Empirical approach of studying individual risk preference

Boyan Markov

How likely are you to risk?

Would you pay 500$ to bet on a coin flip?

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Would you risk losing 2000$ at 50/50�Or would you rather lose 1000$.

Would you risk 50/50 to gain 2000$ �or take a sure deal for 1000$.

How it all started - are you willing to risk?

I believe I am very risk averse:

Motivation behind studying risk

• I understand financial risk
• I understand (basic) investment strategy
• I am very risk averse

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• I enter high risk low reward trades
• I close losing positions fast but …
• I also hold some positions until they breakeven

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Some basic risk concepts

Prospect Theory Value Function

The Value Function in Prospect Theory, represented as an S-shaped graph, illuminates the psychological values assigned to losses and gains, and not simply their monetary worth.

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1. Loss Aversion: The steeper slope for losses implies that losses are felt more intensely than gains. Our questionnaire explores this by offering choices between certain and risky losses.�
2. Diminishing Sensitivity: As gains or losses increase, the associated psychological impact becomes less pronounced. We incorporate a wide range of monetary values (€2 to €200,000) to assess this aspect.�
3. Risk Attitudes: The value function's shape suggests risk-averse behavior for gains and risk-seeking behavior for losses. Our scenarios of certain vs. risky gains or losses are structured to observe these patterns.

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Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291.

Decision making as a component of risk

Some basic risk concepts

Risk

Uncertainty

Using questionnaires to access risk

We used a Risk Preference Questionnaire (RPQ), designed to probe into the complexities of individual financial risk tolerance. Our tool uses hypothetical scenarios, placing the respondent at a crossroads between certain outcomes and risky propositions.

Key Features:

• Four distinct sections, each analyzing different aspects of financial decision-making under uncertainty.
• Scenarios ranging from guaranteed profits/losses to 50-50 odds for a double return or no return.
• Monetary values ranging from €2 to €200,000, enabling us to assess the impact of different financial stakes on decision-making.

Goal: Uncover a nuanced understanding of risk preference, moving beyond the binary concept of risk-averse and risk-seeking behavior.

Publishing pending

Advantages and Disadvantages of Questionnaires and Online Surveys

• Scalability vaa collection from a large sample size, improving generalizability.
• Cost-Effective when compared to other data gathering methods
• Anonymity - ensures privacy, often leading to more honest responses.
• Standardization - offers consistency as every participant answers the same set of questions.
• Ease of Distribution - can be shared widely and quickly.
• Automated Data Entry - reduces errors and time spent on data entry.

• Response Bias - participants answer in a certain way, irrespective of their true feelings.
• Misinterpretation - participants may misunderstand questions, affecting data validity.
• Low Response Rates - participants might ignore the questionnaire, or fill them out without carefully considering questions
• Lack of Personalization: The same set of questions may not apply or make sense to every participant.
• Lack of Physical Presence to clarify doubts, which might affect response accuracy.

Advantages

Disadvantages

Demographics of the Study: A Comprehensive Overview

Demographics of the Study: A Comprehensive Overview

Deciphering the Risk Preference Questionnaire: An In-Depth Look at the Questions

1. Profit with Certainty vs. Risky Profit: Choose between a guaranteed profit or a risky deal with a chance for a doubled profit or no profit. (Q1 - Q6; X = 1 EUR -> 100 000 EU )�
2. Certain Loss vs. Risky Loss: Make a choice between a sure loss or a risky proposition that could either double the loss or eliminate it. (Q7 - Q12; X = -1 EUR -> -100 000 EU )�
3. Profit Trade-off: Determine the guaranteed profit amount that would make you refuse a risky deal offering a chance at a specific profit or no profit. (Q13 - Q18; X = 2 EUR -> 200 000 EU )�
4. Loss Trade-off: Identify the certain loss amount that would lead you to reject a risky deal presenting a possibility of a specific loss or no loss. (Q19 - Q24; X = -2 EUR -> - 200 000 EU )

Visualizing Risk Preference: The Risk Score Graph

(n = 825)

High risk propensity sample

Key Findings: Demographics, Question Correlations, and Influencing Factors

Our analysis revealed several intriguing findings:

1. Absence of Strong Correlations with Demographics: ��Contrary to literature expectations, we found no strong correlations between our risk metric and demographics data. Typically, risk tolerance is expected to decrease with age, be higher among males, and increase with higher education and income levels.

2. Non-correlation with the First Half of Questions: ��The first 12 questions of our questionnaire showed no significant correlation with our risk metric. This may suggest that these questions are not capturing aspects of risk preference effectively or are tapping into other dimensions not reflected in our risk metric.

These findings highlight areas for potential refinement in our questionnaire and provide interesting directions for further analysis and research into the multifaceted nature of risk preference.

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Applying Cronbach's Alpha: Assessing Internal Consistency

Upon discovering a lack of correlation between the first half of the questions and our risk metric, we turn to Cronbach's Alpha. This statistical tool allows us to assess the internal consistency or reliability of our questionnaire.

What is Cronbach's Alpha?

• Cronbach's Alpha is a measure of internal consistency that gauges how closely related a set of items are as a group. An alpha > 0.7 is generally considered acceptable.

Why Use Cronbach's Alpha in Our Context?

• Reliability Check: It can help identify if the questions in the first half of the questionnaire are reliably measuring the same underlying construct - risk preference in this case.�
• Item Redundancy: If alpha significantly increases when a question is deleted, it might indicate that question is redundant or not contributing valuable information.�
• Questionnaire Refinement: It could guide us in refining our questionnaire, whether that involves rewording, replacing, or eliminating certain questions.

Through this method, we aim to ensure the integrity and efficacy of our questionnaire in capturing the multifaceted nature of risk preference.

Deciphering the Components of Cronbach's Alpha

Cronbach's Alpha (α), sometimes referred to as tau-equivalent reliability (ρ_T), hinges on several key components:

• k: The number of items or questions. The value of k directly influences Cronbach's Alpha - as k increases, Alpha typically increases, assuming that all items measure the same construct.�
• σ_ij: The covariance between item i and item j. This represents the degree to which these two items vary together. A higher covariance suggests that the items are related and may be measuring the same underlying construct.�
• σ²_X: This is the sum of all item variances and inter-item covariances. Item variance measures how much the responses on an item vary, while inter-item covariance measures how much the items vary together. �A higher value of σ²_X suggests that there is considerable common variance among items, indicating good internal consistency.

Cronbach's alpha provides an estimate of the proportion of the total score variance that is due to the true score variance, relative to the total score variance. Higher values of alpha indicate a greater proportion of reliable variance in the measure, suggesting higher internal consistency.

Applying Cronbach's Alpha: Assessing the First Six Questions

Internal consistency of first 6 questions - 0.62��Q6 has the least internal consistency and removing it would improve the metric by .04

Applying Cronbach's Alpha: Assessing the Second pair of Questions

Internal consistency of first 6 questions - 0.67��Q12 has the least internal consistency and removing it would improve the metric by .01

Respondents Behavior Q7-Q12

Applying Cronbach's Alpha: Assessing the Third pair of Questions

Internal consistency of first 6 questions - 0.17��Respondents likely did not understand the question and gave extremely nuanced answers.

Respondents Behavior Q13-Q18

Applying Cronbach's Alpha: Assessing the Last pair of Questions

Internal consistency of first 6 questions - 0.18��Respondents likely did not understand the question and gave extremely nuanced answers.

Respondents Behavior Q19-Q24

Preliminary Observations: Questionnaire Consistency and Respondent consistency

Upon applying Cronbach's Alpha, our observations reveal interesting insights about the internal consistency of our questionnaire and respondent behavior:

• Acceptable Consistency in Questions 1-6 and 7-12: Cronbach's Alpha results indicate that both these sections of the questionnaire have acceptable internal consistency. This suggests these questions are reliably measuring risk preference and contributing valuable data.

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• Respondent Confusion in Later Questions: Response patterns suggest that respondents experience confusion in the latter half of the questionnaire. The reasons behind this confusion—whether it's due to question complexity, fatigue, or other factors—warrant further investigation.

Reworking Question Values: A Categorical Approach

In an attempt to address the challenges observed in the latter half of the questionnaire, we are reworking the values of questions 13-24 into categorical results. Here is how:

For Questions 13-18: Responses will be categorized based on their relation to the expected value.

• Premium: If a respondent's answer is greater than the expected value, indicating they expect a premium to refuse the risk.
• Discount: If a respondent's answer is below the expected value, suggesting they're willing to accept a discount to avoid risk.
• Neutral: If the expected value equals the answer, indicating a neutral risk position.

For Questions 19-24: Responses will also be categorized based on their relation to the expected loss.

• Premium: If a respondent's answer is less than the expected loss, implying they'd prefer a premium (i.e., lose less) to accept the risk.
• Discount: If a respondent's answer is more than the expected loss, indicating they'd accept a discount (i.e., lose more) to avoid risk.
• Neutral: If the expected loss equals the answer, indicating a neutral risk position.�

By transforming these responses into categorical variables, we aim to enhance the clarity of data interpretation. Following these changes, we will reassess the internal consistency using Cronbach's Alpha to evaluate the improvement in questionnaire reliability.

Post-Transformation Cronbach's Alpha: Evaluating Questionnaire Reliability

Enhanced Reliability: Cronbach's Alpha Post-Transformation

After transforming the last 12 questions into categorical results, we've re-evaluated our questionnaire using Cronbach's Alpha.

Achieving Improved Consistency:

• The Cronbach's Alpha for the reworked last 12 questions together with the initial 12 is approximately 0.734, exceeding the generally acceptable threshold of 0.7. ��This suggests the transformed questions are reliably measuring the same underlying construct - risk preference.

What Does this Mean?

• The transformation of responses into categories has enhanced the internal consistency of our questionnaire. This suggests that the reworked questions have become more effective in measuring risk preference.�
• This categorization simplifies interpretation of responses, aiding in our understanding of how respondents perceive and manage risk.

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Optimal Questionnaire Structure: Highest Internal Consistency

Our study reveals that certain combinations of questions yield superior internal consistency, as measured by Cronbach's Alpha:

• Questions QT13-QT24: This combination yielded the highest Cronbach's Alpha of 0.74, indicating excellent internal consistency.�
• Whole Questionnaire: The full set of questions achieved a Cronbach's Alpha of 0.733, equivalent to the third combination, demonstrating good internal consistency throughout.�
• Questions Q1-Q6 + QT13-QT24: This combination resulted in a robust Cronbach's Alpha of 0.722, also showing strong internal consistency.�
• Questions Q7-Q12 + QT13-QT24: These question groups together produced a Cronbach's Alpha of 0.729, indicating good internal consistency.�

Key Insights:

Potential for Shortening - These results indicate that the questionnaire could potentially be shortened without compromising its ability to assess risk preference effectively.

Stronger Signal for Risk Seeking - Our data suggests that risk aversion tends to be a stronger signal for a common construct than risk seeking among respondents, a finding that may guide future questionnaire design and interpretation.

These findings will be instrumental in refining our questionnaire design and understanding of risk preference going forward.

Challenges of Using Questionnaires in Strategic Management

Respondents get easily confused, can’t comprehend different stakes and display high variance to risk propensity.

• Misinterpretation Potential
• Response Bias
• Lack of Depth and Context
• Limited Customization

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291.

Testing the Unidimensionality of Risk Perception: An Empirical Study Using Cronbach's Alpha on Online Surveys (Markov, B., Marchev, A. 2023) *currently under review

*Preliminary findings

Game-based Approaches for Risk Propensity Calculation

Interactive and Engaging: Game-based methods can engage participants in a more immersive and dynamic way than traditional surveys or questionnaires, potentially leading to more authentic responses.�

Simulating Real-world Decisions: Games can simulate complex real-world situations where risky decisions must be made, capturing nuances that a simple questionnaire might miss.�

Dynamic Decision Making: Unlike static questionnaires, games allow for dynamic decision-making, where one decision can influence subsequent choices and outcomes.�

Quantifiable Measures of Risk Propensity: Games can provide quantifiable metrics such as points or win/lose outcomes, which can be used to calculate a participant's risk propensity based on their decision-making in the game.�

Controlled Environment: Games provide a controlled environment where researchers can manipulate variables to study their impact on risk-taking behaviors.

Methodology - key design aspects of a risk propensity game

1. Game design needs to be centered around engaging respondents meaningfully.�
2. Strong focus on immersion via dynamic scenarios.�
3. Decision making needs to be broken down into granular parts.�
4. Individual risk propensity via comparison of large participant pool.

Advantages of Online Implementation in Game-Based Risk Propensity Assessment

• Easy access and convenience around sample size�
• Efficient & Granular data collection�
• Generalization opportunities for player behavior.�
• Measurement of decision-making as a step in this process

Modelling individual risk propensity based on decision distributions

Game-based risk assessment has practical applications and implications for strategic management practitioners. It provides a realistic and engaging approach to understand risk perception and decision-making behaviours, enabling the development of tailored risk management strategies.

Preliminary findings

• Examination of risk versus reward trade-offs in a highly controlled environment enables us to observe not only propensity in risk but also adaptability and risk variance of participants.�
• Ability to quantify individual differences in risk-taking behavior. (E.g. younger male individuals more likely to take risks)�
• Context, emotional state and situational factors like game fatigue, tilt or early success that influence risk propensity.�
• Portfolio value as a proxy for wealth and time taken to consider the tradeoff as strong signals for likelihood of risk taking.

Balloon analog risk task (Lejuez, 2002) 1/3

1. The respondent essentially sees this core game loop screen

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• They can choose to inflate the bag using the “more” button or “collect” it.

Balloon analog risk task (Lejuez, 2002) /3

• The player has no information about the value of each "more" button, but has access to his intermediate score after each turn. Total 50 per count.

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Balloon analog risk task (Lejuez, 2002) 3/3

1. Three types of bags with different probabilities of loss.
2. Uncertainty is introduced and the respondent is expected to adjust his strategy and risk appetite based on the color of the bag.
3. Bag 1 -> 1 / 8; Bag 2 -> 1 / 32; Bag 3 -> 1 / 128

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Lejuez’s approach to risk estimation

Risk Decision-making in Bag Inflation: A Study Involving Professors, Lecturers, and Students from Three Universities

1. This study explores the decision-making process related to risk-taking in the context of bag inflation. The participants in this research consist of professors, lecturers, and students from three prestigious universities: University of National and World Economy, New Bulgarian University, and Rousse University "Angel Kanchev". A total of 1181 respondents participated in the survey, providing valuable insights into their risk preferences during the bag inflation game.
2. The study employs a classification approach to analyze the responses of the participants during the bag inflation game. Each time a player inflates the bag, they have two choices: "take a risk - 1" or "refuse the risk - 0". The researchers collected data using an online survey and considered the participants' academic roles (professors, lecturers, and students) in the analysis.

BART Core Game Loop

• The respondent perceives a bag
• Identifies associated risk with the next click
• Other factors
• Risk or Not risk

Source: Own

Game Evolutions - the more you play the more variance we observe

Source: Own

Bart Model Pipeline

Modeling Pipeline

• Data Scaling & Categorical one hot encoding
• Outlier detection and feature engineering
• Minority oversampling (6.4:1)
• Variance threshold features
• XGB Classifier
• Cross validation

Modeling Pipeline

Risk KPI estimation

Geometric average of every risk decision

Propensity distribution

Methodology for risk estimation

The conclusion that can be drawn is as follows:

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A) The distribution itself is not normal.

and/or

B) More respondents are needed to achieve a normal distribution, suggesting that there might be a biased sample in the available data.

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We confirmed hypothesis from the literature

We can’t prove that our method is normally distributed

Conclusions: Reflecting on Our Journey and Looking Ahead

Advantages of Game-based Risk Assessment:

• Provides immersive, realistic environments
• Captures granular data
• Enhances understanding of decision-making patterns

Role of Machine Learning:

• Complements game-based data analysis
• Offers deeper insights into risk perception dynamics
• Practical Benefits for Practitioners:

Enhances understanding of risk perception and decision-making behaviors

• Supports development of tailored risk management strategies
• Facilitates better talent management through insights into individual risk profiles