cingulate cortex, and inferior frontal gyrus”, Frontiers in Neuroscience, https://doi.org/10.3389/fnins.2018.00553

Ghosh VE, Gilboa A. (2014), “What is a memory schema? A historical perspective on current neuroscience literature”, Neuropsychologia, Vol. 53, pp. 104–114

Ghosh VE, Moscovitch M, Melo Colella B, Gilboa A. (2014), “Schema representation in patients with ventromedial PFC lesions”, Journal of Neuroscience, Vol. 34, pp. 12057–12070

Gilboa, A., and Marlatte, H. (2017), “Neurobiology of schema and schema mediated memory”, Trends in Cognitive Science, Vol. 21, pp. 618-631.

Gershman, S. J., Horvitz, E. J. & Tenenbaum, J. B. (2015), “Computational rationality: A converging paradigm for intelligence in brains, minds, and machines”, Science, Vol. 349, pp. 273–78

Hampson, P. J. & Morris, P. E. (1996) Understanding Cognition. Cambridge, MA. Blackwell Publishers.

Hare TA, O’Doherty J, Camerer CF, Schultz W, Rangel A. (2008), “Dissociating the role of the orbitofrontal cortex and the striatum in the computation of goal values and prediction errors”, Journal of Neuroscience, Vol. 28, pp. 5623–30

Hendershott, Livdan, and Rosch (2019), “Asset pricing: A tale of night and day”, Journal of Finance (Forthcoming)

Jegadeesh, N. and Titman S. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance 48 (1993), 65-91.

Jostova, G. and Philipov, A. (2005), “Bayesian Analysis of Stochastic Betas”, Journal of Financial and Quantitative Analysis 40(4), 747–778.

Jylha, P. (2018), “Margin constraints and the security market line”, Journal of Finance, Forthcoming.

Kim, D. (1997), “A Re-examination of Firm Size, Book-to-Market, and Earnings Price in the Cross-section of Expected Stock Returns”, Journal of Financial and Quantitative Analysis 32, 463–490.

Leider F, and Griffiths, T. (2020), “Resource-rational analysis: Understanding human cognition as the optimal use of limited computational resources”, The Behavioral and Brain Sciences, Vol. 43, E1, DOI: 10.1017/S0140525X1900061X

Leider, F., and Griffiths, T., Huys, Q., and Goodman, N. (2018), “The anchoring bias reflects rational use of cognitive resources”, Psychonomic Bulletin & Review, Vol. 25, pp. 322-349.

Levy, D., Glimcher, P. (2012), “The root of all value: a neural common currency for choice”, Current Opinions in Neurobiology, Vol. 22, pp. 1027-1038.

Levi, Y. & Welch, I. (2017), “Best Practice for Cost-of-Capital Estimate”, Journal of Financial and Quantitative Analysis, Vol. 52, Issue 2, pp. 427-463.

Lin, W., Horner, A., Bisby, J., and Burgess, N. (2015), “Medial prefrontal cortex: Adding value to imagined scenarios”, Journal of Cognitive Neuroscience, Vol. 27, Issue 10, pp. 1957-1967.

Lintner, J. (1965), “The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets”, Review of Economics and Statistics, Vol.47, pp. 13-37.

McClure, S., Laibson, D., Loewenstein, G., and Cohen, J. (2004), “Separate Neural Systems Value Immediate and Delayed Monetary Rewards.” Science 306, 503-506.

Mossin, J. (1966), “Equilibrium in a capital asset market”, Econometrica, Vol. 34, pp. 768-783

Murphy, A. (1990), “Using Bayesian Betas to Estimate Risk Return Parameters: An Empirical Investigation”, Journal of Business Finance and Accounting 17 (3), 471-477.

Preuschoff K, Bossaerts P, Quartz S. (2006), “Neural differentiation of expected reward and risk in human subcortical structures”, Neuron, Vol. 51, pp. 381–90.

Ohki and Takei (2018), “Neural mechanisms of mental schema: a triplet of delta, low beta/spindle and ripple oscillations”, European Journal of Neuroscience, Vol. 48, pp. 2416-2430.

Pankin, J. (2013), “Schema theory and concept formation”, Mimeo, MIT. Available at: http://web.mit.edu/pankin/www/Schema_Theory_and_Concept_Formation.pdf

Perfetti, Charles & Liu, Ying & Fiez, Julie & Taylor, Jessica & Bolger, Donald & Hai, Li. (2007), “Reading in two writing systems: Accommodation and assimilation of the brain's reading network”, Bilingualism: Language and Cognition, Vol. 10, pp, 131-146.

Peters, J., and Buchel, C. (2007), “Neural representations of subjective reward value”, Behavioural Brain Research, Vol. 213, pp. 135-141.

Piaget, J. (1936). Origins of intelligence in the child. London: Routledge & Kegan Paul.

Plassmann H, O’Doherty J, Rangel A. (2007), “Orbitofrontal cortex encodes willingness to pay in everyday economic transactions”, Journal of Neuroscience, Vol. 27, pp. 9984–88

Rangel, A., and Hare, T. (2010), “Neural computations associated with goal-directed choice”, Current Opinions in Neurobiology, Vol. 20, pp. 162-170.

Rushworth, M. F., and Behrens, T. E. (2008), “Choice, uncertainty and value in prefrontal and cingulate cortex”, Nature Neuroscience, Vol. 11, pp. 389–397.

Savor, P., and Wilson, M. (2014), “Asset pricing: A tale of two days”, Journal of Financial Economics, Vol. 113, Issue 2, pp. 171-201.

Sharpe, W. (1964), “Capital asset prices: A theory of market equilibrium under conditions of risk”, The Journal of Finance, Vol. 19, No. 3, pp. 425-442.

Sescousse, G., Caldu, X., Segura, B., and Dreher, J. (2013), “Processing of primary and secondary rewards: a quantitative meta-analysis and review of human functional neuroimaging studies”, Neuroscience & Biobehavioral Reviews, Vol. 37, pp. 681-696.

Siddiqi, H. Anwar, S. (2020), “Financial Innovations the Curse of Safety”, Available at SSRN: https://ssrn.com/abstract=3526183 or http://dx.doi.org/10.2139/ssrn.3526183

Siddiqi, H. (2019), “Anchoring-Adjusted Option Pricing Models”, Journal of Behavioral Finance, Vol. 20, Issue 2, pp. 139-153.

Siddiqi, H. (2018), “Anchoring-Adjusted Capital Asset Pricing Model”, Journal of Behavioral Finance, Vol. 19, Issue 3, pp. 249-270.

Siddiqi, H. (2017), “Certain and Uncertain Utility: A New Perspective on Financial Innovation”, Economics Letters, Vol. 158, pp. 7-9.

Spalding, Jones, Duff, Tranel, and Warren (2015), “Investigating the Neural Correlates of Schemas: Ventromedial Prefrontal Cortex Is Necessary for Normal Schematic Influence on Memory”, Journal of Neuroscience, Vol. 35, pp. 15745-15751.

Stangor, C. (2011), “Principles of Social Psychology”, Print ISBN: 978-1-77420-014-8.

Stoll, H. and Whaley (1983), “Transaction Costs and the Small Firm Effect”, Journal of Financial Economics 12 (1983), 57-79.

Sweegers, Coleman, van Poppel, Cox, and Talamini (2015), “Mental schemas hamper memory storage of goal-irrelevant information”, Frontiers in Human Neuroscience, Vol. 9, pp. 6-29.

Tse D, Takeuchi T, Kakeyama M, Kajii Y, Okuno H, Tohyama C, Bito H, Morris RG (2011), “Schema-dependent gene activation and memory encoding in neocortex”, Science, Vol. 333, pp. 891–895

Tse D, Langston RF, Kakeyama M, Bethus I, Spooner PA, Wood ER, Witter MP, Morris RGM (2007), “Schemas and memory consolidation”, Science, Vol. 316, pp. 76–82.

van Kesteren MT, and Meeter (2020), “How to Optimize Knowledge Construction in the Brain”, Science of Learning, 5, Article Number 5

van Kesteren MT, Ruiter DJ, Fernandez G, Henson RN (2012), “How schema and novelty augment memory formation”, Trends in Neuroscience, Vol. 35, pp. 211–219.

van Kesteren MTR, Rijpkema M, Ruiter DJ, Fernández G. (2010), “Retrieval of associative information congruent with prior knowledge is related to increased medial prefrontal activity and connectivity”, Journal of Neuroscience, Vol. 30, pp. 15888–15894

Wadsworth, B. J. (2004), “Piaget's theory of cognitive and affective development: Foundations of constructivism”, New York: Longman.

Wallis, J. D. (2007), “Orbitofrontal cortex and its contribution to decision-making”, Annual Review of Neuroscience, Vol. 30, pp. 31-56.

Wu, L. (2018), “Estimating risk-return relations with analysts price targets.” Journal of Banking and Finance 93 (2018), 183-197.