Anchoring and Probability Weighting in Option Prices

• Published date: 01 June 2017
• Author: Andy Fodor,Dean Diavatopoulos,Kevin Krieger,R. Jared DeLisle
• DOI: http://doi.org/10.1002/fut.21833
• Date: 01 June 2017

Anchoring and Probability Weighting

in Option Prices

R. Jared DeLisle,* Dean Diavatopoulos, Andy Fodor and Kevin Krieger

Cumulative prospect theory argues that the human decision-making process tends to

improperly weight unlikely events. Another behavioral phenomenon, anchoring bias, is the

failure to update beliefs away from established anchor points. In this study, we find evidence

that equity option market investors both anchor to prices and incorporate a probability

weighting function similar to that proposed by cumulative prospect theory. The biases result in

inefficient prices for put options when firms have relatively high or relatively low implied

volatilities. This has implications for the cost of hedging long portfolios and long individual

equity positions. © 2017 Wiley Periodicals, Inc. Jrl Fut Mark 37:614–638, 2017

1. INTRODUCTION

Many financial studies use aspects of behavioral theories to examine phenomena observed in

equity markets.

1

In this study, we employ two well-documented behavioral theories to explain

the underperformance of put options with very low and very high implied volatilities relative

to other put options with the same moneyness and maturities. We find evidence that equity

option investors anchor to prices (or implied volatilities) and incorporate a probability

weighting function similar to that proposed by cumulative prospect theory (CPT). CPT

(Tversky & Kahneman, 1992), unlike standard utility theory, argues that the human decision-

making process depends on relative gains and losses, not final wealth, as losses impact utility

more negatively than gains of the same magnitude increase utility. The asymmetry of an

R. Jared DeLisle is at the Department of Economics and Finance, Jon M. Huntsman School of Business, Utah

State University, Logan, Utah. Dean Diavatopoulos is at Department of Finance, Albers School of Business

and Economics, Seattle University, Seattle, Washington. Andy Fodor is at Department of Finance, College of

Business, Ohio University, Athens, Ohio. Kevin Krieger is at Department of Accounting and Finance,

University of West Florida, Pensacola, Florida. We thank the editor (Robert Webb) for his insightful

suggestions. We are grateful for the valuable comments from the participants of the 2015 Financial

Management Association meeting, 2016 Derivatives Markets Conference, and the 2016 Annual Conference

of the Asia-Pacific Association of Derivatives.

JEL Classification: G1, G13

*Correspondence author, Utah State University, Department of Economics and Finance, Jon M. Huntsman School

of Business, 3565 Old Main Hill, Logan, UT 84322-3565. Tel: 435-797-0885, Fax: 435-797-2701,

email: jared.delisle@usu.edu

Received November 2016; Accepted November 2016

1

Prospect theory (Kahneman & Tversky, 1979), cumulative prospect theory (Tversky & Kahneman, 1992), mental

accounting (Henderson & Peterson, 1992; Shefrin & Thaler, 1988; Thaler, 1980, 1985), and heuristics (Kahneman

& Tversky, 1972; Tversky & Kahneman, 1974) have been successfully applied to many stylized facts in financial

markets that are difficult to explain in a standard rational efficient markets framework (e.g., Fama, 1965, 1970;

Friedman, 1953; Markowitz, 1952a,b).

The Journal of Futures Markets, Vol. 37, No. 6, 614–638 (2017)

© 2017 Wiley Periodicals, Inc.

Published online 2 February 2017 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21833

individual’s utility due to gains versus losses is referred to as loss aversion. Tversky and

Kahneman also contend humans are poor at internalizing event probabilities and appear to

use a unique weighting function to convert an actual probability into a perceived probability

which assigns a high value to low probability events, resulting in overly risk averse or risk-

seeking behavior, depending upon whether the outcome of the event is a loss or a gain.

Anchoring is a documented psychological bias that is independent of CPT, but it is required

by CPT to determine a reference point that defines regions of gains and losses.

In addition, the literature over the past two decades presents considerable evidence that

investors use anchor points in their investing decisions. Kahneman, Slovic, and Tversky

(1982) define anchoring as the process of making adjustments away from a reference point

(the anchor) where the adjustments are biased toward this reference point. The anchor point

may come from the problem at hand (Kahneman et al., 1982) or even a random value such as

the last two digits of a Social Security Number (Ariely, Loewenstein, & Prelec, 2003).

Kahneman et al. (1982) and Kahneman (1992) survey studies providing evidence of

anchoring by individuals. Using laboratory experiments, Myagkov and Plott (1997) and

Marsat and Williams (2013) also find support for the usage of anchor points. Benartzi and

Thaler (1995) contend that investors use a reference stock price, that is, the current price, as

an anchor point and determine, consistent with loss aversion, that investors weigh a loss

about twice as much as a similar gain.

Supporting this assertion, George and Hwang (2004) identify an investing strategy that

utilizes an anchor point of a stock’s 52-week high price that bests Jegadeesh and Titman’s

(1993) simple momentum strategy. The 52-week high price should not contain any

information about a stock’s future value in a weak-form efficient market. Yet, the evidence

George and Hwang presents suggest investors anchor to the 52-week high and are reluctant

to value the stock price above that price, even if a higher price is well justified. Bhootra and

Hur (2013) strengthen the anchoring argument by demonstrating an increase in the

profitability of George and Hwang’s strategy by conditioning on the timing of the 52-week

high anchor point, which is consistent with Grinblatt and Han’s (2005) theoretical model

where the purchase price of the stock serves as the investor’s anchor point.

2

Similarly, Baker,

Pan, and Wurgler (2012) find managers use price anchors in determining premiums paid in

mergers and acquisitions.

In addition to looking for evidence of anchoring, we also investigate the tendency of

individuals to improperly weight low-probability events. In general, humans tend to do a poor

job of internalizing probabilities. A series of studies by Teigen (1974a,b, 1983) shows that an

individual’s sum of interpreted probabilities of a set of outcomes often exceeds one.

Kahneman and Tversky (1984) and Tversky and Kahneman (1992), show that, under CPT,

individuals overweight (underweight) small (moderate or high) probabilities. Figure 1 shows

a graphical example of their findings. The perceived probability of an event, p(P), is much

higher than the actual probability, P, when Pis low. Thus, when individuals apply such a

weighting function to observed probabilities, it gives rise to extremely risk averse (seeking)

behavior when dealing with highly improbable losses (gains) as the value of each outcome is

multiplied not by an additive probability, but by a decision weight.

Another implication of a weighting function is that individuals evaluate a risk of 1 in

100,000 similarly as 1 in 10,000,000. Kunreuther, Novemsky, and Kahneman (2001)

empirically confirm such a notion. The regime of extremely small probabilities is unstable,

where the risks are either grossly overweighted or ignored (e.g., rounded down to zero).

2

In the context of Grinblatt and Han’s model, the concept of an anchor is important with respect to loss aversion

because individuals use it as a fixed reference to determine if selling an asset (i.e., the capital gains overhang)

provides pain in the form of a loss or pleasure in the form of a gain.

Anchoring, Probability Weighting, and Options 615