نظریه چشم انداز و کیفیت بازار

We study equilibrium trading strategies and market quality in an economy in which speculators display preferences consistent with Prospect Theory (Kahneman and Tversky, [39]; Tversky and Kahneman, [63]), i.e., loss aversion and mild risk seeking in losses. Loss aversion (risk seeking in losses) induces speculators to trade less (more), and less cautiously (more aggressively), with their private information – but also makes them less (more) inclined to purchase private information when it is costly – in order to mitigate (enhance) their perceived risk of a trading loss. We demonstrate that these forces have novel, nontrivial, state-dependent effects on equilibrium market liquidity, price volatility, trading volume, market efficiency, and information production.

Over the past two decades, a large and long-standing body of experimental evidence on human behavior has provided support to the notion, first formulated by Kahneman and Tversky [39] as Prospect Theory, that the decision-making process of any economic agent may depart from the predictions of standard expected utility theory. In Tversky and Kahnemanʼs [63] version, Prospect Theory postulates that economic agents assess gambles with a value function defined over gains and losses relative to a reference point (instead of the absolute level of financial wealth or consumption), concave over gains (risk aversion), but convex (risk seeking) and steeper (loss aversion) over losses. Recent work employs modified versions of this theory to interpret the behavior of financial investors and study the pricing of financial securities. Prospect Theory arguments have been proposed to explain such known asset pricing puzzles as the magnitude of the equity premium, excess stock return volatility, momentum and the disposition effect, the value premium, or stock return predictability and its implications for portfolio selection. 2 The past two decades have also been characterized by an increasing interest in the study of the process of price formation in financial markets. Market microstructure research has studied (both theoretically and empirically) such issues as the mechanisms through which private information is acquired, utilized, and impounded into prices, agentsʼ reasons for trade and optimal trading strategies, and the implications for liquidity and volatility.3 Yet, to our knowledge, this literature has not examined any of these issues when investors make decisions according to Prospect Theory. The main objective of this paper is to investigate the effects of Prospect Theory on market quality. Our theoretical analysis makes two related contributions to the literature. First, its predictions are novel and indicate that these effects are nontrivial and may play an important role in explaining financial market quality. Second, its predictions are testable, thus possibly refutable rather than aimed at matching extant features of the data. As such, they provide an unbiased, albeit more challenging opportunity to assess the empirical relevance of unconventional utility models. Our theory is based on a one-period model of sequential trading in the spirit of Grossman and Stiglitz [29], Kyle [45], and Vives [67]. The model is populated by a continuum of informed traders (competitive, price-taking speculators endowed with a noisy signal of the asset payoff) submitting demand schedules (i.e., generalized limit orders), noise traders submitting market orders, and competitive, risk-neutral market makers (MM). If a speculatorʼs preferences are described by an exponential utility function (MV speculation), the modelʼs implications for trading strategies, market depth (the inverse of Kyleʼs [45] “lambda,” or price impact of noise trading), price volatility, informed trading volume, and price informativeness are well-known in the literature (e.g., Vives [68]). We depart from this standard setting by assuming that (PT) speculators display preferences capturing parsimoniously all of the aforementioned main features of Kahneman and Tverskyʼs [39] Prospect Theory – as well as their relative importance (as assessed by Tversky and Kahneman [63]). 4 The modelʼs ensuing noisy rational expectations equilibrium yields several novel, microfounded predictions for financial market quality. First, we show that PT speculation improves a risky assetʼs market liquidity (i.e., reduces the average price impact of noise trading) but worsens its price efficiency and lowers its aggregate trading volume relative to standard MV speculation. Intuitively, loss aversion (LA) not only induces a speculator to trade less (or not at all) with her noisy signal – especially when her perceived marginal probability of a trading loss is high – but also increases her trading intensity (i.e., the sensitivity of her demand function to private information shocks) – especially when such probability is low – in order to decrease her conditional expected trading loss. In turn, speculatorsʼ trading intensity has two effects of opposite sign on market quality. Ceteris paribus, less cautious speculation increases both the likelihood of informed trading in the aggregate order flow and its information content. The former effect (labeled selection) worsens the MMʼs adverse selection problem, while the latter effect (labeled efficiency) alleviates it. In equilibrium, the efficiency effect of LA speculation on MMʼs perceived adverse selection risk, relative to MV speculation, dominates the corresponding selection effect, leading to greater market depth but lower price volatility, informativeness, and trading volume. Risk seeking in losses (RSL) instead induces a speculator to trade more, and more aggressively, with her noisy signal – especially when her perceived cumulative probability of a trading loss is high – in order to increase her conditional trading loss variance. As for LA speculation, the equilibrium efficiency effect of RSL speculation on market quality dominates its selection effect, yielding greater market depth and trading volume, but lower price volatility and informativeness. According to Tversky and Kahneman [63], agentsʼ risk seeking in losses is mild relative to loss aversion. 5 Thus, for preference parameters consistent with their assessment, the effects of loss aversion on market quality prevail over the effects of risk seeking in losses in equilibrium, leading to greater market liquidity but worse efficiency and lesser trading than with MV speculation. As importantly, we also show that PT speculation makes equilibrium market quality state-dependent. In the presence of standard MV speculation, market quality instead varies exclusively with exogenous preference and technology parameters. An intuitive explanation for this result is that ceteris paribus, the effects of loss aversion and risk seeking in losses on a speculatorʼs trading intensity depend on the absolute magnitude of the noisy signal she observes relative to its mean, since so does her perceived probability of a trading loss. In particular, RSL (LA) speculationʼs trading intensity is (first increasing then) decreasing in absolute private signals. In equilibrium, the prevalence of efficiency over selection (for the MMʼs perceived adverse selection risk from trading) and of loss aversion over risk seeking in losses (in PT speculatorsʼ preferences) makes price impact, volatility, informativeness, and relative trading volume first decreasing then increasing in those signals. In most financial markets private information about asset payoffs is costly. This motivates us to extend our model to consider whether Prospect Theory preferences affect speculatorsʼ endogenous information acquisition. The amended model generates a rich set of additional, novel implications. In particular, we show that when the noisy signal is sufficiently expensive, the presence of PT speculation diminishes information production and amplifies its effects on market quality but attenuates its state-dependence. Intuitively, the availability of private information mitigates a speculatorʼs perceived risk of a trading loss, yet at a certain cost. When private information is sufficiently expensive, risk aversion induces a fraction of MV speculators faced with this trade-off not to purchase it. In those circumstances, the MMʼs vulnerability to adverse selection may either decline (if a selection effect prevails) or increase (if an efficiency effect prevails). Loss aversion makes a speculator even less inclined to purchase the noisy signal to mitigate that risk; yet, her lesser trading with it increases returns to private information. Risk seeking in losses makes a speculator more inclined to purchase the noisy signal to magnify that risk; yet, her greater trading with it decreases returns to private information. As above, prevalence of the former set of effects on the latter yields lower information production by PT speculators in equilibrium. In turn, more limited market participation of informed PT speculators not only lowers price impact and market efficiency but also attenuates the state-dependence induced by their trading activity. These insights are important for they suggest that the extent to which Prospect Theory preferences affect financial market quality is sensitive to the marketʼs information environment. Our work is related to Subrahmanyam [61] and Foster and Viswanathan [24]. Subrahmanyam [61] shows that allowing for imperfectly competitive, risk-averse speculators submitting market orders in the one-period noisy rational expectations model of Kyle [45] has ambiguous effects on market liquidity (but unambiguously lowers price efficiency) relative to risk-neutral speculation. Yet, equilibrium market quality remains non-state-dependent (as in Kyle [45]). In this paper we show that Prospect Theory preferences have unambiguous effects on equilibrium market quality (relative to competitive, risk-averse speculation) and make it state-dependent. Foster and Viswanathan [24] demonstrate that representing strategic speculatorsʼ beliefs with nonnormal, elliptically contoured distributions makes price volatility and trading volume (but not price impact) state-dependent. However, there is little or no evidence guiding such modeling choice for those unobservable beliefs. In our model state-dependent market quality ensues from speculatorsʼ microfounded (i.e., Prospect Theory-inspired) preferences even when all random variables are normally distributed.6 Another related literature explores asset pricing implications of investors exhibiting either irrationality or bounded rationality.7 All agents in our model, including the speculators displaying nonconventional preferences, are instead fully rational.8 We proceed as follows. In Section 2, we construct a model of trading with PT speculation and discuss its implications for market quality. In Section 3, we enrich the model by endogenizing PT speculatorsʼ decision to become informed. We conclude in Section 4.