Share price formation, market exuberance and financial stability under alternative accounting regimes

Abstract

This paper develops a theoretical analysis of share market price formation driven by accounting and market structures. Heterogeneous investors are assumed to discover and process fundamental information disclosed by accounting system of share-issuing entity. Information set available to share market investors for decision-making comprises then market-driven and firm-specific (non-market) information. On the one side, accounting system provides collective signal of fundamental information; on the other side, price system provides collective signal of market-driven information over time. Both jointly drive the formation of aggregate share market prices through limited knowledge, hazard, and social interaction. Numerical simulations are provided under alternative accounting designs (namely, historical cost and fair value accounting regimes), to derive implications and recommendations for the concept and occurrence of speculative bubbles and herd behavior; the cyclical effects of accounting regime on share market dynamics; and the “value relevance” of accounting information and its role in the formation of share market prices over time. This numerical statistical analysis contributes to shed light on accounting anomalies and fundamental analysis.

Appendix

This appendix explains in further details the market clearing process designed by our approach. Formation of market clearing price $p_{t+1}^{*}$ over time depends on aggregation of individual bids of demand and supply at each period $t$. In particular, every shareholder ($j=S$) $i$ wishes to sell if $p_{t+1}^{*}\ge \left. E_{t}(p_{t+1})\right| _{i}^{S}$, while every prospective investor ($j=D$) $i$ wishes to buy if $p_{t+1}^{*}\le \left. E_{t}(p_{t+1})\right| _{i}^{D}$.

By assuming uniform distribution of individual investors within each group $j=S,D$, individual price expectation (focal price) $\left. E_{t} (p_{t+1})\right| _{i}^{j}$ of investor $i$ belonging to group $j$ may be rewritten as a function of expectations expressed by extreme investors $i=0$ and $i=1$ as follows:

$$\begin{aligned} \left. E_{t}(p_{t+1})\right| _{i}^{j}=p_{t}+\alpha _{t}^{j}\left( p_{t}-p_{t-1}\right) -\beta _{i}^{j}\left( \left. E_{t-1}(p_{t})\right| _{i}^{j}-p_{t}\right) +\gamma ^{j}\varphi _{i}F_{t} \end{aligned}$$

(6)

with $j=S$ (Inside), $D$ (Outside); $i,\varphi _{i}\in \left[ 0,1\right]$; $\alpha _{t}^{j}\in \left[ 0,1\right]$; $\beta _{i}^{j}\in \left[ 0;1\right]$; $\gamma ^{j}>0$.

In this paper, we assume that $\alpha _{t}^{j}=\alpha \in \left[ 0,1\right]$, $\gamma ^{j}=\gamma =1$ and $\beta _{i}^{D}=0$ $\forall i$.¹⁴ On this basis, individual price expectation (focal price) by individual investor $i$ may be rewritten as:

$$\begin{aligned} \left. E_{t}(p_{t+1})\right| _{i}^{j}=p_{t}+\alpha \left( p_{t} -p_{t-1}\right) -\left( \beta _{0}^{j}\left( 1-\varphi _{i}\right) \varepsilon _{0,t}^{j}+\beta _{1}^{j}\varphi _{i} \varepsilon _{1,t}^{j}\right) +\varphi _{i}F_{t} \end{aligned}$$

where

$$\begin{aligned} \left. \varepsilon _{t}\right| _{0}^{j}&\equiv \left( \left. E_{t-1}(p_{t})\right| _{0}^{j}-p_{t}\right) \\ \left. \varepsilon _{t}\right| _{1}^{j}&\equiv \left( \left. E_{t-1}(p_{t})\right| _{1}^{j}-p_{t}\right) . \end{aligned}$$

Extreme values of $\varphi _{i}=0,1$ define four extreme investors: two with $\varphi _{i}=0$, which are “pure speculators” (either inside $j=S$ or outside $j=D$ the market) and do not care of fundamental signal $F_{t}(\cdot )$; and two with $\varphi _{i}=1$, which are “pure fundamentalists” (either inside or outside the market, that is, $j=S$ or $j=D$) and attribute full confidence to fundamental signal $F_{t}(\cdot )$ inferred by fundamental analysis. Since time $t=0$ when share-issuing entity $k$ offers its shares on the primary market, aggregate demand and supply depend on these four focal prices with $i=0$ and $i=1$ $\forall j=S,D$ (shareholding/potential fundamentalist and shareholding/potential speculator), defined as follows:

$$\begin{aligned} \overline{P_{t}^{j}}&\equiv \max \arg \left[ \left. E_{t}(p_{t+1} )\right| _{i=0}^{j}\text {; }\left. E_{t}(p_{t+1})\right| _{i=1}^{j}\right] \\ \underline{P_{t}^{j}}&\equiv \min \arg \left[ \left. E_{t}(p_{t+1} )\right| _{i=0}^{j}; \left. E_{t}(p_{t+1})\right| _{i=1} ^{j}\right] . \end{aligned}$$

All together, these focal prices determine a “marketable area” (that could not exist) where share exchanges are wished by some shareholding and potential investors (Fig. 6). Inside and outside the share market, investors observe the aggregate share market price $p_{t}$ and the fundamental signal $F_{t}(\cdot )$ of business firm $k$. According to their own expectations on $p_{t+1}$, they decide then whether change their position through selling or buying, or simply wait until the next period.

Share market design defines how trades may be eventually performed within the “clearing area” (Fig. 5). This design decides how orders passed by investors are satisfied within this clearing area. This area denotes the width of the share market possible pricing at period $t$. By assuming linear distribution of investors for both potential demand side and potential supply side of the share market, aggregate supply $x_{t+1}^{S}$ and demand $x_{t+1}^{D}$integrate individual bids as follows:

$$\begin{aligned} \left\{ \begin{array}{c} x_{t+1}^{S}=\int _{\underline{P_{t}^{S}}}^{p_{t+1}^{*}}\frac{1}{\overline{P_{t}^{S}}-\underline{P_{t}^{S}}}dx\\ x_{t+1}^{D}=\int _{p_{t+1}^{*}}^{\overline{P_{t}^{D}}}\frac{1}{\overline{P_{t}^{D}}-\underline{P_{t}^{D}}}dx. \end{array}\right. \end{aligned}$$

(7)

On this basis, aggregate clearing price arises from matching demand with supply ($x_{t+1}^{S}=x_{t+1}^{D}$):

$$\begin{aligned} x_{t+1}^{S}=x_{t+1}^{D}\Longrightarrow \left\{ \begin{array}{l} \frac{p_{t+1}^{*}-\underline{P}_{S,t}}{\overline{P}_{S,t}-\underline{P}_{S,t}}=\frac{\overline{P}_{D,t}-p_{t+1}^{*}}{\overline{P} _{D,t}-\underline{P}_{D,t}}\\ \text {if }\max \arg \left( \underline{P}_{S,t};\underline{P}_{D,t}\right) <p_{t+1}^{*}<\min \arg \ \left( \overline{P}_{S,t};\overline{P}_{D,t}\right) \\ \text {never otherwise.} \end{array}\right. \end{aligned}$$

(8)

Figures 6 and 7 show this matching between aggregate demand and supply. In particular, Fig. 5 shows the case when aggregate clearing price exists.

Fig. 5

Aggregate potential demand and supply when clearing is possible according to extreme investors’ focal pricing

Fig. 6

Aggregate potential demand and potential supply when clearing is possible

Fig. 7

Aggregate potential demand and potential supply when clearing is impossible

Figure 7 shows the case when aggregate clearing price does not. In the latter case, no share exchanges occur. Aggregate clearing price is then settled by some institutional market-making rule.

Please refer to Biondi et al. (2012) for full analytical development of this approach.