Reference point formation: Does the market whisper in the background?

Well‐established studies in behavioral finance confirm that investors are highly influenced by subjective reference points when making economic decisions. Although the literature examines reference point formation for individual stocks based on observed price sequences, the stocks are often treated without considering market context. We extend this literature by incorporating market price information as background to the behavior experiment, and we consider both prospect theory and anticipation/disappointment‐based utility functions in a combined framework to investigate the impact of market context on reference point formation. Our article provides new evidence and insights for investment practitioners and behavioral researchers.

Keywords: Behavioral Finance; Market Contextual; Reference‐point Formation

A common assumption in behavioral finance is that individuals measure gains and losses relative to a subjective reference point. This assumption underlies Kahneman and Tversky's (1979) prospect theory, which posits that perceived value derives not from absolute wealth but from changes in wealth, in contrast to standard expected utility (EU) theory (Savage, 1972; Von Neumann & Morgenstern, 1947), which assumes that utility is based solely on final wealth.

Because reference points play such a critical role in behavioral finance, researchers are naturally interested in understanding the processes by which reference points form and evolve. For instance, Kőszegi and Rabin (2006) propose a model in which reference points form and adapt by a process of anticipation. Baucells and Hwang (2016) suggest that reference points are determined by a psychological process and link it to a variety of behavioral biases, including sunk‐cost effects, payment depreciation, reluctance to trade, preference for prepayment, and flat‐rate bias.

In reality, reference points may shift over time in response to price changes and other factors, reflecting the phenomenon that decision makers habituate to new wealth levels just as individuals adapt their sensory perceptions to physical changes in brightness or temperature. In investment contexts, a shift in the reference point toward a newly realized price is called adaptation. Adaptation is naturally a dynamic process and therefore reference points should be viewed as a function of both current and past prices such as a weighted average of values in an observed price sequence (Feng & Seasholes, 2005; Grinblatt & Keloharju, 2001; Odean, 1998; Shefrin & Statman, 1985). In an experimental setting, Baucells et al. (2011; hereafter BWW) analyze reference point dynamics in which subjects formulate reference points for hypothetical stocks based on contrived price patterns. BWW show that although the reference point initially anchors to the purchase price, it subsequently adapts as the price path evolves to include intermediate prices and the current price, and may also have a built‐in profit expectation. Recent work by Riley et al. (2020) shows that the traditional capital gains overhang model can be significantly improved by incorporating reference point adjustments based on the BWW framework.

Despite the success of the BWW framework in explaining reference point formation for individual stocks, its simplified setting only considers each stock price movement as isolated from market contextual information and hence overlooks the market backdrop as one key feature of investments in reality. Toward that end, we incorporate market information as background to the BWW experiment to develop a new platform for analyzing the impact of market context on reference price formation.

There are several reasons why market context might affect reference point formation for individual stocks. Because covariation between stocks and the market is well known, investor expectations about the stock price may depend on the observed market state in combination with comovement measures such as beta or correlation. The current market trend combined with observed comovement may induce feelings of optimism or pessimism about the stock. Investor beliefs about mean reversion (Odean, 1998) or momentum (Grosshans & Zeisberger, 2018) may transfer to individual stocks, biasing expectations. Comparisons between own stock performance and the overall market may influence investor satisfaction (Merkle et al., 2015), affecting expectations and the propensity to sell or hold the stock (Grosshans & Zeisberger, 2018). Moreover, the limited attention theory (Kahneman, 1973) suggests that when market information is available, investors may pay less attention to some stock‐related variables, focusing instead on market factors such as current market trend. Investor attentiveness or nonattentiveness to the stock may be selective based on the observed market state due to the psychological utility of positive or negative information, as suggested by the asymmetric ostrich effect (Karlsson et al., 2009). In addition, investors may worry more about losses for stocks that are highly correlated with the market, as suggested by the downside risk hypothesis (Ang et al., 2006). Last but not least, because of heuristic biases such as anchoring (Tversky & Kahneman, 1974), in which reference points gravitate toward irrelevant or noninformative values, investors may adapt their reference points to the market backdrop as an unconscious anchor even when they have no investment experience and consider the market as irrelevant information.

Recent studies document that context‐specific effects vary by market condition. Lee et al. (2013) report that investors with extreme capital losses are more active in redeeming mutual fund shares in a bear market than in a bull market, whereas investors with moderate capital gains are less active in redeeming fund shares in a bull market. In neutral markets, they find that investors redeem both winner and loser funds except when they have extreme capital losses. Karlsson et al. (2009) conclude that adaptation is faster in rising markets than in falling markets because investors pay more attention in rising markets. However, Arkes et al. (2008) find that adaption to gains is greater than adaptation to losses whether the market is up or down, suggesting that attention is not the only factor. Kliger and Kudryavtsev (2008) find that reference point adaptation is more reactive when stocks are more sensitive to market fluctuations, that is, for high‐beta stocks. All of these findings suggest that reference point effects are context dependent. This limits the generalizability of BWW's findings and complicates the task of sorting the interplay between stock price factors and context‐driven effects, highlighting the need for more work in this area.

In addition to incorporating market context in the experimental methodology, we contribute to the literature by broadening the analysis to consider both prospect theory and emotion‐based explanations of reference point behavior in a unified framework, whereas BWW focus only on prospect theory. Although prospect theory has largely been supported empirically, research has shown that some of its key results are unstable across different contexts or framing domains (Fischhoff, 1983; Hershey & Schoemaker, 1980; Schneider & Lopes, 1986), thus motivating the need for an expanded framework.

One of the well‐known results associated with prospect theory is the disposition effect, which is based on Kahneman and Tversky's (1979) reflection effect or the tendency for decision makers to reverse preferences in loss versus gain domains relative to some neutral reference point, in a manner that exhibits risk seeking in the negative domain and risk aversion in the positive domain. The reflection effect and the related concept of mental accounting (Thaler, 1985) form a theoretical basis in prospect theory for what Shefrin and Statman (1985) call the "disposition effect," which states that investors tend to dispose of gains quickly but resist selling at a loss.

Empirical support for the disposition effect has been documented in studies using aggregate market data (Kliger & Kudryavtsev, 2008; Lakonishok & Smidt, 1986), individual investor trading accounts (Barber & Odean, 1999; Karlsson et al., 2009; Odean, 1998), and experimental settings (Arkes et al., 2008; Weber & Camerer, 1998). However, empirical validation is not uniform, and recent studies show that cognitive biases related to the visual processing of graphical information can affect investor behavior and reference point formation in ways not necessarily consistent with disposition effect behavior. In addition, investor perceptions of risk are frequently shaped by intuitive or heuristic processing of graphical features of price series, rather than orthodox optimization rules based on statistical moments. This is relevant in real‐world settings where investment performance is frequently displayed graphically to investors, and in experimental settings such as in our article where stock and market price sequences are presented in graphical format to subjects.

Duclos (2015) documents an end‐anchoring bias or the unconscious tendency to attach disproportionately high importance to the last trading day in a visual price sequence when forming expectations such that when controlling for other factors, an upward (downward) sloping last trade direction results in a higher (lower) willingness to purchase the stock. This is consistent with momentum investing or a belief in short‐term trend continuation.

Grosshans and Zeisberger (2018) document order preferences for gains and losses in visual price patterns and demonstrate that investor satisfaction is highest for down‐up patterns and lowest for up‐down patterns, when controlling for other factors. They conclude that higher levels of satisfaction associated with down‐up patterns correlate with more optimistic forecasts and lead to greater holding propensity for the stock. Their results are consistent with end‐anchoring and momentum beliefs. They find that reference point adaptation for stocks is more complete in the gain domain than in the loss domain, and they suggest that in up‐market environments, overall momentum beliefs may transfer to winner stocks and amplify the increase in reference point adaptation. In an experimental setting, they find that the disposition effect sometimes occurs without mean reversion beliefs, and they document that an inverted or reverse disposition effect can occur for relatively straight price patterns.

Duxbury and Summers (2018) analyze risk perceptions of observed price sequences in an experimental setting and document that investor perceptions of risk and volatility are driven by salient features of price path characteristics rather than by standard deviation of return. Although standard deviation of return may have a role to play in perceptions of price sequences, the authors show that other price‐based factors play a far greater role. Based on such price sequences, they find that price‐based factors, such as the number of peaks or the number of accelerated changes in direction within the price sequence, better predict risk and volatility perception. Furthermore, they report evidence to support the view that the extent to which prices appear irregular is a separate aspect of volatility, distinct from the extent to which prices deviate from central tendency. Borsboom and Zeisberger (2020) show that investors focus on heuristics in looking at visual stock price patterns and that investor risk perceptions are driven by salient features of price path characteristics such as high and low prices and short‐term crashes rather than standard deviation, consistent with Duxbury and Summers (2018). They also document investor belief in short‐term trend continuation consistent with end‐anchoring.

Sobolev and Harvey (2016) use a fractal structure to simulate price patterns and show that investor risk perceptions depend on the Hurst exponent, which measures the degree of roughness or smoothness in a price series. They find that when viewing only graphical information, subjects who measure highest for risk sensitivity based on their emotional instability perceive price charts with greater "roughness" to be riskier. Overall, they find that risk perceptions are more strongly influenced by the Hurst exponent than by traditional volatility measures from modern finance theory such as standard deviation.

All of these results suggest that market context effects may be further clarified by our study, in which subjects view simultaneous stock and market price patterns presented in graphical format, and highlight the need for an expanded framework that accommodates visual pattern effects and emotional factors. Although loss aversion under prospect theory is frequently cited as a primary rationale for the disposition effect, Summers and Duxbury (2012) document that emotions are a necessary cause of the disposition effect. Their findings show that prospect theory alone does not provide a sufficient cause for the effect and that specific emotions related to the task (i.e., elation for winners and regret for losers) are necessary for the effect to manifest. Shefrin and Statman's (1985) explanation for the disposition effect includes components of regret aversion and self‐control as supporting elements. Muermann and Volkman Wise (2006) develop a model in a dynamic portfolio setting to show that the disposition effect can be explained without loss aversion by positing preferences based on anticipated emotions of regret and pride. Other rationales for the disposition effect that appear in the literature include mean reversion beliefs (Odean, 1998) or preferences based on heuristics such as realization utility (Barberis & Xiong, 2012) where investors experience selling a given asset above (below) its purchase price as a positive (negative) investment "episode."

The disposition effect can be rationalized based on a combination of prospect theory and mental accounting with emotional factors playing a supporting role (Shefrin & Statman, 1985), or alternatively based solely on emotional mechanisms such as the balancing of conflicting feelings of regret and pride (Muermann & Volkman Wise, 2006). There is a broad literature on the role of emotion in shaping preferences, with seminal works that include anticipatory feelings of regret (Bell, 1982; Loomes & Sugden, 1982) or disappointment (Bell, 1985; Gul, 1991). Related to this literature, we incorporate in our analysis the Gollier and Muermann (2010; hereafter GM) model of ex ante savoring and ex post disappointment that combines Bell's (1985) disappointment theory with Akerlof and Dickens's (1982) concept of anticipatory feelings.

In analyzing market context we examine reference point adaptation through the lens of both prospect theory and the GM emotion‐based model. This overarching framework adds clarity to BWW's original findings and provides a decomposition of their results based on stock‐ and market‐related factors. We document evidence of market context effects both graphically and in regression analyses.

Our overarching framework combines the BWW and GM models, which both are behavior‐based alternatives to standard EU theory but differ in how they accommodate market context effects. A primary way that behavior‐based models differ from EU is through the assumption of probability‐dependent preferences (PDPs), where perceived utility depends not only on the shape of the utility function but also on subjective decision weights that may differ from objective probabilities. It is through the subjective decision weights that market context can matter.

Fehr‐Duda and Epper (2012) identify two main classes of PDP models: rank‐dependent models (Quiggin, 1982; Tversky & Kahneman, 1992), which include cumulative prospect theory as a variant, and disappointment aversion models (Gul, 1991). The BWW and GM models represent these two broad frameworks, respectively. These frameworks are differentiated by the manner in which subjective decision weights are formed. In rank‐dependent models, the decision weights are based on a ranking of possible outcomes, and gains and losses are measured relative to an exogenous reference point. In disappointment aversion models, decision weights and the reference point are determined endogenously and concurrently to optimally balance a trade‐off between feelings of anticipation and disappointment. We investigate market context‐related effects under each of these two broad frameworks.

Our experimental framework is similar to BWW who presented subjects with scenarios portraying a hypothetical sequence of stock prices $${y}_{1},\text{\unicode{x02026}},{y}_{n}$$ . For each observed price sequence, they elicited a reference price $${y}_{n+1}$$ from the subject. From these reference points, they inferred decision weightings on beginning, ending, and intermediate prices of the sequence for a representative subject. This is similar to the rank‐dependent model of Tversky and Kahneman (1992) but uses a ranking based on the timeline ordering of the price sequence to infer the relative weight that subjects attach to the position of each time point.

BWW consider two possible mechanisms of reference point formation to describe how subjects arrive at their reported values of $${y}_{n+1}$$ . Under the integrated mechanism, past prices are aggregated into a single reference value, $${r}_{n+1}=f({y}_{1},\text{\unicode{x02026}},{y}_{n})$$ , and experienced utility at time $$n+1$$ is determined by comparison of this reference value to the price at time $$n+1$$ . The subject's reported value $${y}_{n+1}$$ solves $$\nu ({y}_{n+1}\mbox{--}{r}_{n+1})=0$$ , where $$\nu $$ is a prospect theory value function such that $$\nu (0)$$ represents emotional neutrality. In other words, the reported value $${y}_{n+1}$$ is the subject's unique reference price. Under the segregated mechanism, the value function is applied separately to each past price, and overall utility is taken as a weighted average of the separate utility measures $${\sum }_{i=1}^{n}{\bar{\pi }}_{n,i}\upsilon ({y}_{n+1}-{y}_{i})$$ , where the weights sum to 1. The reported reference price $${y}_{n+1}$$ solves $${\sum }_{i=1}^{n}{\bar{\pi }}_{n,i}\upsilon ({y}_{n+1}-{y}_{i})=0$$ . The weights do not represent probabilities but are "prevalences" that measure subjective importance to the subject of each price in the sequence. For example, if only the purchase price matters, then $${\bar{\pi }}_{n,1}=1$$ and all of the other weights are 0.

BWW define five price factors based on the chart sequence: purchase price ( $${PP}$$ ) defined as $${y}_{1}$$ , current price ( $${CP}$$ ) defined as $${y}_{n}$$ , average intermediate price ( $${AIP}$$ ) defined as $${\sum }_{i=2}^{n-1}{y}_{i}/(n-2)$$ , high price ( $${HP}$$ ) defined as $${\rm{\max }}({y}_{i}),$$ and low price ( $${LP}$$ ) defined as $${\rm{\min }}({y}_{i})$$ . BWW find that $${PP}$$ and $${CP}$$ are heavily weighted, indicating high salience on initial and ending prices, and less decision weight for intermediate price factors. We follow BWW's definitions but subscript them by stk and mkt to refer to the stock and market patterns, respectively.

Rank‐dependent models like BWW can help to explain non‐EU behaviors such as the disposition effect but are limited in their ability to explain market context effects involving emotional or expectational elements, as the decision weights under prospect theory are normally based on a limited range of psychological factors. Alternatively, the GM model postulates an explicit behavioral process for the formation of decision weights based on feelings of anticipated disappointment and ex ante savoring. These feelings correspond to the human traits of pessimism and optimism, which are perhaps the most common characterizations of market sentiment, making the GM model a natural choice for analyzing the impact of market context on reference point formation.

The GM model assumes a set of lottery payoffs $${c}_{1},\text{\unicode{x02026}},{c}_{S}$$ with corresponding objective probabilities $$Q={q}_{1},\text{\unicode{x02026}},{q}_{S}$$ . The decision agent forms an anticipated payoff $$y$$ that provides satisfaction from ex ante savoring but at the same time increases ex post disappointment. The agent chooses subjective probabilities $$P={p}_{1},\text{\unicode{x02026}},{p}_{S}$$ simultaneously with y to optimally balance the utility trade‐off between savoring and disappointment. The reference point is the optimal value $${y}^{\star }$$ that equates the expected payoff to the certainty equivalent of the risky lottery. GM express this as a maximization problem over an intertemporal preference functional $$W(Q)$$ that is a weighted sum of anticipatory satisfaction at date 1 and expected satisfaction from the final payoff at date 2:

The first term in Equation (1) measures ex ante utility from anticipatory savoring based on subjective probabilities P, and the second term computes utility of ex post consumption based on objective probabilities Q. The certainty‐equivalence condition is imposed by the constraint, and parameter k is an intensity measure of the agent's anticipatory feelings.

Next, we identify specific behavioral mechanisms that account for market background effects underlying each of the two modeling frameworks, starting with BWW. Market context in BWW is best understood in terms of the dual‐process theory of human behavior (Alós‐Ferrer & Strack, 2014) that differentiates affective and cognitive components of decision processes. In cumulative prospect theory, these components are identified as two parallel stages: an unconscious editing stage where objective payoffs are transformed via a weighting function, and a cognitive evaluation stage where the transformed payoffs are ranked via the prospect theory value function. The editing stage involves unconscious emotions and decision heuristics to simplify the choice set before the more reasoned/reflective processing stage. Context shifts in prospect theory are dealt with at the editing stage, as noted by Vlaev (2018) who refers to the editing stage as an example of local rationality.

The dual‐processing view clarifies the distinct role of beliefs versus preferences in prospect theory, and the corresponding role of context. Beliefs are exogenous but can be "bent" or shaped in the editing stage via the subjective weighting function to reflect behavioral biases or contextual information, whereas preferences are defined by the value function and are normally considered to be relatively stable across contexts (Ungemach et al., 2011). Although decision weights are akin to subjective probabilities, Kahneman and Tversky (1979) emphasize that they are not beliefs and may be in direct contradiction to stated objective probabilities. For our experiment, objective probabilities governing future stock payoffs are specifically stated in the instructions to subjects, as was done in BWW and similar studies to minimize expectational bias.

Through the weighting function, subjects can manipulate objective probabilities behaviorally, for example, by over‐ or underweighting different payoffs based on their degree of objective uncertainty as in Kahneman and Tversky (1979). One such incremental effect associated with market context might be a visual impression of covariation between stock and market prices that may cause subjects to change their subjective weightings in the editing stage, but this happens unconsciously and does not necessarily correspond to a change in objective beliefs. We purposely relegated market context information to the background by portraying it only in graphical form, and we made minimal reference to it in the instructions to subjects to avoid making it focal to the decision task.

The presence of market information in the background can influence the editing process in various ways, one of which is through affect. For instance, the simple act of viewing a rising or falling market can evoke feelings or emotions such as optimism or pessimism. Or as mentioned earlier, the market viewed in conjunction with a stock price pattern may unconsciously suggest something about future stock price movement because of perceived covariation. This does not mean that subjects necessarily compute or even conceptualize a formal covariation parameter such as beta or correlation, as the editing stage operates unconsciously on the basis of emotion and heuristic simplification to set the stage for cognitive processing. The notion that subjects perceive volatility or comovement information directly from the visual pattern in the editing stage without formal computation of statistical parameters is consistent with Duxbury and Summers (2018), Borsboom and Zeisberger (2020), and Sobolev and Harvey (2016), as well as Grosshans and Zeisberger (2018) who state that the specific mechanism in prospect theory for the cognitive biases they address is the weighting function. In addition, reference point formation in general may reflect aspirational thinking as mentioned by BWW, or other factors such as anchoring or attention. These different interpretations are not mutually exclusive and may be reinforcing or offsetting.

In the GM framework, context effects are modeled through their impact on investor emotions of anticipated disappointment and ex ante savoring. The relevant information in forming such emotions in our experiment is the market price graph. A natural question is whether contextual market information may introduce a form of expectational bias in beliefs, which it may, but in the GM model it does so by design with regard to subjective probabilities $$P$$ , not objective probabilities $$Q$$ . Expectational bias is not problematic in GM and may involve counterfactual thinking in forming expectations about the future. Moreover, GM point out that the manipulation of subjective beliefs by the decision agent in their model is fully rational. Market context matters not by changing the objective payoff distribution, but by coaxing out emotions such as optimism or pessimism that are reflected in the formation of subjective probability beliefs that are intentionally distorted by subjects to optimally balance their conflicting emotions. GM point out that the optimal subjective belief distribution is not unique to a given solution and that multiple possible belief distributions can support the same optimal reference point. This is consistent with the notion that different explanations for behavioral phenomena are not mutually incompatible and that a combination of factors may operate simultaneously for a given decision agent or between agents.

In terms of the specific mechanism for market context in their model, GM point out that the parameter $$k$$ "depends upon both psychological and contextual elements" (p. 1276). They show that more anticipatory feelings correspond to a larger $$k$$ (optimism), whereas less anticipatory feelings correspond to a smaller $$k$$ (pessimism). We argue that $$k$$ , along with subjective beliefs that are determined endogenously in GM, subsume the same types of emotional and behavioral factors that prospect theory addresses in its editing stage.

One way to conceptualize our combined modeling framework is to start with BWW and then add market context to see if/how it changes the outcome. BWW document primacy and recency effects where subjects anchor to the initial and terminal prices, which the authors explain by the prospect theory weighting function. Our experiment adds market context, which creates the possibility for emotion‐based and expectational effects that are not easily explained by prospect theory but that are easily accommodated in a GM framework that allows endogenous belief formation. In GM, decision makers can reoptimize their utility in response to incremental information by forming a new combination of reference price $${y}^{* }$$ and subjective probabilities $${P}^{* }$$ .

Consider a thought experiment where a GM decision agent forms a reference price based on past stock price information, as in BWW. Now, add market context information that changes the decision agent's outlook, making her more optimistic or pessimistic. The agent can recalibrate her subjective probabilities to form a new reference price and achieve a new level of utility, which may be either higher or lower than before, but one that is optimal (and rational) given the new information. The resulting change in the reference price represents the marginal effect of the new information. We designed our experiment with the aim of capturing this incremental effect. The market pattern in our experiment is presented concurrently with the stock pattern; therefore, the new information does not arrive intertemporally but is incremental in a comparative static sense. Also, the market information is not focal to the decision task but is "additional" in the sense that it adds a contextual element to the modeling framework, not in the sense that enlarges the focal information set for the decision task (as would, say, adding an additional price point to the stock chart). Market context operates largely through unconscious mechanisms and can change outcomes without changing objective beliefs about returns, for example, through its impact on emotional state or heuristic biases. Our overarching hypothesis is that market context matters, which we can demonstrate by conditioning BWW's results on different market states.

The change in perceived utility related to the addition of market context requires no conscious action on the part of the agent. However, it does require the agent to deliberately balance "wishful thinking" with realistic expectations in a way that, as GM point out, involves managing some cognitive dissonance. But this is something humans do all the time to feel better about situations they may not control. New information may provide a signal that triggers a rebalancing of the trade‐off between apprehension and elation. A person may contemplate this trade‐off even if he does not act on it. Such contemplation, whether unconscious or volitional, is equivalent to changing the amount the person is willing to pay if he imagined placing a hypothetical bet; that is, it is equivalent to changing his reference point.

Following our previous discussion of possible reasons and mechanisms, we create several hypotheses on how the market context may affect the reference point formation of individual stocks, which we investigate through our experiment as detailed in the following sections.

H1: Covariation effects: Perceived covariation may lead investors to base reference point decisions on the observed market state in combination with covariation measures such as beta or correlation.

Previous findings mentioned earlier (e.g., Kliger & Kudryavtsev, 2008; Lee et al., 2013) suggest that reference point formation may depend on covariation between stock and market patterns. Other studies (e.g., Duxbury & Summers, 2018) suggest that such covariation effects may be gleaned from visual patterns even if investors do not formally compute statistical parameters. Such effects may operate unconsciously through the prospect theory weighting function (Grosshans & Zeisberger, 2018) or, in the GM framework, through their impact on optimism/pessimism.

H2: Divided attention theory: When market information is available, investors may reduce their attention on some intermediate stock price factors (AIP, HP, and/or LP), focusing instead on the main stock price factors of PP and CP, as suggested by the Kahneman (1973) model of divided attention.

The Kahneman (1973) model of divided attention suggests that attention is a limited resource and that individuals performing a task may selectively concentrate their attention on a salient subset of input variables while ignoring less salient variables. In forming reference prices based on stock price patterns, BWW document primacy and recency effects where subjects place greater decision weight on initial and terminal prices, suggesting that $${PP}$$ and $${CP}$$ are the more salient stock price factors. We hypothesize that when market context is added, investors pay less attention to intermediate stock price factors, focusing instead on contextual market information such as direction of market trend or last price direction, in conjunction with the more salient stock factors.

H3: Asymmetric ostrich effect: Investors may exhibit greater adaptation of their reference point in a rising versus falling market environment because of attentional differences (Karlsson et al., 2009).

Karlsson et al. (2009) suggest that asymmetric attention in different market states derives from investor preferences. They posit a utility function that exhibits positive utility of information in up‐market states and disutility of information in down‐market states. This is in contrast to the divided attention theory, which is based on limited attentional resources.

H4: Asymmetric adaptation in gain versus loss domains: Investors may exhibit greater adaptation of their reference point in the region of stock gains versus losses as a result of hedonic maximization as suggested by (Arkes et al., 2008).

In an experimental setting, Arkes et al. (2008) find that reference point adaptation is greater in states where the stock is in a capital gain ( $${CP}\gt {PP}$$ ) versus capital loss ( $${CP}\lt {PP}$$ ) position. They attribute this to positive hedonic consequences of closing out one's mental account in the gain domain versus negative hedonic consequences of doing so in the loss domain. They obtain this result whether the stock is held in isolation or as part of a portfolio. Although our experimental framework does not involve direct selling decisions by subjects, it does evoke a reservation price at which subjects would be willing to sell, allowing us to infer indirect evidence consistent with the disposition effect by examining the extent of asymmetric adaptation exhibited by subjects in loss versus gain domains, using purchase price as the reference point for judging gains and losses. Similar to Arkes et al. (2008), we argue that evidence of subjects fully adapting to the current price in the gain region but not in the loss region (or adapting asymmetrically to a greater extent in the gain region) reflects the differing hedonic consequences of closing one's mental account in each domain and is consistent with the disposition effect even though we do not provide direct evidence.

H5: Investors may exhibit a higher reference price when they are optimistic versus pessimistic about their own stock or the overall market because of feelings of ex ante savoring and ex post disappointment (GM).

The GM model implies that the reference price is higher when the investor is more optimistic and lower when the investor is more pessimistic. We hypothesize that investor optimism or pessimism may depend on the economic state, such that higher stock or market price leads to greater optimism and a higher reference price, and lower stock or market price leads to greater pessimism and a lower reference price.

H6: Investors may exhibit a higher reference price for visual price patterns that follow down‐up versus up‐down patterns (Grosshans & Zeisberger, 2018).

Grosshans and Zeisberger (2018) find that investors feel a greater sense of investor satisfaction for down‐up patterns, leading them to be more optimistic, and less investor satisfaction for up‐down patterns, leading them to be more pessimistic. The GM model implies a higher reference point for more optimism and a lower reference point for more pessimism.

H7: Investors may anchor to the market and bias their reference price to the market direction (Tversky & Kahneman, 1974).

The unconscious cognitive bias of anchoring to the market may lead to higher reference prices in up‐market states and lower reference prices in down‐market states. Market direction in this case may be defined by either short‐term price movement, such as last trade, or long‐term price direction, such as linear trend.

H8: Investors may exhibit end‐anchoring and bias their reference price toward the most recent directional move in a price sequence (Duclos, 2015).

End‐anchoring applies specifically to the direction of the last market price move and is consistent with investor beliefs about short‐term trend continuation in the market transferring to the stock. It implies that the reference price may move in the direction of the last market price move.

In the experiment, we examine the impact of market information on the formation and updating of the reference point adopted by participants. Experiments were conducted in a classroom setting at a major state university in the United States on groups of subjects consisting of a roughly equal proportion of male and female undergraduate finance students who had completed at least one junior‐level principles of finance course. A majority of the subjects are US citizens and about 6% are international students. Three separate group sessions were held with similar room conditions for each session and subjects completed the experiment individually on personal computers. Professors proctored the sessions and subjects were awarded a small amount of extra credit toward their final grade to facilitate engagement and to ensure the quality of the experiments. Of 77 subjects who completed the experiment, 14 were eliminated because of outliers or other reasons described next, resulting in a final sample of 63 subjects. Subjects were given a regular class period (75 min) to finish the experiment and were not allowed to communicate with each other to prevent any exchange of opinions that may influence their reference point formation processes. We believe that the chosen time limit was sufficient but required some budgeting of cognitive resources to provide an appropriate balance between reflexive and contemplative subject responses.

Outliers were eliminated by a combination of formal outlier detection criteria and visual inspection, yielding overlapping results with the exception of one subject. The formal outlier analysis eliminated 9 subjects who reported at least one reference price with p‐value less than 0.0001 in absolute value based on a two‐tailed test applied separately to each visual pattern. The visual inspection method eliminated 1 additional subject who stated a reference price as 100 times the current price, which we suspect is due to a missing decimal point. In addition, 4 subjects were eliminated for uniformly choosing a reference price equal to the current stock price for every price chart; we do not believe these subjects devoted sufficient time or reflection to actually engage the underlying behavioral mechanisms hypothesized by the theories under investigation.

Following BWW, we presented each subject with a series of simulated stock price patterns on a computer screen. Order effects were controlled for by randomizing the order of presentation of charts across subjects (see Grosshans & Zeisberger, 2018; Loewenstein & Prelec, 1993; Read & Powell, 2002). For each pattern, we asked the subject to imagine that they purchased the stock several days ago and then immediately went on vacation to a locale where they could not trade the stock or monitor its price. Upon returning from vacation, the subject viewed a sequence of stock prices that occurred during their absence. Similar to Arkes et al. (2008) and BWW, we elicited a reference point by asking the subject to enter a price that would produce "emotional neutrality" if they were to sell the stock at their stated price.

For comparability with BWW, we used essentially the same language as theirs in our instructions to the subject. Unlike BWW, however, in addition to the stock pattern, we displayed a simultaneous price pattern for the overall stock market, to which students could either pay attention or ignore. To avoid introducing semantic or framing effects, we made no mention of the market information verbally and made only minimal reference to it in the written instructions, simply modifying the BWW language to state that the subject "will be shown the stock price and market index development chart." We added the market price sequence to the chart as subtle background information, giving no indication of its relevance. The exact set of instructions given to subjects appears in Figure 1.

For each stock price path, we are interested in the extent of reference point adaptation, that is, the degree to which a subject's reference point tends toward the most recently observed stock price. Adaptation is measured as a proportion of the cumulative observed stock price change as follows:

$$${A}_{i}=\frac{{R}_{i}-\,{PP}}{{CP}\,-\,{PP}},$$$

where i denotes the ith subject, and PP and CP denote the stock's purchase price and current price, respectively. An illustration of adaptation levels for two illustrative simple stock patterns appears in Figure 2, where Panel (a) represents a capital loss situation (CP < PP) and Panel (b) represents a capital gain situation (CP > PP). Complete adaptation is defined as Ai = 1, implying a reference price of Ri = CP, whereas 0 adaptation implies Ai = 0 and Ri = PP. Reference price adaptation can exceed 1 or be negative. For example, if a stock is purchased at $200 and ends at $250, a reference price of $275 implies overadaptation with Ai = 1.5, and a reference price of $175 implies negative adaptation with $${A}_{i}=-0.5$$ .

BWW devised a methodology to measure the impact of each price factor ( $${PP}$$ , $${CP}$$ , $${AIP}$$ , $${HP},$$ and $${LP}$$ ) on subjects' reference point formation by constructing "orthogonal" pairs of price sequences such that the sequences in each pair were identical with respect to exactly four factors; hence, any difference between the reference points from those two sequences must be attributable to the fifth factor. We extend BWW's methodology by associating each stock price pattern with four market price paths that can be strategically paired to analyze interaction effects between stock and market factors. Specifically, we first selected a subset of 20 BWW stock price patterns, then we augmented each stock pattern by constructing four associated market patterns, creating four subcases labeled a–d for each original stock pattern. This resulted in 80 total cases where each case consists of a stock pattern and an associated market pattern. Our choice of which BWW patterns to retain was based on our judgment of which patterns were best suited to our design framework for incorporating market context effects. We contrived our market patterns in a manner to facilitate analysis of both stock and market characteristics, as well as covariation effects. A complete listing of our stock and market patterns appears in Table 1.

1 TableThe 160 stock and market price sequences used in the experiment

1 Note: The yi columns contain the ith price of each sequence. The last column contains the elicited reference price, averaged across subjects. Price units are dollars. Subjects saw the 80 paired stock/market price charts in random order.

To be consistent with BWW we kept the same numbering of stock patterns; therefore, as we only used a subset of patterns there are gaps in our numbering.

Each of the 63 subjects reported reference prices for 80 unique stock/market price patterns, resulting in 5040 reference point observations that we analyzed in several different ways. The average reported reference price for all subjects for each pattern appears in the last column of Table 1.

The stock and corresponding market price patterns were devised to systematically analyze interactions between stock and market effects on reference price behavior. For instance, Figure 3 displays an example involving Stock Price Patterns 1 and 2 from Table 1, which are denoted by $$j$$ and $$k$$ , respectively.

In each panel of Figure 3, stock patterns $$j$$ and $$k$$ are identical with respect to all factors except purchase price; therefore, any difference in the reference prices, $${R}_{j}-{R}_{k}$$ , must be attributable to the purchase price. In Panel (a), the average reference prices differ by 33.05 and the purchase price differs by 100; therefore, the unit increase in reference price for each dollar of price differential is 0.33, other factors held constant. The market price in Panel (a) follows a down‐up pattern. Panel (b) is similar except that its market pattern is up‐down. The unit effect in Panel (b) is 0.44, which is one‐third higher than Panel (a), showing that stock price adaptation can be influenced by subtly displayed differences in market background.

Each panel in Figure 3 measures the unit impact of purchase price on the reference point under a different market scenario. In all, of the 80 unique stock/market patterns, eight orthogonal pairs can be formed to similarly measure the unit impact of $${PP}$$ under different market scenarios. These eight patterns are shown in Table 2, along with similar sets of eight orthogonal pairs formed to measure the impact of each of the other stock price factors, $${CP}$$ , $${AIP}$$ , $${HP},$$ and $${LP}$$ , under various market contexts. This table shows the eight pairs used to isolate each factor and displays the reference price differential that is observed on average, both in dollar terms and per currency unit. For a given stock price factor, different reference price differentials are observed for different orthogonal pairs, indicating that the impact of the price factor depends on market context.

2 TableFactor pairings and results of matched‐pairs tests (N = 63)

2 Note: This table shows the price pattern pairings used to isolate stock price factors, and results of paired‐sample analyses consisting of a t‐test of different means and a matched‐pair sign test. Price patterns are designed to isolate the effect of each stock price factor on the reference price, with eight pairings designed for each factor: purchase price (PP), current price (CP), average intermediate price (AIP), high price (HP), and low price (LP). Reported p‐values are two‐tailed and are Bonferroni adjusted to take into account multiple pairwise comparisons for each factor. The sample proportion P̂ refers to the fraction of subjects with positive values of (Rj – Rk) after eliminating ties in conducting the sign test.

For each pair, we perform a matched‐pair sign test to test the significance of results for each row in the table, similar to BWW. In performing their matched‐pairs sign tests, BWW use the definitional formula for $${AIP}$$ ( $${\sum }_{i=2}^{n-1}{y}_{i}/(n-2)$$ ) to compute the unit effect, but for control purposes in constructing orthogonal pairs, BWW include the terminal price points in computing the arithmetic average, that is, $${\sum }_{i}^{n}{y}_{i}/n$$ . On both counts, we replicate the BWW methodology for comparability. Our tests are conducted at the 5% significance level, and our reported p‐values for the sign test are Bonferroni corrected (unlike BWW) to account for the fact that there are multiple pairwise comparisons for each factor. In addition to the sign test performed by BWW, we perform a t‐test of difference‐in‐means, and the reported p‐values are similarly adjusted. Results are summarized in Table 2.

For $${PP}$$ and $${CP}$$ , the p‐values indicate uniformly strong statistical significance, with mixed results obtained for the other factors. Table 2 results are summarized as follows:

• Purchase price (PP): We find an overall average unit effect of 0.38 for $${PP}$$ , with substantial differences observed across market patterns. For example, the four cases comparing Stock Patterns 1–2 produce unit effects ranging from 0.33 to 0.44, conditioned on the market pattern. For Stock Patterns 7–8, the conditional unit effects range from 0.28 to 0.45, suggesting that market context matters. Our findings for $${PP}$$ are uniformly significant, with p‐values of 0 (after Bonferroni correction) for all eight treatments for both the sign test and the mean difference test.
• Current price (CP): For $${CP}$$ , the overall average unit effect is 0.42. Similar to purchase price, we observe considerable variability across market scenarios. Notably, Stock Patterns 11–12 exhibit unit effects ranging from 0.41 to 0.61, and Stock Patterns 15–16 exhibit less variable unit effects, ranging from 0.31 to 0.37. Again, all p‐values are 0 for all eight treatments for both the sign test and the mean difference test.
• Average intermediate price (AIP): For $${AIP}$$ , the overall average unit effect is 0.12. Again, the conditional effect exhibits wide variation; however, for both tests only one‐fourth of cases are statistically significant after Bonferroni correction. Overall, these results suggest a relatively weak influence of $${AIP}$$ compared to $${PP}$$ and $${CP}$$ , with market information being less influential on reference price formation compared to $${PP}$$ and $${CP}$$ .
• High price (HP): We find HP to be largely noninfluential. The overall average unit effect is only 0.04, and none of the orthogonal pairs involving $${HP}$$ is statistically significant.
• Low price (LP): $${LP}$$ exhibits an overall average unit effect of −0.22. Notably, Stock Patterns 35–36 indicate highly influential and significant results, with wide variation across market patterns. The conditional unit effects range from −0.30 to −0.57, all with p‐values of 0. These results suggest that investors might sometimes anchor to the stock's historical low price, depending on the market situation. The sign of the unit effect is unexpectedly negative for $${LP}$$ , as in BWW, but in subsequent regression analyses we show that this appears to be due to stock and market interaction effects, as the statistical significance on $${LP}$$ in our regressions (see Table 5 later) disappears when we add indicator variables to control for up and down stock and market states.

Overall, these results suggest that observed differences in unit effect across treatments can be attributed to market context. In Table 3 we formally test for differences in unit effect across market patterns using a two‐stage process. First, in Panel A we perform homogeneity tests on the mean difference unit effect for each stock factor using a one‐way analysis of variance (ANOVA) test. For each price factor, the treatments are split into two subgroups for analysis based on the stock pairings, resulting in four treatments for each subgroup. Then, for any subgroup found to be significantly heterogeneous at the 10% level, in Panel B we perform a post hoc analysis of pairwise differences in mean unit effect for all possible pairwise combinations of treatments within each subgroup that advances to this stage. The post hoc test is performed at the 5% significance level. Panel B can be viewed as a multiple‐treatment framework; therefore, we Bonferroni‐correct the p‐values to control for the familywise error rate. In Panel B we report both single‐test (unadjusted) and Bonferroni‐corrected p‐values.

3 TableImpact of market pattern on unit effect

3 TableImpact of market pattern on unit effect

3 Note: This table displays results of subgroup analyses to investigate whether differences in the unit effects in Table 2 can be attributed to differing market background information. In Panel A, one‐way analysis of variance (ANOVA) F‐tests of homogeneity are performed on treatment subgroups selected to differ only with respect to market pattern. In Panel B, post hoc analysis is performed on subgroups found to be significantly heterogeneous at α =.10. Post hoc analysis consists of paired‐difference t‐tests of differences in mean unit effects between all possible within‐subgroup treatment pairs. The p‐values reported in Panel B include both single‐test and Bonferroni‐adjusted values. See Table 2 for factor definitions.

In Panel A of Table 3 we find that the following 4 of 10 subgroups exhibit sufficient heterogeneity to advance to the post hoc stage: $${PP}$$ Subgroup B, $${CP}$$ Subgroup A, and $${AIP}$$ Subgroups A and B. This results in 24 total pairwise comparisons in Panel B (6 from each subgroup). Of the 24 comparisons, 13 (or approximately one‐half) are found to have significantly different mean unit effects at the 5% level when looking at single‐test p‐values. However, only five pairwise tests (approximately one‐fifth) survive the Bonferroni correction, with 4 appearing in $${AIP}$$ subgroups and 1 appearing in a $${CP}$$ subgroup. Therefore, we can conclude from Tables 2 and 3 that although $${PP}$$ and $${CP}$$ are the most influential price factors in determining reference points, the most significant variation is with $${AIP}$$ . Overall, these results document that market context matters.

In analyzing the average unit effect in Tables 2 and 3, we do not condition the results on the market; therefore, our results can be compared to the unconditional impact measured by BWW who do not include market information in their experiment. When taken together, our results are remarkably consistent with BWW for most of the stock price factors. Notably, our overall average unit effect across all scenarios for all five factors combined is equal to 0.74, compared to an overall average of 0.75 for BWW. In Section 5 we decompose BWW's unconditional measures by examining stock and market interaction effects to provide a more nuanced explanation of reference point formation.

Following BWW, we analyze the impact of relevant factors by performing a regression of the reference prices reported by subjects on relevant factors in a combined model containing data from all of the paired comparisons. Whereas BWW consider only the five stock‐related factors discussed earlier, we include market‐related factors as additional independent variables. Results appear in Table 4. Significance of coefficients is examined at the 5% level. For comparison purposes, we include BWW's findings in Table 4. As in BWW, standard errors are clustered by subject to remove correlation bias.

4 TableRegression of Rk on stock‐ and market‐related factors (N = 5040)

• 4 Note: Baucells et al. (2011; BWW) results from their five‐factor model that includes only stock factors (defined in Table 2). LASTLEG denotes the magnitude of price change from the last inflection point in the visual pattern, and TREND denotes the slope of a linear best fit line fitted to the price sequence. UP_DOWN and DOWN_UP are indicator variables denoting patterns that follow strictly up/down or down/up shapes, respectively. BETA is the conventional beta measure computed from the returns implied by stock and market patterns, and POS_BETA and NEG_BETA are indicator variables denoting observations in the top and bottom beta terciles, respectively. Standard errors are clustered by subject.
• 5 * p < 0.10;
• 6 ** p < 0.05;
• 7 *** p < 0.01.

In Table 4, we first perform a "naı̈ve" regression (Model 1) using the same five stock‐related factors used by BWW. In comparing our results to BWW, we note that BWW obtain significance for all five stock‐related factors, whereas we obtain significance for only three factors: PP, CP, and LP. The difference in results can be explained by the fact that BWW used only stock price information to form their reference price, whereas our subjects used additional market information. We suggest that the presence of market information led investors to focus less on intermediate stock price factors, consistent with the divided attention hypothesis (H2).

Our intercept of 57.53 is significantly higher than BWW's intercept of 15.20. We explain this difference by noting that even though it is the same regression equation, subjects in the two studies had different information when they formed their reference points. Our subjects had additional market information that BWW subjects did not. We contend that our intercept is higher because it absorbs the explanatory power associated with market‐related factors, which represent omitted variables in our Model 1. BWW's subjects did not have market information when forming their reference prices, so those are not "omitted variables" in BWW. This argument is reinforced by the observation that when we add the missing market factors in our subsequent models, the intercept drops to a level that is commensurate with what BWW find using the five stock variables. BWW attribute their intercept to the possibility that subjects may haved added a built‐in profit, which is a viable interpretation for both models. In Model 1 our coefficients on PP and CP are 0.38 and 0.43, respectively, compared to BWW's coefficients of 0.50 and 0.27.

In Model 2 we add five market‐related price factors: $$P{P}_{{mkt}}$$ , $$C{P}_{{mkt}}$$ , $${AI}{P}_{{mkt}}$$ , $$H{P}_{{mkt}},$$ and $$L{P}_{{mkt}}$$ . Again, we find that purchase price and current price are significant with coefficients of 0.37 and 0.45, respectively. Low price is also significant but is only slightly different from zero. In addition, current price and average intermediate price for the market are also significant, with relatively small coefficients of 0.06 and −0.05, respectively. The intercept is considerably lower than the previous model and is not significant. Apparently, when market information is available, investors still pay attention to the stock's current price and purchase price, but pay less attention to other stock‐related variables. They focus instead on market factors such as current price and recent intermediate price trend, which implies that investors may have limited attention to some stock‐related variables during the investment process (H2).

In Models 3 and 4, respectively, we add terms for both the stock and the market related to short‐ and long‐term price trends. In Model 3 we add a factor called LASTLEG to capture the current short‐term price trend as measured by the magnitude of price change from the last inflection point in the visual pattern. In Model 4 we add a factor called TREND to capture the long‐term overall linear price trend, defined by the slope of a best‐fit line computed for each price sequence plotted as a function of time using ordinary least squares. We find that for LASTLEG, the coefficient is positive and significant for both the stock and the market, indicating end‐anchoring effects (H8) for both charts, although the magnitude of the coefficient is close to 0, equaling 0.03 in both cases. This is consistent with short‐term trend continuation beliefs for both the stock and the market. It is also consistent with the GM explanation that reference points are influenced by feelings of investor optimism or pessimism gleaned from viewing the stock or market chart (H5). For TREND, we find that the coefficient is significant only for the market pattern, with a negative coefficient of −0.13. This contradicts both H5 and H8 when market direction is defined by the longer term linear trend as opposed to last price move, suggesting that perhaps this overall result is driven by stock/market interaction effects, which we explore in subsequent analyses that partition on stock and market states.

In Model 5 we add BETA as a measure of covariation, defined as the slope of the characteristic line obtained by regressing the stock return on the market return using returns implied by each pair of stock and market price sequences. BETA is not significant in Model 5. In Model 6 we add indicator variables $${{UP}}_{\_}{DOWN}$$ and $${{DOWN}}_{\_}{UP}$$ to the set of stock price factors to test the visual pattern effect documented by Grosshans and Zeisberger (2018). We find that both factors are significant, with the predicted sign and large coefficient magnitudes confirming a strong preference for down‐up versus up‐down stock reversal patterns (H6).

Finally, in Model 7 we add two indicator variables to represent covariation effects based on positive or negative beta; these variables represent the top and bottom terciles of beta and are named $${{POS}}_{\_}{BETA}$$ and $${{NEG}}_{\_}{BETA}$$ , respectively. We interact each of these with LASTLEG to look for asymmetric effects. We find a negative sign and statistical significance for the $${{POS}}_{\_}{BETA}$$ intercept dummy, and a negative sign and statistical significance for the interaction term between $${{NEG}}_{\_}{BETA}$$ and LASTLEG. We suggest that the negative sign for $${{POS}}_{\_}{BETA}$$ relates to risk, and this finding combined with the nonsignificance of $${{NEG}}_{\_}{BETA}$$ indicates that a negative beta may be perceived as less risky because of its diversification potential. The significant interaction term for $${{NEG}}_{\_}{BETA}$$ is of the correct sign in that it implies the reference price moves opposite the market direction when the stock covaries negatively with the market. In other words, for negative beta stocks an up‐market move may lead investors to become more pessimistic about the stock (H5). Taken together, these results confirm that investors pay attention to covariation effects (H1).

Overall, for the models considered we find that the significance of market factors varies depending on which measures of stock and market trend are included in the model. At the same time, we find that the stock's purchase price and current price remain consistently significant across all model specifications with fairly stable coefficient values of approximately 0.37 for $$P{P}_{{stk}}$$ and 0.45 for $$C{P}_{{stk}}$$ , suggesting that when market information is available, investors continue to focus on the purchase price and current price of the stock as the two most important stock characteristics, but pay less attention to intermediate stock price factors (H2).

To further disentangle the stock and market effects, we perform regressions on indicator variables corresponding to different combinations of up/down price scenarios. We examine both one‐way effects (stock or market direction considered separately) and two‐way effects (combined stock and market directions). We include the five stock price factors in the regressions and add $${{{UP}}_{\_}{DOWN}}_{{stk}}$$ , $${{{DOWN}}_{\_}{UP}}_{{stk}}$$ , and BETA to control for visual pattern and covariation effects. We regress both the reference price $${R}_{k}$$ and the adaptation level $${A}_{k}$$ on these factors. Regression results for each dependent variable, $${R}_{k}$$ and $${A}_{k}$$ , appear in Tables 5 and 6, respectively.

5 TableRegression of Rk on stock and market states

• 8 Note: In this table we regress the reference point (Rk) on the five Baucells et al. (2011; BWW) stock factors (defined in Table 2) plus indicator variables to represent different combinations of up/down price scenarios using three criteria: stock price direction is based on positive or negative capital gains (GAIN), and market price direction is based on positive/negative price trend (TREND) or positive/negative last leg price direction (LASTLEG). Additional variables are included to control for the impact of the visual pattern on investor satisfaction and for covariation effects. UP_DOWN and DOWN_UP are indicator variables denoting patterns that follow strictly up/down or down/up shapes, respectively, and BETA is the conventional beta measure computed from the returns implied by stock and market patterns. STKUP and STKDN are dummy variables indicating up‐ and down‐stock states, respectively, and MKTUP and MKTDN are dummy variables indicating up‐ and down‐market states. The regression coefficients are used to perform hypothesis tests of stock/market interaction effects. The one‐way analysis model corresponds to Equation (2), and the two‐way analysis model corresponds to Equation (3). Standard errors are clustered by subject.
• 9 * p < 0.10;
• 10 ** p < 0.05;
• 11 *** p < 0.01.
• 6 TableRegression of Ak on stock and market states

• 12 Note: In this table we regress reference point adaptation (Ak) on the five Baucells et al. (2011; BWW) stock factors (defined in Table 2) plus indicator variables to represent different combinations of up/down price scenarios using three criteria: stock price direction is based on positive or negative capital gains (GAIN), and market price direction is based on positive/negative price trend (TREND) or positive/negative last leg price direction (LASTLEG). Additional variables are included to control for the impact of the visual pattern on investor satisfaction and for covariation effects. UP_DOWN and DOWN_UP are indicator variables denoting patterns that follow strictly up/down or down/up shapes, respectively, and BETA is the conventional beta measure computed from the returns implied by stock and market patterns. STKUP and STKDN are dummy variables indicating up‐ and down‐stock states, respectively, and MKTUP and MKTDN are dummy variables indicating up‐ and down‐market states. The regression coefficients are used to perform hypothesis tests of stock/market interaction effects. The one‐way analysis model corresponds to Equation (4), and the two‐way analysis model corresponds to Equation (5). Note that 1260 observations were lost due to undefined Ak resulting from equal current and purchase stock prices. Standard errors are clustered by subject.
• 13 * p < 0.10;
• 14 ** p < 0.05;
• 15 *** p < 0.01.

For Table 5, the regression equations for one‐way and two‐way analyses are, respectively:

• 2 $$$\begin{array}{c}{R}_{k}={\beta }_{0}+{\beta }_{1}{STKUP}+{\beta }_{2}{ST}{KDN}+{\beta }_{3}{MKTUP}+{\beta }_{4}{MKTDN}\\ +\,{\beta }_{9}P{P}_{{stk}}+{\beta }_{10}C{P}_{{stk}}+{\beta }_{11}{AI}{P}_{{stk}}+{\beta }_{12}H{P}_{{stk}}+{\beta }_{13}L{P}_{{stk}}\\ +\,{\beta }_{14}{UP}{\rm{\_}}{DOW}{N}_{{stk}}+{\beta }_{15}{DOWN}{\rm{\_}}U{P}_{{stk}}+{\beta }_{16}{BET}{A}_{{stk}}+e,\end{array}$$$
• 3 $$$\begin{array}{c}{R}_{k}={\beta }_{0}+{\beta }_{5}{STKUP}{\rm{\_}}{MKTUP}+{\beta }_{6}{STKUP}{\rm{\_}}{MKTDN}+\,{\beta }_{7}{STKDN}{\rm{\_}}{MKTUP}\\ +\,{\beta }_{8}{STKDN}{\rm{\_}}{MKTDN}+{\beta }_{9}P{P}_{{stk}}+{\beta }_{10}C{P}_{{stk}}+{\beta }_{11}{AI}{P}_{{stk}}+{\beta }_{12}H{P}_{{stk}}+{\beta }_{13}L{P}_{{stk}}\\ +{\beta }_{14}{UP}{\rm{\_}}{DOW}{N}_{{stk}}+{\beta }_{15}{DOWN}{\rm{\_}}U{P}_{{stk}}+{\beta }_{16}{BET}{A}_{{stk}}+e.\end{array}$$$

For Table 6, the regression equations for one‐way and two‐way analyses are, respectively:

• 4 $$$\begin{array}{c}{A}_{k}={\beta }_{0}+{\beta }_{1}{STKUP}+{\beta }_{2}{STKDN}+{\beta }_{3}{MKTUP}+{\beta }_{4}{MKTDN}\\ +\,{\beta }_{9}P{P}_{{stk}}+{\beta }_{10}C{P}_{s{tk}}+{\beta }_{11}{AI}{P}_{{stk}}+{\beta }_{12}H{P}_{{stk}}+{\beta }_{13}L{P}_{{stk}}\\ +{\beta }_{14}{UP}{\rm{\_}}{DOW}{N}_{{stk}}+{\beta }_{15}{DOWN}{\rm{\_}}U{P}_{{stk}}+{\beta }_{16}{BET}{A}_{{stk}}+e,\end{array}$$$
• 5 $$$\begin{array}{c}{A}_{k}={\beta }_{0}+{\beta }_{5}{STKUP}{\rm{\_}}{MKTUP}+{\beta }_{6}{STKUP}{\rm{\_}}{MKTDN}+\,{\beta }_{7}{STKDN}{\rm{\_}}{MKTUP}\\ +\,{\beta }_{8}{STKDN}{\rm{\_}}{MKTDN}+{\beta }_{9}P{P}_{{stk}}+{\beta }_{10}C{P}_{{stk}}+{\beta }_{11}{AI}{P}_{{stk}}+{\beta }_{12}H{P}_{{stk}}+{\beta }_{13}L{P}_{{stk}}\\ +{\beta }_{14}{UP}{\rm{\_}}{DOW}{N}_{{stk}}+{\beta }_{15}{DOWN}{\rm{\_}}U{P}_{{stk}}+{\beta }_{16}{BET}{A}_{{stk}}+e.\end{array}$$$

In implementing these regressions, for the focal stock variable we define the price state in terms of capital gains and losses, computed as ( $${CP}-{PP}$$ ). But for the market state we consider two definitions of what constitutes an up or down market. In one case we define the market state in terms of the LASTLEG variable, and in the other case we use the linear TREND variable. We implement Equations (2)–(5) both ways, providing two forms of partitioning which we define as GAIN/LASTLEG and GAIN/TREND, which are differentiated by the way market price direction is defined. For all of the regressions in Tables 5 and 6, we cluster standard errors by subject to remove correlation bias.

In Table 5 we observe that for the one‐way analysis, when market direction is defined by LASTLEG the two significant states are MKTUP and MKTDN with observed coefficients of 4.94 and −2.69, respectively. Both of the stock state indicators are nonsignificant. This suggests that end‐anchor effects are stronger for the contextual market variable than they are for the focal stock variable. We suggest that this may be because the focal stock variable is driven by a combination of hedonic maximization considerations and end‐anchoring effects, such that these may be competing or offsetting effects for some chart patterns, whereas market direction arguably does not entail the same type of hedonic consequences that may pertain to own‐stock gains and losses. The observed signs for the market‐related coefficients are consistent with anchoring to the market (H7, H8) or alternatively by optimism/pessimism (H5). We formally test these conjectures in subsequent analyses.

When market direction is defined by TREND, for the one‐way analysis the only state variable that is significant in the GAIN/TREND partition is MKTDN with a negative coefficient of −4.72. We see that for the two‐way analysis this result is reinforced where the only combined market state that is significant is $${{STKDN}}_{\_}{MKTDN}$$ with a negative coefficient of −5.49. It appears that when investors are focusing on the long‐term linear trend of the market, their feeling of pessimism is most salient when both the stock and the market are down. The corresponding $${{STKDN}}_{\_}{MKTDN}$$ variable is not significant in the GAIN/LASTLEG partition, suggesting that significant feelings of pessimism may be evoked by a sustained simultaneous downturn in the stock and the market, but not by a short‐term price decline. Again, we formally test these conjectures in subsequent analyses.

For the two‐way analysis in the GAIN/LASTLEG partition, we observe that the $${{STK}{UP}}_{\_}{MKTDN}$$ and $${{STKDN}}_{\_}{MKTUP}$$ state variables are significant with coefficients of −4.96 and 5.51, respectively. The signs are consistent with end‐anchoring to the market, but this effect is significant only when the stock and the market move in opposite directions, and not when they move together.

In Table 6, the dependent variable is $${A}_{k}$$ instead of $${R}_{k}$$ . We observe for the one‐way analysis in the GAIN/LASTLEG partition, adaptation is positive and significant only in the MKTUP state. This is consistent with the asymmetric ostrich effect (Karlsson et al., 2009; H3) with respect to short‐term price swings, and is reinforced by the two‐way analysis that shows positive and significant adaptation only in states $${{STKUP}}_{\_}{MKTUP}$$ and $${{STKDN}}_{\_}{MKTUP}$$ where the market is up.

In the GAIN/TREND partition, for the one‐way analysis only the MKTDN state is significant with a negative coefficient of −0.70. This implies there is less adaptation when investors are focusing on long‐term market trend. It is reinforced by the two‐way analysis where only the $${{STKDN}}_{\_}{MKTDN}$$ partition is significant with a negative sign of −0.166, which is of higher significance than the one‐way effect. Lower adaptation in the loss domain for stocks is consistent with hedonic maximizing by investors (Arkes et al., 2008), but this effect appears only in the two‐way analysis, not in the one‐way analysis where all market states are aggregated. Our combined modeling framework incorporating both BWW and GM theory can help explain this finding. Perhaps the propensity for investors to exhibit hedonic maximizing exists but is magnified in extreme pessimistic states when both the stock and the market are in a sustained downtrend. We suggest that the two frameworks are not mutually exclusive but both frameworks can coexist in offsetting or reinforcing ways. In this case we conjecture that the editing stage of prospect theory is shaped by the investor's emotional state.

The regressions described earlier are used to formulate hypothesis tests to examine stock and market interaction effects more formally. To guide our interpretation of results we first develop the sign predictions shown in Table 7.

7 TablePredicted signs for hypothesis tests

• 16 Note: This table reports the derivation of predicted signs for hypothesis tests to be performed on Equations (2)–(5). MKTUP and MKTDN are dummy variables indicating up‐ and down‐market states, respectively, and ALL_MKT is a dummy variable indicating the combined set of observations. The predicted stock effect is based on prospect theory with a null hypothesis that the focal stock effect exhibits greater adaptation in the gain versus loss domain. Two contrasting mechanisms of market context effect are considered: optimism/pessimism and attention. For optimism/pessimism, we hypothesize that up‐market states lead to higher reference prices relative to down‐market states due to feelings of optimism or pessimism as suggested by the Gollier and Muermann (2010) model. For attention, we hypothesize that adaptation is greater for up‐ versus down‐market states due to greater attention as suggested by the asymmetric ostrich effect (Karlsson et al., 2009). Focal and contextual effects may be reinforcing or offsetting, resulting in a combined effect that may be positive, negative, or neutral.
• 17 a For this table, identical results would obtain if market context effects were based on optimism/pessimism or anchoring to the market, as either mechanism would be implemented by moving the reference price in the market direction. This is not a general result but depends on how market direction is defined among other assumptions. In our empirical tests we contrast differing definitions of market direction based on TREND or LASTLEG.

Numerous studies document asymmetric adaptation in the gain versus loss domains, and for the focal stock effect we use this hypothesis as a base assumption for purposes of developing our sign predictions. Because the stock direction is defined by paper gains and losses, $${R}_{k}$$ and $${A}_{k}$$ must be the same sign in the gain domain and opposite signs in the loss domain. In Table 7 the primary stock effect is driven by $${A}_{k}$$ as a function of the gain or loss state, and this automatically determines the direction of $${R}_{k}$$ as a corollary effect.

To analyze contextual effects, we add market effects that are theorized two ways: (1) using the GM framework based on feelings of optimism/pessimism where the reference price is assumed to be higher for up‐market states and lower for down‐market states and (2) an attention‐based framework where adaptation is assumed to be higher in up‐market states versus down‐market states because of attentional differences as suggested by the asymmetric ostrich effect (Karlsson et al., 2009). For the first framework, the primary effect occurs through $${R}_{k}$$ , and the direction of $${A}_{k}$$ is a corollary effect based on the market state, whereas for the second framework, the primary effect is through $${A}_{k}$$ , and $${R}_{k}$$ is the corollary effect.

Focal and contextual effects may be reinforcing or offsetting, resulting in a combined effect that may be positive, negative, or neutral. In our modeling framework the hypothesized signs in the GM framework are identical to what would be predicted under an assumption of anchoring to the market, as each mechanism implies the reference point moves in the market direction. This is not a general result but is a convenient factor when interpreting our regressions. The empirical question of what market effects are actually observed plausibly depends on the definition of market direction. In our empirical tests, the GAIN/LASTLEG and GAIN/TREND indicator variables allow us to test our hypotheses under the two alternate definitions of market direction.

In Table 8 we perform hypothesis tests on $${R}_{k}$$ and $${A}_{k}$$ based on coefficients from Equations (2)–(5) to test for stock and market interaction effects for each dependent variable. Panel A tests the hypothesis that the dependent variable is higher in STKUP versus STKDN states against the null hypothesis of no difference between states. One‐way effects are tested in Row 1, which represents the overall stock effect when not conditioned on market state. Two‐way interaction effects that are conditioned on up‐ and down‐market states appear in Rows 2 and 3. In Panel B the roles are reversed and we test the hypothesis that the dependent variable is higher in MKTUP versus MKTDN states. The predicted coefficient signs are shown in the table for reference.

8 TableResults of hypothesis tests

• 18 Note: This table reports the results of hypothesis tests performed on Equations (2)–(5) to analyze stock/market interaction effects. MKTUP and MKTDN are dummy variables indicating up‐ and down‐market states, respectively, and ALL_MKT is a dummy variable indicating the combined set of observations. Row 1 in both panels presents one‐way analyses of pure stock or market effects, and Rows 2 and 3 present two‐way analyses. Predicted signs are from Table 7 and are based on three alternative theories for the market context effect: optimism/pessimism ("Opt"), anchoring to the market ("Anchor"), and attention ("Attn"). Note that optimism/pessimism and anchoring to the market produce identical sign forecasts in the specific framework of this study. Standard errors are clustered by subject. p‐values are presented in parentheses.
• 19 a The test is two‐tailed. Positive coefficient difference indicates right‐tail significance; negative coefficient difference indicates left‐tail significance.
• 20 * p < 0.10;
• 21 ** p < 0.05;
• 22 *** p < 0.01.

Row 1 in Panel A of Table 8 indicates that when market states are combined, the unconditional stock effect is exactly as hypothesized for each dependent variable, and it supports the prospect theory explanation of asymmetric adaptation in gain versus loss domains (H4). However, Rows 2 and 3 reveal that this effect is moderated when conditioned on market direction. It obtains only in the down‐market state and when market direction is defined by TREND as opposed to LASTLEG. Further insight is obtained from Tables 5 and 6, which indicate that for both dependent variables, the result is driven by $${\beta }_{9}$$ , which is the indicator for $${{STKDN}}_{\_}{MKTDN}$$ . For both $${R}_{k}$$ and $${A}_{k}$$ , we observe that the coefficient of $${\beta }_{8}$$ is negative and significant for the GAIN/TREND partition but is not significant for the GAIN/LASTLEG partition.

For $${R}_{k}$$ this indicates that the observed result does not appear to be driven by investors anchoring to short‐term market swings but is related to both the market and the stock experiencing a persistent downward trend. An explanation consistent with this result is that pessimism is more pronounced in a sustained market downturn that coincides with the stock being in the loss domain, reducing the reference point in that combined state, which increases the coefficient spread ( $${\beta }_{6}-{\beta }_{8}$$ ). This is consistent with a GM explanation (H5). An alternative explanation related to visual pattern effects is that the negative perception of a downward‐sloping price trend (Duxbury & Summers, 2018) is more salient in the loss domain and magnifies the tendency for investors to reduce their reference point in that state.

Focusing on $${A}_{k}$$ , the result is consistent with the hypothesized sign for the divided attention theory (H2) and the asymmetric ostrich effect (H3). In this case the avoidance of attention in down‐market states is magnified when it is a persistent downtrend versus a short‐term market downswing.

Row 1 in Panel B of Table 8 indicates that the pure stock effect is exactly as hypothesized for each dependent variable whether the predicted market effect is through the mechanism of optimism/pessimism (H5) or by attentional factors (H3), and it supports the prospect theory explanation of asymmetric adaptation in gain versus loss domains (H4). However, Rows 2 and 3 reveal that this effect is moderated when conditioned on stock states.

In Panel B of Table 8, we observe that reference point adaptation is uniformly higher in up‐ versus down‐market states for all partitions except one: the GAIN/TREND partition in the STKUP state. The coefficient spread for this test is ( $${\beta }_{5}-{\beta }_{6}$$ ). Examining these coefficients in Tables 5 and 6, we see that for both $${R}_{k}$$ and $${A}_{k}$$ the coefficients are not significant. In fact, among all of the two‐way indicator variables for GAIN/TREND the only one that is significant is $${{STKDN}}_{\_}{MKTDN}$$ , which is seen to drive the stock effect results for Panel A. Except for $${{STKDN}}_{\_}{MKTDN}$$ , the overall results in Panel B are otherwise generally consistent with the hypothesized signs under both the optimism/anchoring mechanism and the attention mechanism.

Turning to the GAIN/LASTLEG partition for which all hypothesis tests in Table 8 are positive and significant, an analysis of the coefficients in Table 5 shows an interesting pattern when analyzing the results for $${R}_{k}$$ . We see that $${\beta }_{6}$$ and $${\beta }_{7}$$ are significant, and their signs reveal that the results in Table 8 are driven by a propensity to anchor to down‐market price moves when the stock is up, and to up‐market price moves when the stock is down, but not when the stock and market prices are moving together. In other words, when market direction is defined by LASTLEG, anchoring to the market (H7) is corroborated when the stock and the market are in opposite directions.

Examining the coefficients for $${A}_{k}$$ in Table 6, we see that coefficients $${\beta }_{5}$$ and $${\beta }_{7}$$ are positive and significant whereas coefficients β6 and $${\beta }_{8}$$ are not significant, supporting an attention‐based explanation for the results in Table 8 and providing further evidence supporting the asymmetric ostrich effect (H3).

To gain additional intuition and further sort out patterns of stock and market influences on reference prices, we provide graphical analysis of our results in Figures 4 and 5. These graphs provide deeper insight and aid in visualizing stock and market interaction effects in a convenient and novel manner.

The extent of adaptation for a given individual may depend on intermediate stock and market price movements, and such factors may affect different individuals in different ways. However, the same individual may exhibit patterns of consistent behavior according to the market state and/or based on whether the stock is in a capital gain ( $${CP}\gt {PP}$$ ) or capital loss ( $${CP}\lt {PP}$$ ) position. In Figure 4 we analyze within‐subject behavior by plotting each individual's combination of mean adaptation in loss versus gain scenarios as an (x, y) ordered pair. For example, the ordered pair (0.40, 0.80) depicts an individual who averages 40% adaptation when sitting on capital losses and 80% adaptation when sitting on capital gains. Each subject is represented by a point in the scatter plot. There are 63 data points corresponding to the number of subjects in the experiment. An individual who plots above the 45 degree line in Figure 1 exhibits asymmetric adaptation, with greater adaptation in the gain domain versus the loss domain (H4). Separate graphs are shown for down‐market scenarios (Panel (a)) versus up‐market scenarios (Panel (b)), where up and down markets are defined by the sign of $${{LASTLEG}}_{{mkt}}$$ . The box‐shaped gridlines in Figure 4 delineate regions where $${A}_{k}\le 0.5$$ and $${A}_{k}\le 1$$ .

The results in Figure 4 indicate asymmetric adaptation in both up and down markets, with a slightly stronger effect when the market trends upward. In up‐market scenarios, 57 subjects (90%) exhibit this behavior versus 49 subjects (78%) in down‐market scenarios. A reverse asymmetric adaptation effect is observed for 6 subjects (10%) in up‐market scenarios and for 13 subjects (21%) in down‐market scenarios.

In Figure 5, we slice the data in a different manner and analyze within‐subject behavior along the dimensions of up versus down markets, where up and down markets are defined by the sign of $${{LASTLEG}}_{{mkt}}$$ . As before, each data point corresponds to a particular subject; however, this time we define the x‐ and y‐axes to measure average adaptation in down versus up markets, as opposed to average adaptation in loss versus gain domains like we did in Figure 4. Separate graphs are shown for scenarios in the loss domain (Panel (a)) versus the gain domain (Panel (b)). Asymmetric adaptation is now discerned by differences between Panels (a) and (b) as opposed to deviations from the 45 degree line. The 45 degree line is now interpreted as the case where investor behavior is identical in up and down markets, which corresponds to the BWW framework where subjects do not have market information. Therefore, departures from the 45 degree line in Figure 4 represent the marginal effect of adding market information to the decision agent's information set.

In the gain domain positive adaptation implies an increase in the reference price, whereas in the loss domain positive adaptation implies a decrease in the reference price. This is because the denominator in the definition equation of adaptation is negative in the loss domain and positive in the gain domain. In Panel (b) of Figure 5, an increase in the reference price corresponds to a rightward (in down markets) or upward (in up markets) shift of data points on the graph. But in Panel (a), an increase in the reference price corresponds to a leftward (in down markets) or downward (in up markets) shift of data points on the graph. The gain and loss regions in the two panels are indicated by shading.

Figure 5 offers interesting insights. First, the inner box depicts individuals who adjust their reference point less than halfway, which indicates that they are focusing more on the purchase price than the current price. This happens mostly in the loss domain. Relatively few individuals in the gain domain exhibit this behavior. Second, points in the upper right quadrant represent individuals who systematically adapt positively in both up and down markets, and anything in the lower left quadrant represents individuals who systematically adapt negatively in both up and down markets. There is virtually no negative adaptation in the gain domain; but in the gain domain negative adaptation means the reference point is lower than $${PP}$$ even though the stock price has increased. There is some negative adaptation observed in the loss domain, for about 20 individuals. Intuitively, these individuals may be holding out for a selling price that is higher than what they originally paid ( $${R}_{k}\gt {PP}$$ ).

The region outside of the inner box represents adaptation greater than 0.5 suggesting that an individual is focusing more on the current price than the purchase price. This happens frequently in the gain domain but infrequently in the loss domain, as would be expected as greater adaptation in the loss domain approaches capital loss territory with respect to the purchase price as adaptation approaches 1. The region outside of the outer box represents adaptation greater than 1, which occurs frequently in the gain domain but rarely in the loss domain. This is intuitive, as in the loss domain this implies a capital loss relative to the purchase price. These types of observations are not evident when all up/down scenarios are lumped together, but these observations motivate the partitioning of the data.

In the gain domain, the data points in the first quadrant that lie outside the larger box represent overadaptation ( $${A}_{k}\gt 1$$ ) in both up and down markets. This encompasses about half of the individuals. But there are only a few such individuals in the loss domain. In the gain domain, more than complete adaptation means that $${R}_{k}\gt {CP}$$ ; that is, the subject's reservation price is above the current price whether the market is up or down. In the loss domain, it means that $${R}_{k}\lt {CP}$$ ; that is, the subject's reservation price is below the current price whether the market is up or down.

In this article, we develop an experimental framework for analyzing the effect of market context on reference point formation, synthesizing and extending previous studies by BWW and GM. By presenting market information additionally to the stock price path, we explore the influence of market contextual information on reference point formation and updating for stock investments given different price path scenarios. The results support our overall hypothesis that market context matters and information about the market influences the formation and updating of reference points in some systematic ways.

Based on theories in the literature, we create specific hypotheses on how market contextual information may affect the reference point dynamics of individual stocks. Through our extended experimental framework, we investigate and analyze how reference point adaptation depends on market context. In addition, we develop a novel method of graphical portrayal that helps visualize behavioral effects on reference point formation and provides additional insights.

We note the following limitations of our study. Like numerous other studies that use artificial charts, our results may be affected by round‐number bias and by the use of short chart lengths in our stock and market patterns, which result in less realistic measures for variables like beta. However, we believe the benefit of retaining these features from the BWW study for comparability outweigh the disadvantages of trying to correct for these effects. In addition, by originating the stock and market patterns at different price points, we do not control for differences in the rate of return or beta across stock and market sequences. Finally, because we do not include a control group of subjects to view just the stock pattern without the market information as in BWW, comparing our results with those of BWW does not constitute a formal control.

Although our study does not consider every possible factor that may influence reference point formation in different market states, we believe it is a step in that direction. Our methodology provides a rich framework for analyzing reference price formation that will be a useful platform for performing future research in this area. Possible areas for future inquiry may include, for example, an examination of heterogeneous subject types (e.g., with respect to momentum vs. contrarian beliefs or exhibiting reference point formation consistent with different investment styles such as growth vs. value) to determine whether subject behavior changes under different economic states. Another area that may benefit from further investigation is using our combined framework to further explore covariation effects or to examine effects related to higher moments such as skewness or coskewness (e.g., Ang et al., 2006; Bajtelsmit et al., 2015).

The authors greatly appreciate comments and help from the editor, anonymous reviewers, and participants at the Academy of Behavioral Finance & Economics Annual Meeting, Society for Experimental Finance Annual Meeting, American Society of Business and Behavioral Sciences Annual Meeting, Eastern Finance Association Annual Meeting, Midwest Finance Association Annual Meeting, and Southwestern Finance Association Annual Meeting.