Accounting and the formation of share market prices over time: a mathematical institutional economic analysis through simulation and experiment

Abstract

This article develops a heterogeneous agents-based model to examine the emergent dynamic properties of share market price formation over time, with a view on financial market stability under alternative accounting regimes. In the model, individual heterogeneous investors interact with each other and with institutional devices which are an accounting system (related to the business firm) and a price system (related to the Share Exchange). These interactions provide mechanisms for transmission through which firm-specific (accounting signal) and market-driven (aggregate price) factors can act. A baseline simulation analysis assesses the financial market stability under three alternative accounting designs, namely two kinds of historical cost accounting regime and one kind of fair-value (mark-to-market) accounting regime. The former prove to better stabilize the financial system in terms of market volatility and exuberance in perfectly balanced conditions between speculative and fundamentalist beliefs and intentions. An evolutionary analysis is then developed by varying the relative degree of speculative attitudes between the two sides of the market. Historical cost accounting regimes further prove to make the financial system more resilient to speculative waves occurring at inter-individual level. Baseline findings are further corroborated through experimental analysis in twelve artificial financial systems. This mathematical institutional economic analysis has general implications for both designing accounting systems aimed at enhancing financial market stability and preventing procyclicality, and the study of accounting information process in the formation of share market prices over time.

Keywords:

• financial stability
• financial resilience
• accounting model
• fair value
• international accounting
• market efficiency
• market exuberance
• market volatility
• accounting procyclicality

JEL Classification:

• M40
• D40
• G38
• L22
• D47

Acknowledgements

I thank Martin Shubik, Shyam Sunder, Serge Galam, Pierpaolo Giannoccolo, Larry Bensimhon and Maxim Frolov who have contributed to the development of this analysis and its performance through simulation and experiment. This article was presented at the third ISCEF Conference (Paris, 10–12 April 2014, www.iscef.com) and prepared to be read at Laboratorio Fibonacci (Cnrs - UMI 3483), Scuola Normale Superiore di Pisa, Italy, 27 February 2013. This research work has been presented at several conferences and workshops, including: keynote speech at the 3rd International Conference of The Japanese Accounting Review (TJAR) in Kyoto, organized by Kobe University, Kyoto University, and Doshisha University, 9 November 2012; The Unexpected Conference on ‘SOCIOPHYSICS: Do humans behave like atoms?’, CREA, Paris, 14–16 November 2011; Banque de France Foundation Research Seminar, 23 November 2010; W.E.H.I.A. 2012, ESHIA, 17th Annual Workshop on Economic Heterogeneous Interacting Agents, University of Pantheon-Assas, Paris, 21–23 June 2012; First Cost International Conference on ‘Remodeling finance and its governance in times of uncertainty’, University of Paris 8, 12–14 May 2011; American Accounting Association (AAA) Annual Meeting, San Francisco, 31 July–4 August 2010; keynote speech at MODAV 2010, 7th International Accounting Conference (AACF 2010), Istanbul, 14–15 October 2010; Nordic Conference on Financial Accounting, Copenhagen, 25–26 November 2010; 7th Paris Finance International Meeting, Paris, 17–18 December 2009.

Notes

¹ For sake of simplicity, we consider ‘mark-to-market’ accounting and ‘fair value’ accounting synonymously. While the first approach implies the use of observable market prices to measure the value of every asset and liability, the second approach includes the recourse to observable and unobservable inputs to reproduce that value.

² A further analysis may consider a blurred accounting system whose direction signals (sign) are not agreed (known) by all the investors.

³ This number of replications is sufficient to stabilize the first order of most descriptive statistics that apply here to comparatively assess the relative efficacy of accounting regimes in coping with market volatility and exuberance.

⁴ This model of generic investor’s forecasting revision combines a ‘first order adaptive model’: $E_t(P_{t+1})=E_{t-1}(P_t)+{\beta }^{\prime }\left(P_t-E_{t-1}(P_t)\right)$, where ${\beta }^{\prime }$ weights the revision of the most recent expectation error, with an ‘extrapolative expectation model’: $E_t(P_{t+1})-(P_t)=\gamma (P_t-P_{t-1})$ where $\gamma$ weights the most recent price change (trend). With $\gamma >0$, any market price increase results in increasing investor’s price expectation.

⁵ Fama (1970) distinguishes three forms of share market efficiency depending on the composition of the information set treated by investors. Regarding the weak-form, the information set includes only the history of market prices; in the semi-strong form, it includes all publicly available information and the strong form tests it against all existing information, see also Fama (1991).

⁶ The presence of this random error ${\epsilon }_t=N(0,1)/100$ could involve here the working of a drunk auctioneer! In fact, this is a minor assumption without material impact on simulation results.

⁷ A comprehensive analysis of these consequences goes beyond the scope of this article.

⁸ A further experiment may analyse the market price formation when the respective timings of payout index and market price differ. Biondi et al. (2012) modelled this latter generalized approach, taking into account the respective timings of individual and inter-individual decision-making, fundamental information and the market pricing.

⁹ These liquidation values cannot be considered as the fundamental values of reference in its usual meaning. Nevertheless, they provide collective signals about the payoffs linked to holding shares, and those signals are common knowledge for all the investors.

¹⁰ A full calibration of the simulation model to fit experimental data is beyond the scope of this article.