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Reference-Point Formation and Updating with Additional Market Information

Tianyang Wang
Assistant Professor of Finance
Department of Finance and Real Estate
Colorado State University
Fort Collins, CO 80523-1272
Tel: (970) 491-2381
tianyang.wang@colostate.edu

Sriram V. Villupuram
Assistant Professor of Finance
Department of Finance
University of Texas-Arlington
Tel: (817) 272-3705
sriramv@exchange.uta.edu

Robert G. Schwebach
Associate Professor of Finance
Department of Finance and Real Estate
Colorado State University
Fort Collins, CO 80523-1272
Tel: (970) 491-5547
rob.schwebach@colostate.edu

Presented at Southwest Finance Association 2015 Annual Meeting

Reference-Point Formation and Updating with Additional Market Information

ABSTRACT

Experimental studies in behavioral finance historically have confirmed that subjects are highly
influenced by reference points when making economic decisions. A recent study by Baucells, Weber
and Welfens (2011) analyzed the dynamics of reference price formation using experimental methods
with subjects forming reference prices for stocks based on observed price sequences. Their study helps
to clarify behavioral effects of past prices on reference price formation but it does not consider
contextual information. We extend the BWW study by adding market price information as background
to the experiment, and we investigate how this additional information affects reference point formation
and updating. Our overarching hypothesis is that if the market background information has no impact
then it should not alter the results of BWW; otherwise, the additional market information should be an
explanatory variable for the reference point. Our results confirm the hypothesis that market information
matters. We also investigate the impact of pessimism and optimism on reference prices by the combining
the BWW framework with a model of disappointment aversion developed by Gollier and Muerman
(2010). Our study fills a void in the literature by providing new evidence on the impact of contextual
market information on reference point formation in an investment setting.

Keywords: behavioral finance; reference-point formation; reference-dependent preferences

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Reference-Point Formation and Updating with Additional Market Information

1. Introduction

Behavioral theories of risky choice are a widely accepted alternative to the standard expected utility

(EU) framework of von Neumann and Morgenstern (1947) and Savage (1954). A key element of behavioral

models is reference dependence, which Stracca (2004) contends is “perhaps the most important single element

of the behavioral finance literature.” Reference dependence is the basis for Kahneman and Tversky’s (1979)

prospect theory (PT) which posits that economic decision makers derive utility not only from absolute wealth,

but from changes in wealth relative to a subjective reference point.

PT assumes an S-shaped value function that is concave over gains and convex over losses. This implies

diminishing marginal value away from the origin so that losses are felt more intensely than gains, resulting in

decision behavior that is risk averse in the gain region and risk seeking in the loss region. PT and the related

concept of mental accounting [Thaler (1985)] help to explain emprical violations of EU such as the disposition

effect [Shefrin and Statman (1985)] which states that investors tend to dispose of gains quickly but resist selling

at a loss. The disposition effect implies that reference point adaptation to new price information will be more

complete for an increase in price from an assumed reference point versus a decrease of equal magnitude.

A strand of research over several decades provides empirical [e.g., Odean (1998)] and experimental

[e.g., Weber and Camerer (1998)] support for prospect theory explanations of the disposition effect in

investment settings, including an experimental study of reference price formation by Baucells, Weber and

Welfens (2011) (BWW) in which subjects formulate reference prices for hypothetical stocks based on simulated

price patterns presented on a computer screen. BWW use the subjects’ elicited reference prices and an assumed

PT utility function to parameterize a rank-dependent probability weighting function that they use to construct

out-of-sample reference price forecasts.

While PT has largely been supported empirically, research has shown that some of its key results are

unstable across different contexts or framing domains [Hershey and Shoemaker (1980), Fischhoff (1983), and

Schneider and Lopes (1986)]. In addition, several studies document alternative explanations for the disposition

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effect such as portfolio rebalancing [Samuelson (1969), Merton (1969)], selective attention [Barber and Odean

(2007), Karlsson, Loewenstein and Seppi (2009)], irrational beliefs about mean reversion [Barber and Odean

(1999), Barberis and Xiong (2012)], and anticipatory feelings of regret [Bell, (1982), Loomes and Sudgen

(1982)] or disappointment [Bell (1985), Gul (1991)]. In the latter category, Gollier and Muerman (2010) (GM)

introduce a decision criterion based on disappointment aversion where the reference point is determined

endogenously based on certainty-equivalence criteria prior to resolution of uncertainty.

All of the above theories share the common finding that reference point effects are context-dependent.

This limits generalizabilty and complicates the task of sorting out the interplay between inherent and context-

driven effects, highlighting the need for more work in this area. Toward that end, we synthesize previous

research and develop a new platform for experimentally analyzing the impact of market context on reference

price formation. Our model combines BWW and GM into a unifying framework that considers both prospect

theory and disappointment-aversion explanations of reference point effects. Our work adds additional clarity to

BWW’s original findings and provides a decomposition of their results based on stock- and market-related

factors.

2. Methodology

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. Fehr-Duda and Epper (2015)

identify two main classes of PDP models: rank-dependent models [Quiggin (1982), Tversky and Kahneman

(1992)], which include cumulative prospect theory as a variant; and disappointment-aversion (DA) models [Gul

(1991)]. These two general types are differentiated by the manner in which subjective decision weights are

formed. In rank-dependent models the weights are based on a ranking of possible outcomes, where gains and

losses are measured relative to an exogenous reference point, whereas in DA models the probability weights and

the reference point are determined simultaneously and endogenously so as to optimally balance a tradeoff

between feelings of anticipation and disappointment. BWW assumed a rank-dependent weighting process,

whereas our extended framework considers disappointment-aversion explanations of reference point effects in

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addition to looking at prospect theory explanations.

BWW presented subjects with scenarios portraying a hypothetical sequence of stock prices y1, . . . , yn.

For each observed price sequence they elicited a reference price (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) from the subject. From these reference

points they inferred decision weightings on beginning, ending, and intermediate prices of the sequence for a

representative subject. The present study extends BWW in two primary ways. First, we contextualize the

hypothetical stock price sequences by adding market price sequences as background information. Second, we

consider a more general decision framework that incorporates anticipatory feelings of ex ante savoring and ex

post disappointment using the Gollier-Muerman (2010) disappointment-aversion model.

BWW considered two possible mechanisms of reference point formation to describe how subjects arrive

at their reported values of (cid:1)(cid:2)(cid:3)(cid:4)(cid:5). Under the integrated mechanism, past prices are aggregated into a single

reference value, rn+1 = f(y1, . . ., yn), 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 (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) solves υ((cid:1)(cid:2)(cid:3)(cid:4)(cid:5) – rn+1) = 0, where υ is

a prospect theory value function such that υ(0) represents emotional neutrality. In other words, the reported

value (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) is the subject’s unique reference price. Under the segregrated 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: ∑ (cid:7)(cid:8)(cid:3),(cid:10)(cid:11)((cid:1)(cid:3)(cid:4)(cid:5) − (cid:1)(cid:10))

(cid:3)
(cid:10)(cid:15)(cid:5)

, where the weights sum to 1. The reported reference price (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) solves:

∑ (cid:7)(cid:8)(cid:3),(cid:10)(cid:11)((cid:1)(cid:16)

(cid:3)
(cid:10)(cid:15)(cid:5)

(cid:3)(cid:4)(cid:5) − (cid:1)(cid:10))

= 0. The weights do not represent probablities 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 (cid:7)(cid:8)(cid:3),(cid:5) = 1 and all of the other weights are zero. BWW find that initial and ending prices are heavily

weighted, indicating high salience, and that intermediate prices receive less decision weight.

Rank-dependent models can help to explain apparent anomalies such as the disposition effect but they

generally do not specify an underlying behavior mechanism for the subjective weighting. Disappointment-

aversion models explicitly postulate a type of behavioral process for the formation of decision weights based on

anticipated feelings of disappointment and savoring. These feelings correspond to the human traits of

pessimism and optimism which are perhaps the most common characterizations of market sentiment. Hence,

the DA model is a natural choice for analyzing the impact of market context on reference point formation.

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The GM model assumes a set of lottery payoffs {c1, . . . , cS} with corresponding objective probabilities

Q={q1, . . . , qS}. Without loss of generality, c1< c2< ∙ ∙ ∙ < cS. The decision agent forms an anticipated payoff y that provides satisfaction from ex ante savoring but at the same time increases ex post disappoinment. The agent chooses subjective probablities P={p1, . . . , pS} simultaneously with y so as to optimally balance the utility tradeoff between savoring and disappointment. The reference point is the optimal value y* 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: (cid:20)((cid:21)) = max (cid:25),(cid:26) ! (cid:28) ∑ (cid:30)(cid:15)(cid:5) (cid:29)(cid:30)(cid:31)( (cid:30), (cid:1)) ! + ∑ (cid:30)(cid:15)(cid:5) #(cid:30)(cid:31)( (cid:30), (cid:1)) (1) ! s. t. (cid:31)((cid:1), (cid:1)) = ∑ (cid:30)(cid:15)(cid:5) (cid:29)(cid:30)(cid:31)( (cid:30), (cid:1)) (2) The first term measures ex ante utility from anticipatory savoring based on subjective probabilities P, whereas the second term computes utitlity 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. In our expanded framework, the relevant connection between BWW and GM is through the role of information. In the GM framework, at any time prior to the resolution of uncertainty, decision makers can re- optimize their utility in response to new 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. Prior to resolution of uncertainty, new information arrives that changes the decision agent’s outlook, making her either more optimistic or more pessimistic. The agent can reassess the situation and recalibrate her 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 given the new information. The resulting change in the reference price represents the marginal impact of the new information. We designed our experiment with the aim of capturing such incremental effects, where the information in this case is market context. Our overarching hypothesis is that market context matters, which we are able to demonstrate by conditioning BWW’s results on different market states. 6 Note that the change in perceived utility requires no 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. However this is something humans do all the time in order to feel better about situations they may not control. Suppose, for example, that your favorite sports team is in a tournament and you feel good about their chances, but you resist getting too excited for fear of a letdown. New information arrives that makes you feel more secure about your team’s prospects. Now you can indulge in feeling more excitement without intensifying your apprehension, or alternatively you can reduce your fear of disappointment without dampening your elation. You may contemplate this tradeoff even if you don’t act on it. Such contemplation, whether subconscious or volitional, is equivalent to changing the amount that you would be willing to pay if you imagined placing a hypothetical bet – i.e., it is equivalent to changing your reference point. 2.1 Design of Experiment Following BWW, we presented each subject with a series of simulated stock price patterns on a computer screen under a hypothetical situation. We asked the subject to imagine that they purchased a stock several days ago and then immediately went on vacation to a locale where they could not trade or monitor its price. Upon their return from vacation, the subject views the simulated sequence of past prices that occurred during their vacation. Then, following Arkes et al. (2008) and BWW, we elicit 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 in our instructions to the subject. We made no mention of the market information either verbally or in writing; we simply added the market price sequence as background information on the computer screen, giving no explanation or clarification as to its relevance. The exact set of instructions that we gave to subjects appears in Exhibit A. [ insert Exhibit A approximately here ] BWW devised a methodology to measure the impact of various price factors on subjects’ reference points by constructing ‘orthogonal’ pairs of price sequences so as to isolate the effects of individual factors. Specifically, BWW focused on the following five factors: purchase price (PP); current price (CP); average 7 intermediate price (AIP); highest price (HP); and lowest price (LP). BWW formed orthogonal pairs such that each pair of price sequences was identical with respect to eactly four factors; hence any difference between the reference points from those two sequences must be attributable to the fifth factor. For example, in BWW’s Table 3, stock patterns 1 and 2 are identical with respect to all factors except purchase price; therefore any difference in the reference prices for these two patterns, where the difference is denoted by R1 - R2, must be attributable to the difference in purchase price, PP1 - PP2. BWW’s table 3 indicates that for this orthogonal pair the average difference in reference prices across all subjects was 52.8 currency units (euros). Correspondingly, the average difference in purchase price was 100 euros. Hence, the observed unit effect was 0.528 for this orthogonal pair. In all, BWW constructed five orthogonal pairs for each factor. The top row in BWW’s Table 3 lists all of the pairs associated with changes in PP. The combined average unit effect for PP across all five pairs in the top row was a 0.48 for each one unit increase in purchase price. We extended BWW’s design as follows. First, we selected a subset of 20 BWW stock price patterns, then we expanded on this subset by constructing four market patterns for each stock pattern, resulting in four sub-cases for each original stock pattern that we labeled a-d. For example, the stock patterns 1 and 2 were expanded by adding market patterns as follows: This design produces four subcases that we can use to condition the reference price effect R1 - R2 on the market pattern. If our four subcases yield different results across different market patterns, this would indicate that market context matters. Similarly we expanded all of the patterns in our subset of 20 stock sequences, resulting in 80 total cases where each case consists of a stock pattern and associated market pattern. We contrived our market patterns in a manner that allows us to isolate both stock and market characteristics, as well as covariation effects. A complete listing of our stock and market patterns appears in Table 1. [ insert Table 1 approximately here ] 8