Introduction

When returns are associated with specific probabilistic outcomes, risk aversion describes a person’s insistence on requiring additional return when taking on an additional unit of risk. This approach to decision making is appropriate when operating in understood environments with clearly defined outcomes. However, this does not describe real world situations people find themselves in for the first and possibly only time, when even experts are unsure how laws will be applied, and when the actions of other parties are untested and uncertain. In these cases, it is nearly impossible to assign to any reasonable degree the probability of a particular outcome, much less identify the potential outcomes themselves. Instead, these situations can best be described as ambiguous, leading researchers to differentiate between Risk Aversion and Ambiguity Aversion.

The seminal work of Kahneman and Tversky (1979), known as prospect theory, finds that losses hurt roughly twice as much as gains feel good, and as such, people will take reasonable measures to avoid the loss domain. The extant literature has found that people are generally Ambiguity Averse over gains and small losses, and that this is an important region to examine in a world where financial leverage is limited, and investments represent a small portion of an investor’s overall wealth. But, this poorly describes the environment surrounding a typical mortgage borrower. Even high quality, conforming loans have a loan-to-value (LTV) ratio of 80% at origination. And many have an LTV of 0.97, a leverage ratio unheard of in other areas of finance and economics. Add to this that a home is the largest investment a person will typically ever make, and we can quickly understand that borrower behavior can change when homeowners find themselves substantially underwater (i.e., negative equity) due to sharp home price declines as they did during the 2008 Great Financial Crisis (GFC). When borrowers defaulted during the 2008 GFC, the system was ill prepared to handle the crisis, resulting in a level of uncertainty like no other investment. Collectively, the high percentage of a person’s overall wealth tied up in a mortgage, the extreme financial leverage used in mortgages, and the high degree of uncertainty surrounding how defaults would be handled, combine to create a unique laboratory to examine Ambiguity Aversion in the loss domain. Golman and Loewenstein (2018) explain that Ambiguity Aversion is context specific. Chen and Chang (2019) examined the role of Ambiguity Aversion in insurers’ pricing of mortgage insurance; however, no study has applied Ambiguity Aversion to the extremely uncertain environment of borrower decisions surrounding mortgage defaults. We view this as a unique opportunity to understand decision making in an understudied region of the loss domain - extreme losses.

We employ a large, non-student sample and assess participants’ willingness to pay (WTP) to successfully resolve either a risky or an ambiguous mortgage default situation in both the gain and loss domains. To measure Ambiguity Aversion, we employ the multiple price listing instrument developed by Gneezy et al. (2015). We are careful to control for financial history and literacy, factors known to be related to the frequency of mortgage defaults (Harrison et al. 2020). We also include personality traits identified in the psychology literature that explain decision making behaviors.Footnote 1

We find that Ambiguity Aversion is negatively related to the amount participants are willing to pay to resolve the mortgage default proceedings and that Risk Aversion is not significantly related to the amount participants are willing to pay in either the gain or loss domains. We also find that participants who are most financially literate and those who have not previously defaulted on a loan tend to have a stronger relation between Ambiguity Aversion and the amount willing to pay to resolve the settlement. The result is consistent with the most Ambiguity Averse engaging in costly efforts to increase literacy, but not the most Risk Averse. The difference highlights the distinction between the measures. Ambiguity inherent in a financial decision is associated with literacy, but the systematic (i.e., nondiversifiable) risk inherent is immutable.

With respect to personality traits, extraverts - regardless of their ambiguity and risk preferences - are willing to pay more to ensure positive outcomes in both the gain and loss domains, but only for participants with low financial literacy. Personality had little influence on the decision of the highly financially literate. This finding that feelings about a subject may influence behaviors controlling for ambiguity and risk preferences highlights the need to conduct further research at the intersection of the economics and psychology literature. That financial literacy may reduce the influence of personality on mortgage default settlement decisions underscores the importance of financial education. Additionally, understanding the role ambiguity plays in mortgage default behavior is critically important to help policymakers manage borrower behavior when facing economic challenges like the GFC or the more recent COVID-19 pandemic.

Literature Review

Since the seminal work of Ellsberg (1961), ambiguous decisions involving unknown probabilistic payoffs have been distinguished from risky ones involving known probabilistic payoffs. Numerous behavioral studies of ambiguity and risk followed, usually involving participants making a gamble with outcomes that vary the amount of money (or balls in an urn) to be won. The evidence overwhelmingly supports Ellsberg’s finding that people dislike ambiguity and will incur significant costs to avoid situations with uncertain payoffs while in the gain domain. The insights of Ambiguity Aversion in the gain domain help explain real-world phenomena such as when investors choose to exercise stock options (Izhakian and Yermack 2017), equity portfolio puzzles including poor portfolio diversification (Bossaerts et al. 2010; Dimmock et al. 2016; Bianchi and Tallon 2018; Peijnenburg 2018), the equity premium puzzle (Maenhout 2004; Collard et al. 2018; Gollier 2011; Ju and Miao 2012), the stock market participation puzzle (Dow and Werlang 1992; Easley and O’Hara 2009), and mortgage insurance premiums (Chen and Chang 2019). Recent research though calls into question Ambiguity Aversion’s influence in the loss domain. Kocher et al. (2018) provide experimental evidence of ambiguity attitudes when subjects are presented with different likelihoods of positive and negative payoffs. Subjects, on average, exhibit Ambiguity Aversion behavior for moderate likelihood gain prospects (consistent with Ellsberg 1961), but less is known about Ambiguity Seeking behavior for large likelihood loss prospects.

The subject of Ambiguity Aversion has not received much attention in the real estate literature. The paper closest to ours is Chen and Chang’s (2019) study of the effect of insurer’s Ambiguity Aversion on the pricing of mortgage insurance. The authors find that Ambiguity Aversion is associated with increases in mortgage insurance premiums, an effect that increases with higher LTV. We extend this line of research by investigating Ambiguity Aversion’s effect on borrower decisions rather than pricing decisions of the insurer.

Experimental Design

Bellemare et al. (2008) argue that experiments are particularly useful for understanding consumers’ economic decision making. Not surprisingly, research into choice under risk typically employs an experimental approach (Ellsberg 1961; Halevy 2007; Baillon and Bleichrodt 2015). Our experiment implements a revealed preference (in contrast to a stated preference) design to provide evidence concerning consumer choice and the difference between Risk Aversion and Ambiguity Aversion. Although some may argue the use of experiments does not indicate how people would make decisions in the real life, Gneezy et al. (2006) find that participants answer questions in the same way in both hypothetical and actual scenarios.

Willingness to Pay in the Gain and Loss Domains

Our experiment examines the relation between Risk Aversion and Ambiguity Aversion in both the gain and loss domains during the process of mortgage default settlement negotiations. The exact wording of all experimental treatments can be found in the appendix. Participants are informed they are in a dispute with their mortgage lender with two possible outcomes. In the gain (loss) domain, they will potentially have a decrease (increase) in the mortgages unpaid balance (UPB) by either $30,000 or $80,000. The risky treatment provides the probability that each choice will occur, while the ambiguous treatment states they “have absolutely no idea how likely it is that either outcome will occur.” Using a within-subjects design, participants see both the risk and ambiguous versions in both the gain and loss domains. Participants are then asked the amount they are willing to pay to lock in the more favorable result: reducing the UPB by $80,000 in the gain domain and increasing the UPB by $30,000 in the loss domain. Participants move a slider to record a value from $0 to $50,000, indicating their willingness to pay in each domain to achieve the more favorable outcome. The likelihood of a favorable outcome varies randomly from 0 to 100%. To avoid presentation order effects, participants are randomly assigned to eight pools, with either the risk or ambiguous treatments in either the gain or loss domain before proceeding to the other treatments.

Measuring Risk Aversion and Ambiguity Aversion

An important aspect of understanding the relation between Risk Aversion and Ambiguity Aversion is being able to measure the degree of aversion for participants. Since Holt and Laury (2002), multiple price listing instruments have become a popular way to elicit risk preferences.Footnote 2 These instruments are efficient in collecting risk preferences because they ask participants to choose between a series of gambles. Participants’ choices reveal underlying Risk Aversion levels. Accordingly, we assess each participant’s Risk Aversion and Ambiguity Aversion using the multiple price listing instruments of Gneezy et al. (2015). This instrument is based on an α-MEU model developed by Ghirardato et al. (2004) with a constant relative Risk Aversion and von-Neumann-Morgenstern utilities.

Personality

The information gap literature maintains that both Risk Aversion and Ambiguity Aversion are rooted in people’s discomfort with a lack of information (Loewenstein 1994; Golman and Loewenstein 2018; Golman et al. 2020). This implies personality may play a role in economic decision making. In fact, personality has been shown to be important in explaining market participation, day trading, and CEO performance (Lo et al. 2005; Peterson 2007; Puri and Robinson 2007; Borghans et al. 2008; Guiso et al. 2008; Kaplan et al. 2012). Altogether, the literature suggests experiments seeking to understand Risk Aversion and Ambiguity Aversion should include personality measures. There are several methods for discussing the traits that make up a personality. One of the most common is the Big Five personality factors (Borghans et al. 2008). Using factor analysis, this concept distills personality into five traits: conscientiousness, agreeableness, neuroticism, openness to experience, and extraversion. Several studies of financial choice have found trust, a component of agreeableness, to be an important factor in financial decisions (Guiso et al. 2008; Dimmock et al. 2016). We control for personality traits using Rammstedt and John’s (2007) Big Five Personality Instrument.

Financial Literacy and Demographics

Studies show that financial literacy and demographics may influence economic decisions (Guiso et al. 2008; Van Rooij et al. 2011; Lusardi and Mitchell 2014; Dimmock et al. 2016). Furthermore, Golman and Loewenstein (2018) find that personal preferences and competencies may also play a role in Ambiguity Aversion. That is, people may display higher levels of Ambiguity Aversion in subjects they dislike, with which they are unfamiliar, or in which they lack skill. We therefore include a financial literacy control variable constructed with five questions from the FINRA Investor Education Foundation (Zahirovic-Herbert et al. 2016)Footnote 3 and demographic variables including the Male dummy that takes the value of 1 if male, and 0 otherwise; the White dummy that takes the value of 1 if the participant is White, and 0 otherwise; the Number of dependent children; the Married dummy that takes the value of 1 if married, and 0 otherwise; and the participant’s Age in years.

Sample

Research into economic decision making is often conducted using a small sample primarily consisting of students (Holt and Laury 2002; Gneezy et al. 2006; Halevy 2007; Baillon and Bleichrodt 2015). While student samples are convenient and may be instructive, they are clearly not representative of the overall population. Students are generally younger and have less life and financial experience than the population at large. Recently, several studies have employed surveys to investigate the ability of Ambiguity Aversion to explain financial puzzles, including underdiversification and underparticipation in equity markets and the timing of stock option exercises (Dimmock et al. 2015; Dimmock et al. 2016; Peijnenburg 2018). We follow this line of research by using a large,Footnote 4 national, sample collected via a MTurk, an established online clearinghouse. This clearinghouse provides several functions helpful in conducting our experiment. For a nominal fee, it maintains the anonymity of participants and provides a method for compensating them. The clearinghouse also has a rating system allowing researchers to assess the quality of participants. To increase the accuracy and reliability of our results, participants must have at least a 95% approval rating to take part in our experiments. In addition to the clearinghouse’s quality control measures, we also institute our own methods to ensure participants are carefully considering their responses and to reduce noise in the data. To ensure they understand the experiment, the first validity check requires participants to spend at least 5 s reading the initial instruction page.Footnote 5 The second validity check requires them to select the numbers “9” and “2” in response to two separate questions.Footnote 6 Our initial dataset included 2457 observations. Of those, 86 observations were discarded because participants failed to take the required time to read the instructions, and 529 observations were discarded because they failed at least one of our internal validity checks. Twenty-five additional observations were missing descriptive characteristics, leaving a final sample of 1817 - a very large sample for experiments of this kind.

One advantage of a large, national sample is that it is in many ways representative of the United States as a whole, which increases the generalizability of the results. The sample includes participants from all 50 states and Washington, D.C. with demographics similar to those of homeowners, in general. Table 1 reports the descriptive demographics and behavioral characteristics of the sample. Participants are 52% male, 62% are married, and have an average of 1.14 children. The average participant age is 37 years, somewhat younger than the average homeowner. Our sample identifies as 74% White, a similar percentage as the United States in total (77%).Footnote 7

Table 1 Descriptive statistics
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Since our experiment involves mortgage default settlements, we create controls for financial history, including default history, financial literacy, net worth, and income. Fifteen percent of the sample has previously defaulted on a mortgage at some point in their lifetime. Most of the sample (72%) has a positive net worth, with a mean income level between $40,000 and $60,000. On average, participants correctly answered three financial literacy questions out of the five possible from the FINRA Investor Education Foundation inventory.

Risk Aversion and Ambiguity Aversion are measured for each participant using the instruments found in Gneezy et al. (2015). On a scale from 1 (risk/ambiguity seeking) to 11 (risk/ambiguity averse), our sample means are 6.39 and 6.54 for Risk Aversion and Ambiguity Aversion, respectively. This result is in line with prior literature suggesting that, in general, people tend to be Risk and Ambiguity Averse.

The Big Five Personality traits are measured using the Rammstedt and John (2007) instrument. Openness refers to openness to experience and is defined by creativity and thirst for knowledge. Extraversion is the degree to which one is outgoing and talkative. Agreeableness measures how pleasant and trusting one is. Neuroticism is also called emotional stability and reflects how much a person sees the world as threatening. Conscientiousness is the degree to which one is organized and complies with norms. Further information about personality traits can be found in Costa and McCrae (1992) and Borghans et al. (2008). Each personality trait is assessed using the results of two questions, except Agreeableness, which includes three questions. The participant is asked to rate on a scale from 1 to 5 if he sees himself as someone with different characteristics. The instrument reverse scores some questions to increase reliability. The personality scores reported in Table 1 reflect the addition of the results to the two or three questions assigned to each personality trait. Full questions for this instrument are reported in the appendix.

Recall that our research design includes eight pools to mitigate presentation order effects. For simplicity of presentation, we collapse these within-subjects results, but test to ensure our participant characteristics are balanced among the pools. If participant characteristics are not equally distributed among the pools, our sample may be unbalanced and our empirical results may suffer from endogeneity. Accordingly, we perform one-way ANOVA tests for equality for each participant characteristic variable across the eight pools (Armona et al. 2019). The non-significant ANOVA results confirm our variables are equitably balanced across the pools, reducing endogeneity concerns.

Table 2 provides pairwise correlations for the key study variables. Not surprisingly, Risk Aversion and Ambiguity Aversion are positively correlated. However, although personal characteristics are somewhat correlated with Ambiguity Aversion and Risk Aversion, they are not similar across both aversion measures, which supports the literature suggesting they are separate phenomena. Moving on to the financial history variables, financial literacy is positively related to both Ambiguity Aversion and Risk Aversion. Although some relations between the variables are significant, the correlations do not rise to the level that would be a concern for mulit-collinearity in our regressions.

Table 2 Correlations of study variables
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Results

This experiment is designed to assess the effect of Ambiguity Aversion on real estate decision making as it relates to mortgage default settlements in both the gain and loss domains, testing the predictions of prospect theory (Kahneman and Tversky 1979). By conducting an experiment where all respondents see both scenarios, we are able to examine differences between the risk and ambiguity scenarios. The literature suggests Risk Aversion and Ambiguity Aversion are sensitive to the environment in which they are studied, so this method of assessing Ambiguity Aversion may be important (Golman and Loewenstein 2018).

With these important differences in mind, we now present results for the amount of money participants are willing to pay to guarantee a reduction in their UPB by $80,000 during a default settlement negotiation versus a reduction in the UPB by $30,000. This is in the gain domain because both options involve a reduction in UPB. Panel A of Fig. 1 plots the mean dollar amount participants are willing to pay for each probability of a positive outcome. As expected, as the likelihood of a positive outcome increases, the amount participants are willing to pay to ensure the reduction in their UPB by $80,000 declines, resulting in a trendline with a negative slope. Next, we repeat the experiment in the loss domain. Panel B of Fig. 1 displays the mean amount participants are willing to pay to lock in a $30,000 increase in their UPB versus an $80,000 increase per probability of a positive outcome. Note that in the loss domain, the positive outcome is still a loss of $30,000.

Fig. 1
figure 1

Willingness to pay (WTP) to ensure a positive outcome, excluding 0% and 100%. Panel A shows the mean dollar amount participants are willing to pay to guarantee a greater UPB reduction (gain domain) for each probability of a positive outcome, excluding sure bets (i.e., 0% and 100%). Panel B plots results in the loss domain

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Panel A of Table 3 reports the amount participants are willing to pay to lock in the $80,000 UPB reduction separated by Ambiguity Aversion category. We expect Ambiguity Seeking participants to be more comfortable with ambiguity and would therefore expect them to be willing to pay less to ensure the positive result than Ambiguity Averse respondents. However, the results in Table 3 show the opposite: Ambiguity Seeking participants are willing to pay more than Ambiguity Averse participants to ensure a positive outcome. We will explain this result momentarily.

Table 3 Summary statistics for willingness to pay in the gain and loss domains
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Panel B reports the mean amount participants are willing to pay for each category of Ambiguity Aversion. Consistent with Panel A, we find that Ambiguity Seeking participants are willing to pay more than Ambiguity Averse participants to ensure a more positive outcome. At first, these results might seem counterintuitive. However, the experimental design introduces an element of funds availability. In this scenario, if the outcomes are equally likely, the expected payoff would be a $25,000 reduction in UPB in the gain domain or a $25,000 increase in UPB in the loss domain. Participants with sufficient funds would be expected to pay an amount approaching $25,000. However, some participants may not have the funds available to make the payment. This line of thinking suggests that in areas of a quantified payment amount, controlling for financial history is important, which we do next.

Table 4 displays robust regression results in which the dependent variable is the amount participants are willing to pay to ensure a positive result in the loss domain for Columns 1, 2, and 3 and in the gain domain for Columns 4, 5, and 6. As in Table 3, Columns 1 and 4 show a negative relation between Ambiguity Aversion and the willingness to pay to guarantee a positive result. Columns 2 and 5 show the negative result is robust to adding Risk Aversion to the regression and robust to other controls in Columns 3 and 6. Similar to previous findings that Ambiguity Aversion leads people to avoid participating in the stock market (Dow and Werlang 1992; Easley and O’Hara 2009), we find that Ambiguity Averse borrowers are less willing to pay to resolve the uncertainty of mortgage default settlements. Since Ambiguity Averse people prefer known probabilities to unknown uncertainties, they may be unwilling to invest in assuring a positive outcome in settlement proceeedings. Positive net worth, higher income, previous default, and the male dummy variable are positively associated with higher payments. The White dummy variable, age, and financial literacy are negatively associated with the amount people are willing to pay. Financial literacy may be associated with a greater confidence in being able to handle the repercussions from the mortgage default settlement. This greater confidence results in financially literate participants being willing to pay less to resolve the issue than participants with less financial knowledge. Extraversion is positively related to the amount people are willing to pay in both the gain and loss domains, while openness is negatively associated with willingness to pay in the gain domain only. The positive and significant coefficients on income and positive net worth dummy confirm our interpretation of Table 3. Participants’ financial histories should be accounted for when investigating the amount they are willing to pay. We further investigate the effect of financial histories in the following analyses.

Table 4 Regressions for willingness to pay in the loss and gain domains
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Robustness Checks

This first series of robustness tests are conducted in the loss domain with results reported in Table 5. First, we split the sample by high and low financial literacy in Columns 1 and 2 and by whether the participant has previously defaulted on a loan or not in Columns 3 and 4. Participants deemed to possess high financial literacy are those who answered all of the FINRA literacy questions correctly. Ambiguity Aversion is again robust to the inclusion of control variables, but only for participants who have high financial literacy and have not previously defaulted on a loan. For lower financial literacy and those who have defaulted on a loan, Ambiguity Aversion remains non-significant.

Table 5 Robustness checks for willingness to pay regressions in the loss domain
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We next estimate the same series of robustness tests in the gain domain and find similar, but stronger results, which are reported in Table 6. Compared to the results in the loss domain, we find Ambiguity Aversion is negatively related to the amount participants are willing to pay if they have a high level of financial literacy or no previous default history. Both these results are significant at the 99% level.Footnote 8

Table 6 Robustness checks for willingness to pay regressions in the gain domain
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Conclusion

The mortgage market is associated with a high degree of financial leverage, represents a substantial percentage of a borrower’s balance sheet, and when in default, brings about an unparalleled degree of legal ambiguity. These factors come together to make a mortgage default settlement negotiation the ideal laboratory for examining and differentiating between the roles of Risk and Ambiguity Aversion.

Using a large, national sample, we perform a series of experiments to examine the relation between risky decisions and decisions under ambiguous conditions as it relates to mortgage default settlements. Our results suggest that Risk Aversion and Ambiguity Aversion are best studied together. The amount a person is willing to pay to achieve a positive outcome depends not only on the Ambiguity or Risk Aversion level, but also on financial history and demographic characteristics.

Specifically, Ambiguity Aversion is negatively associated with willingness to pay in both the gain and loss domains. This is consistent with Ambiguity Averse people abstaining from stock market participation. However, after parsing the sample, this result is only evident for participants who are highly financially literate. Low financial literacy participants do not have an association between Ambiguity Aversion and WTP. We also find that personality traits are only associated with WTP for the low financial literacy group. Taken together, our findings are consistent with the idea that financially literate borrowers are influenced by Ambiguity Aversion in financial decision making, but low financial literacy borrowers are more influenced by their personality traits. These findings should help inform the strategy for providing financial education to borrowers who have defaulted on their loans.