Risk Aversion Function Research Articles

Recovering risk aversion from Bitcoin option prices and realized returns

ABSTRACT This study recovers the Bitcoin option-implied risk aversion by jointly estimating a cross-sectional dataset of option prices and time-series data of realized returns on underlying asset prices. The empirical analysis of Bitcoin options on Deribit shows that the risk aversion function exhibits a peak shape, with the level of implied risk aversion of Bitcoin options ranging from − 0.2 to 0.05, which is significantly lower than that of the traditional options market; furthermore, maturity affects the level of option-implied risk aversion, with shorter maturity implying higher risk-aversion levels. Moreover, our research indicates that after halving of Bitcoin, investors’ risk aversion function becomes higher and steeper than before.

The premium of uncertain risk based on standard deviation principle

Risk measurement and insurance pricing have always been issues of concern in actuarial science. Under the framework of uncertainty theory, this paper puts forward a new premium principle: uncertain standard deviation premium principle, proposes some of its properties about risk and compares the premiums of different risks. Based on the utility function of risk aversion, the additional premium coefficient is derived and two specific numerical examples are used to calculate the maximum premium. Furthermore, the unknown parameters of the policy with deductible are estimated by uncertain moment estimation and uncertain maximum likelihood estimation.

Calibration of quantum decision theory: aversion to large losses and predictability of probabilistic choices

We present the first calibration of quantum decision theory (QDT) to a dataset of binary risky choice. We quantitatively account for the fraction of choice reversals between two repetitions of the experiment, using a probabilistic choice formulation in the simplest form without model assumption or adjustable parameters. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through their differentiation into two groups: ‘majoritarian’ and ‘contrarian’ (in proportion 3:1). This supports the first fundamental tenet of QDT, which models choice as an inherent probabilistic process, where the probability of a prospect can be expressed as the sum of its utility and attraction factors. We propose to parameterize the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and the attraction factor with a constant absolute risk aversion function. For this dataset, and penalising the larger number of QDT parameters via the Wilks test of nested hypotheses, the QDT model is found to perform significantly better than logit-CPT at both the aggregate and individual levels, and for all considered fit criteria for the first experiment iteration and for predictions (second ‘out-of-sample’ iteration). The distinctive QDT effect captured by the attraction factor is mostly appreciable (i.e. most relevant and strongest in amplitude) for prospects with big losses. Our quantitative analysis of the experimental results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice. The results of the paper can find applications both in the prediction of choice of human decision makers as well as for organizing the operation of artificial intelligence.

Social networking and risk attitudes nexus: implication for technology adoption among smallholder cassava farmers in Ghana

BackgroundTheoretically, social climate and social networking which may affect attitudes, motivations, and readiness towards quality improvement and rewards, influence the adoption decision process by possibly modifying the risk behaviour/attitudes of individuals. Thus for effective promotion of agricultural technologies among farmers in Africa, it is necessary to understand the social context within which risk attitudes are formed and social participation decisions are made. The study, therefore, employed the recursive bivariate endogenous switching probit model to examine how risk attitudes of farmers are shaped through social interactions in the information and communication networks of farmers to influence their technology adoption decisions. Here, the empirical application was done with the contextual case of agriculture intensification technologies in the Root and Tuber Improvement and Marketing Programme (RTIMP) introduced to smallholder cassava farmers in Ghana. This paper makes a contribution to recent advances in the empirical analysis of impact where anticipated problems posed by unobserved confounders are accounted for. This was possible since the approach used allows for the estimation of the treatment effect of endogenous risk attitude variable of interest on farmers’ adoption decisions.ResultsThe study found that the effectiveness and usefulness of social interactions as well as a high degree of trust by cassava farmers in their social networks have higher tendencies to lower the degree of risk aversion behaviour of the farmers to significantly influence RTIMP Technologies adoption decisions positively. The ATE estimate confirms that there has been a significant increase of 38% probability in the likelihood of adopting agricultural intensification technologies in the RTIMP attributable to the non-risk aversion attitudes of cassava farmers. The cassava farmers’ risk attitudes were found to be significantly influenced by the effectiveness and usefulness of social interactions, and a high degree of trust as well as age, frequency of extension services, access to credit, and revenue.ConclusionBy implication, attempts to introduce innovations to improve agricultural commodities value chains that target farmers must pay particular attention to the information and communication network to ensure the effectiveness and usefulness of information dissemination to farmers in an honest manner, so as to build trust; which will go a long way to reduce doubts and uncertainties (function of risk aversion). This will help achieve higher innovation adoption impacts thereby resulting in attaining the overall deliverable objectives of agricultural innovations.

Bank levy and household risk-aversion

We study a bank levy that funds government guarantees in a general equilibrium setting where banks intermediate between risk-averse households and state-contingent investments. We offer an analytical characterization of the optimal bank levy as a function of household risk-aversion and guarantees. We show that household risk-taking is increasing in guarantees, while it is decreasing as the bank levy and household risk-aversion increase. This allows us to establish a non-trivial relationship between the optimal bank levy and household risk-aversion: Higher risk-aversion optimally induces a higher levy when guarantees exceed a threshold; otherwise, a higher levy shall be observed in economies with less risk-averse households.

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions solving the system of HJB equations. We introduce the transformation method for solving the penalized nonlinear partial differential equation. The transformed equation involves possibly non-constant the risk aversion function containing the negative ratio between the second and first derivatives of the utility function. Using comparison principles we derive useful bounds on the option price. We also propose a finite difference numerical discretization scheme with some computational examples.

Analysis the effect of market anomalies and growth options on stock return

در بازارهای مالی اثر هر یک از ناهنجاری‌های سودآوری، درماندگی مالی، بخت‌آزمایی و ریسک غیر سیستماتیک بر بازده سهام به‌تنهایی بررسی شده است. اما ارتباط احتمالی آن‌ها نامشخص است. به‌تازگی این ادعا مطرح‌شده است که فرصت‌های رشد بر تقارن تابع توزیع بازده اثر می‌گذارد و قادر است این ارتباط احتمالی و صرف ریسک ناشی از این ناهنجاری‌ها را توضیح دهد. در این پژوهش با استفاده از خواص آماری حاکم بر گشتاور مرتبه سوم تابع توزیع بازده و با جداسازی چولگی ویژه مورد انتظار ناشی از فرصت‌های رشد این ارتباط بررسی شده است. بدین منظور داده‌های 114 شرکت پذیرفته‌شده در بورس اوراق بهادار تهران با رویکرد حذف سیستماتیک، بین سال‌های 1390 تا 1396 جمع‌آوری شد. فرضیه‌های پژوهش با استفاده از رویکرد سبد بندی و ارزیابی آلفای برخی مدل‌های عاملی آزمون شد. شواهد نشان می‌دهد بین سودآوری، درماندگی مالی، بخت‌آزمایی و ریسک غیر سیستماتیک با بازده آتی رابطه وجود دارد؛ اما مدل‌های مرسوم قیمت‌گذاری دارایی‌های سرمایه‌ای توانایی تبیین صرف ناشی از ناهنجاری‌های مذکور را ندارد. این شواهد به‌صورت غیرمستقیم مؤید وجود معمای سودآوری، بخت‌آزمایی و ریسک غیر سیستماتیک در بازار سرمایه ایران است و نشان می‌دهد سرمایه‌گذاران با گزینش راهبرد سرمایه‌گذاری مبتنی بر این ناهنجاری‌ها می‌توانند بازده متفاوتی داشته باشند.

Optimal Bank Contributions and Household Risk-Aversion

We study bank contributions that ex ante fund government guarantees supported by a fiscal backstop in a general equilibrium setting where banks intermediate between risk-averse households and state-contingent investments. We offer an analytical characterization of optimal bank contributions as a function of household risk-aversion and guarantees. Showing that higher risk-aversion expedites the way bank contributions internalize guarantees' boost of household risk-taking, we establish a non-trivial relationship between optimal bank contributions and household risk-aversion: Higher risk-aversion optimally induces higher contributions when guarantees exceed a threshold; otherwise, higher contributions shall be observed in economies with less risk-averse households.

Risk investment decisions within the deterministic equivalent income model

Purpose The purpose of this paper is to establish a deterministic equivalent income model (DEIM) based on the risk cost (RC) and risk aversion of investors. The model fully considers both subjective and objective factors that affect risk investment and reasonably evaluates risk investment schemes to choose the correct investment scheme and gain greater investment returns. Design/methodology/approach The utility function is used to measure the extent to which an investor is satisfied by investment returns in various scenarios. Risk aversion expresses subjective attitude of investors to risk. RC represents risk loss in currency. This methodology is based on risk aversion function, utility function and RC theory to establish DEIM. Findings This study shows that investors with different risk preferences have different certainty equivalent returns (CER), so their choices of investment options change accordingly. Practical implications In this paper, the authors use DEIM to test an investment case and conclude that the CER and investment scheme both change with different risk preferences. At the same time, case analysis shows that DEIM is reasonable and stable when evaluating risk investment schemes. Originality/value In this study, the authors innovate by introducing both the RC and risk aversion degree into risk investment schemes evaluation and by deriving a utility function from the absolute risk aversion function to build a utility decision matrix and establish DEIM. The model combines the subjective and objective factors that influence risk investment decisions.

The Impact of Customers’ Demand Response Behaviors on Power System With Renewable Energy Sources

This article addresses a new approach to investigating the impact of demand response (DR) on the generation adequacy by considering customers’ willingness to participate in DR. Firstly, to characterize psychological behaviors of the customer, we design a general reference-dependent utility (RU) function, and select the hyperbolic absolute risk aversion (HARA) function as the fundamental function to develop an HARA-RU (H-RU) function for depicting risk attitude of the customer. Secondly, a Q-learning algorithm based on the H-RU function is proposed to simulate customers’ willingness to participate in DR. In this way, the available capacity of DR can be measured. Thirdly, based on the available capacity, a DR scheduling model is developed. And fourthly, according to the scheduling results, an assessment procedure is proposed to evaluate the impact of DR on generation adequacy. Finally, a case study is provided to verify the effectiveness of our method. Besides, one limitation of this study is that transmission congestions are not considered. In future research, it would be interesting to consider this factor and extend our method to the case of a more sophisticated situation.

Macro Asset Allocation with Social Impact Investments

Using a unique dataset of 50 listed companies that meet the majority of the OECD requirements for social impact investments, we construct a social impact finance stock index and investigate how investing in social impact firms can contribute to portfolio risk-return performance. We build portfolios with three different methodologies (naïve, Markowitz mean-variance optimization, GARCH-copula model), and we study the performance in terms of returns, Sharpe ratio, utility, and forecast premium based on a constant relative risk aversion function for investors with different levels of risk aversion. Consistent with the idea that social impact investment can improve portfolio risk-return performance, the results of our macro asset allocation analysis show the importance of a large fraction of investor portfolios’ stake committed to social impact investments.

Research on Risk Avoidance and Coordination of Supply Chain Subject Based on Blockchain Technology

Based on the influence of block chain technology on information sharing among supply chain participants, mean-CVaR (conditional value at risk) is used to characterize retailers’ risk aversion behavior, while a Stackelberg game is taken to study the optimal decision-making of manufacturers and retailers during decentralized and centralized decision-making processes. Finally, the mean-CVaR-based revenue-sharing contract is used to coordinate the supply chain and profit distribution. The research shows that, under the condition of decentralized decision-making, when the retailer’s optimal order quantity is low, it is an increasing function of the weighted proportion and the risk aversion degree, while, when the retailer’s optimal order quantity is high, it is an increasing function of the weighted proportion, and has nothing to do with the risk aversion degree. The manufacturer’s blockchain technology application degree is a reduction function of the weighted proportion. When the retailer’s order quantity is low, the manufacturer’s blockchain technology application degree is a decreasing function of risk aversion, while, when the retailer’s order quantity is high, the manufacturer’s blockchain technology application is independent of risk aversion. The profit of the supply chain system under centralized decision-making is higher than that of decentralized decision-making. The revenue sharing contract can achieve the coordination of the supply chain to the level of centralized decision-making. Through blockchain technology, transaction costs among members of the supply chain can be reduced, information sharing can be realized, and the benefits of the supply chain can be improved. Finally, the specific numerical simulation is adopted to analyze the weighted proportion, risk aversion and the impact of blockchain technology on the supply chain, and verify the relevant conclusions.

A preliminary exploration on stochastic dynamic asset allocation models under a continuous-time sticky-price general equilibrium

ABSTRACTThis article studies asset allocation problems under endogenous macroeconomic dynamics and monetary policy rules, by merging a continuous-time sticky-price general equilibrium model based on the New Keynesian framework with a stochastic dynamic portfolio selection model. Under optimal allocation strategies, the inverse of the Arrow–Pratt relative risk aversion function of investors decreases monotonically with a rising risk-free nominal interest rate, and exhibits a U shape with respect to inflation. This shows that, under the premise of an inflation-targeting monetary policy rule, the investors’ relative inclination for risky assets grows when inflation deviates from its steady state, in expectation for a countervailing nominal policy rate. The article also uses the model to discuss the macro-prudential problem of the feedback effects of the investors’ intertemporal utility-maximizing behaviour on the economy. Preliminary results show that the existence of risky assets in the economy can have an effect similar to that of the financial accelerator. This gives another possible explanation for the wedge effect beyond the traditional incentive theory.

Climate change risks for severe storms in developing countries in the context of poverty and inequality in Cambodia

Least developed countries are generally regarded as particularly sensitive to climate change due to among other vulnerable locations and low adaptation capabilities. In the present study, we address climate change hazards in least developed countries by presenting a methodological framework, which is suitable for the estimation damage costs as a function of risk aversion, equality, income distribution and climate scenario using state-of-the-art climate model projections. As a case study, the methodology is applied to study severe storms in Cambodia based on two future climate scenarios and data on historical damages from storm events, which are used as a proxy in performing a sensitivity analysis on all input parameters. For the assumptions and parameter ranges used here, the study shows a high sensitivity to the income distribution (reflected by discount rates) and risk aversion and smaller effects from equality measures and extreme wind climate scenario. We emphasize that the assumptions on risk aversion reflecting consumption smoothing possibilities of low-income households clearly depicts that climate risks can be particularly high as a consequence of poverty and therefore recommend that context-specific vulnerabilities and equity concerns in climate risk studies should be included when making assessments for least developed countries.

Decision support on the basis of utility models with discordance-related preferential information: investigation of risk aversion properties

A fundamental and widely applied approach to decision-making is the multi-attribute utility theory. Because it aggregates preferences in the compensatory manner, it can be extended with the concept of veto function, which is adopted from the outranking approach, and models full or partial non-compensation of unsatisfactory preferences. This paper discusses the methodological foundations underlying this approach, and introduces the mechanisms of decision support on the basis of utility models with discordance-related information. It then presents the main contribution of the research, in which the forms and properties of veto functions are studied, particularly with respect to risk aversion. Outcomes of risk averse, risk seeking and risk neutral veto functions are analysed and compared. Risk aversion of veto functions is also correlated with risk aversion of utility functions, which are aggregated in the same multi-attribute model and exhibit common complementary preference structures of the decision-maker. The study aims to assess the influence of risk aversion on the decision, to identify possible anomalies in preference structures, to determine the suitability of different risk aversion formats and intensities for various problem settings, and to derive key characteristics. The experimental model considers several evaluation factors, such as validity of results, ability to efficiently discriminate alternatives, richness of output data, extremeness of results and robustness.

Generalized Ordered Weighted Reference Dependent Utility Aggregation Operators and Their Applications to Group Decision-Making

To quantify the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. RUs include S-shaped RU and non-S-shaped RU. Each RU affords a framework where the psychological factors explicitly enter the decision problem via the basic utility function, reference point and loss aversion coefficient. Under the general framework, we derive a generalized ordered weighted S-shaped RU proportional averaging (GOSP) operator and a generalized ordered weighted non-S-shaped RU proportional averaging (GONSP) operator, respectively. The GOSP operator implies the risk attitude of the DM for relative losses is risk-seeking, while GONSP operator indicates the risk attitude in this case is risk-averse. As a special case, GONSP operator can degenerate into GOWPA operator which means that the attitude of the DM is risk-neutral. Each operator satisfies the desirable properties of general operator, i.e., monotonicity, commutativity, idempotency and boundedness. Furthermore, we consider hyperbolic absolute risk aversion (HARA) function as the basic utility function, and define an S-shaped HARA and a non-S-shaped HARA utility functions. Based on the two new RUs, we propose GOSP–HARA operator and GONSP–HARA operator. Every operator covers many existing aggregation operators. To ascertain weights of such operators, the paper builds an attribute-deviation weight model and a DMs-deviation weight model. Based on these RU operators and weight models, an approach is addressed for solving multiple attribute group decision-making problem. At last, an example is provided to show the feasible of our approach.

Rational consumer decisions in a peak time rebate program

A rational behavior of a consumer is analyzed when the user participates in a peak time rebate (PTR) mechanism, which is a demand response (DR) incentive program based on a baseline. A multi-stage stochastic programming is proposed from the demand side in order to understand the rational decisions. The consumer preferences are modeled as a risk-averse function under additive uncertainty. The user chooses the optimal consumption profile to maximize his economic benefits for each period. The stochastic optimization problem is solved backward in time. A particular situation is developed when the system operator (SO) uses consumption of the previous interval as the household-specific baseline for the DR program. It is found that a rational consumer alters the baseline in order to increase the well-being when there is an economic incentive. As results, whether the incentive is lower than the retail price, the user shifts his load requirement to the baseline setting period. On the other hand, if the incentive is greater than the regular energy price, the optimal decision is that the user spends the maximum possible energy in the baseline setting period and reduces the consumption at the PTR time. This consumer behavior produces more energy consumption in total considering all periods. In addition, the user with high uncertainty level in his energy pattern should spend less energy than a predictable consumer when the incentive is lower than the retail price.

Advantages of an Ellipse when Modeling Leisure Utility

This paper characterizes a specification for the utility of leisure that is based on the general equation for an ellipse. We show that this functional form has multiple benefits. The elliptical utility function provides Inada conditions at both the upper-bound and lower-bound constraints on labor supply, which is not the case for the two most common alternative functions. The presence of these two Inada conditions in the elliptical utility of leisure specification speeds up the computation by a factor between three and six times. We further show that the elliptical utility of leisure function is a close approximation to the constant relative risk aversion and constant Frisch elasticity functions in terms of marginal utilities, microeconomic outcomes in a life cycle model, and macroeconomic outcomes in a simple real business cycle model.

Testing for changes in option-implied risk aversion

Purpose – The purpose of this paper is to investigate and test for changes in investor risk aversion and the stochastic discount factor (SDF) using options data on the West Texas Intermediate crude oil futures contract during the 2007-2011 period. Design/methodology/approach – Risk aversion functions and SDFs are estimated using parametric approaches before and after four specific dates of interest. The dates are: the summer 2008 end of the bull market regime; the late 2008 credit freeze trough; the BP Deepwater Horizon explosion; and the Libyan uprising. Findings – Absolute risk aversion functions and SDFs are significantly flatter (less decreasing in wealth) after the end of the bull market and the credit freeze trough. After these two market reversals, oil market participants were less risk-averse for low levels of wealth but more risk-averse for high wealth levels. Oil market investors also increased their valuation of anticipated future wealth in average states of nature relative to very high or very low-asset return states after reversals. The BP explosion and the Libyan uprising led to steeper risk aversion functions (decreasing more rapidly in wealth) and SDF. Oil market investors were more risk-averse for lower future wealth, but less risk-averse for higher future wealth. Oil market investors increased their valuation of anticipated future wealth in extreme states of nature relative to average states of nature after both dates. Originality/value – Documenting statistically and economically significant changes in oil market investors’ attitude toward risk and inter-temporal appetite for risk in relation to changes in financial and political conditions.

Calibration of Quantum Decision Theory, Aversion to Large Losses and Predictability of Probabilistic Choices

We present the first calibration of quantum decision theory (QDT) to an empirical data set. The data comprise 91 choices between two lotteries (two prospects) presented in 91 random pairs made by 142 subjects offered at two separated times. First, we quantitatively account for the fraction of choice reversals between the two repetitions of the decisions, using a probabilistic choice formulation in the simplest possible form with no model assumption and no adjustable parameter. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through a differentiation of the population into two similar sized groups in terms of over-confident and contrarian decision makers. This supports the first fundamental tenet of QDT, which models the choice of an option as an inherent probabilistic process, such that the probability of a choice can be expressed as the sum of its utility and attraction factors. We propose to model (a) the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and (b) the attraction factor with a constant absolute risk aversion (CARA) function. This makes logit-CPT nested in our proposed parameterisation of QDT, allowing for a precise quantitative comparison between the two theories. For this data set, the QDT model is found to perform better at both the aggregate and individual levels, and for all considered fit criteria both for the first iteration of the experiment and for predictions (second iteration). The QDT effect associated with the attraction factor is mostly appreciable for prospects with big losses. Our quantitative analysis of the experiment results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice.