Losers and prospectors in the short‐term options market

• Published date: 01 June 2019
• Author: Hong Miao,Arjun Chatrath,Sanjay Ramchander,Rohan A. Christie‐David
• Date: 01 June 2019
• DOI: http://doi.org/10.1002/fut.21989

Received: 9 April 2018

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Accepted: 6 December 2018

DOI: 10.1002/fut.21989

RESEARCH ARTICLE

Losers and prospectors in the short‐term options market

Arjun Chatrath

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Rohan A. Christie‐David

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Hong Miao

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Sanjay Ramchander

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1

Pamlplin School of Business, University

of Portland, Portland, Oregon

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Finance Discipline, School of Business,

University of Colorado Denver, Denver,

Colorado

3

Finance and Real Estate Department,

College of Business, Colorado State

University, Fort Collins, Colorado

Correspondence

Rohan A. Christie‐David, University of

Colorado Denver, Denver, CO 80202.

Email: rohan.christie-david@ucdenver.

edu

Abstract

Intraday data for weekly options are investigated for behavioral biases implied

in prospect theory (PT) and cumulative prospect theory (CPT). The results

generally support both theories, with losers (winners) observed to be relatively

risk‐seeking (averse). On aggregate, losers (winners) overprice (underprice)

their contracts and overweight (underweight) the probability of winning.

Additionally, the volatility smirk observed in equity options is dampened by PT/

CPT biases. The price distortions are time sensitive, especially for losing traders.

Losers hold out by transacting later in the day and closer to expiration than

their baseline counterparts. This betting‐time effect is absent among winners.

KEYWORDS

losers and prospectors, prospect theory, STOs

JEL CLASSIFICATION

G13, G14, G40

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INTRODUCTION

The psychoanalysis of losers in betting environments conveys an image of especially rash behavior. Numerous

experiments suggest that (a) individuals are risk averse in gains but risk‐seeking in losses, with the latter effect being

more prominent than the former; and (b) individuals overweight the likelihood shifts from near‐impossible to

improbable and from near‐certainty to certainty, with the former effect being more prominent than the latter. Taken

together (a) and (b) suggest that losing traders are more inclined to go for long shots and winning traders seek

insurance. These behavioral elements are formalized in prospect theory (PT; Kahneman & Tversky, 1979) and

cumulative prospect theory (CPT; e.g., Camerer, 1992, 1995; Tversky & Kahneman, 1992), and these constructs are

widely regarded as important determinants in the mispricing of financial assets.

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Not surprisingly, there is a tendency to

also associate these behaviors with the disposition effect, that is, the evidence that stock traders hold onto losing

positions but sell winners prematurely (e.g., Odean, 1998; Shefrin & Statman, 1985). Under PT, the convexity of the

value function in the domain of losses captures the reluctance of certain investors to give up on losing positions. The

purpose of this paper is to examine whether such behavioral biases are manifested in the prices of short‐term index

options, in particular weekly calls on the S&P 500, a venue where the vast majority of positions suffer losses.

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Background and motivations for the study

PT of Kahneman and Tversky (1979) formalizes two behavioral tendencies that go against standard utility theory. The first

relates to the general shape of the utility function, that is, it is judged to be concave for winners and convex for losers; the

J Futures Markets. 2019;39:721–743. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

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These issues have also been examined by Benartzi and Thaler (1995), Hirshleifer (2001), Barberis and Thaler (2003), Coval and Shumway (2005), Gomes (2005), Barberis, Huang, and Thaler (2006),

Barberis and Huang (2008), Kumar (2009), Eraker and Ready (2015), Barberis, Mukherjee, and Wang (2016), among others.

second relates to the shape of the probability‐weighting function—low‐probability events are overweighted relative to mid‐

probability events. CPT combines the value function and the weighting function (e.g., Camerer, 1992, 1995; Tversky &

Kahneman, 1992). It proposes three functions—an S‐shaped value function that is concave in the gains and convex and

steeper in the losses; an inverse‐S‐shaped probability function; and a combined rank‐dependent function for values and

probability weightings. The key innovation over PT is that the transformed cumulative probabilities lead to overweighting of

low‐probability extreme events, rather than overweighting of low‐probability events per se. Henceforth, we employ CPT or

PT interchangeably when discussing probability weightings, understanding that CPT extends the key weighting concepts of

PT. In some instances, when a distinction is needed we refer to CPT without abbreviation (i.e., as CPT).

Studies that examine PT are mostly survey driven, that is, they elicit data from individuals in controlled experiments of

choice. Subjects (often student participants) indicate their preference in a pair of hypothetical bets, for instance, one paying

$1,000 with a probability of 0.50, and the other $500 with certainty. The survey instruments are designed to obtain precise

measures of probability weightings or distortions but are ultimately thought experiments (e.g., Starmer, 2000; Sugden, 2004).

While skepticism about such survey results has been noted, there also has been much support for them. Levy and Levy (2001,

2002) suggest that survey designs bias the results in favor of PT, arguing that data more closely resembling those in financial

markets will produce an inverse‐S‐shaped utility function, opposite to that proposed in PT. However, Wakker (2003) suggests

that Levy and Levy overlook the important role of probability weighting and argue that their data are consistent with

predictions of PT. Along these lines, conclusions from experiments testing rational choice have also been criticized within the

context of the incentives (or lack thereof) provided to subject participants. Smith and Walker (1993) find that subjects become

more rational when their participation reward is enhanced. On this note, Kachelmeier and Shehata (1992) find support for PT

even when subjects earned a fee equivalent to threefold their monthly income (see Tversky & Kahneman, 1992). Camerer and

Hogarth (1999) conclude that “no replicated study has made rationality violations disappear purely by raising incentives.”Fehr

and Tyran (2005) summarize other assertions leveled against PT and provide counterarguments in favor of PT. These include

arguments that the deviations from rationality are random and wash out on aggregate; that individuals learn and become less

irrational over time; and that the double‐auction markets price out irrational behavior. Using the principles of strategic

complementarity and strategic substitutability, the authors conclude that behavioral distortions can be systematic and not

random, individuals do not learn to become unbiased, and markets fail to price out all distortions.

More recent evidence suggests that cognitive biases attributed to PT are also exhibited in venues where real stakes

are tied to decision‐making. Andrikogiannopoulou (2010) examines panel data on the betting activities of 100 gamblers

via an online sports book and finds moderate probability distortions in the aggregate, but a great deal of heterogeneity

among individuals. Snowberg and Wolfers (2010) examine an extensive data set on racetrack betting (over 6 million

horse starts) and uncovers a strong long‐shot bias. They suggest the bias among gamblers is closely linked with

probability distortions in PT.

The validation from financial markets remain sparse vis‐à‐vis PT. While there have been several investigations into the

behavioral tendencies among stock traders, they produce somewhat broad and often indirect evidence on their

correspondence with PT. For instance, Odean’s (1998) results on the disposition effect, which stock investors realize their

gains at about a 50% higher rate than their losses, are inferred as a behavioral bias because other explanations, including

informed trading, transactions costs, and portfolio rebalancing, are excluded.

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More recently, Barberis et al. (2016) assume

traders with behavioral biases look backward to make stock picks. They record 60‐month excess returns for a large number

ofstocksbetween1926and2010andsortthemfromnegativetopositive. Imposing the utility weighting scheme in Tversky

and Kahneman (1992) on this linear ordering, they obtain a “PT value”for each stock. The authors note that the stocks with

large PT values earn lower future returns on average. That is, the cross‐sectional returns data provide support for PT.

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While the behavioral tendencies elicited from stock‐trading data are often associated with some aspects of PT, the

data often are not well‐suited to provide deeper insights into it. With stocks, one has to contend with different

investments and levels of risk, different degrees of loss or gain, and different holding horizons. Even with controls for

some of these elements, research relying on these data may be hard‐pressed to provide meaningful evidence on the

probability‐weighting function, or even on the shifting risk preferences of winners and losers.

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It might be noted that the disposition effect has also been documented among institutional traders (e.g., Frazzini, 2006), and across several countries (e.g., Shapira and Venezia, 2005; Feng and

Seasholes, 2001).

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Other applications of PT can be found in studies examining the cross‐section of average returns (Barberis & Huang, 2008; Eraker & Ready, 2015; Green & Hwang, 2012), explaining anomalies such as

the equity premium puzzle in the stock market (Benartzi & Thaler, 1995), and characterizing investor aggregate preferences for lottery‐type stocks (Kumar, 2009).

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For instance, Ben‐David and Hirshleifer (2012) are unable to link the biases among winning and losing stock traders to PT. Barberis and Xiong (2009) and Brooks, Capra, and Berns (2012) show that

excessive risk‐taking may not predictably explain why losing stock traders hold out. They suggest that the appearance of holding‐out behavior of losers could actually be a manifestation of relatively

conservative behavior, altogether unrelated to risk‐taking. Therefore, one is left unassured about the links between the disposition effect in equities and the cognitive biases in PT.

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