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on Utility Models and Prospect Theory |
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Issue of 2022‒12‒12
fifteen papers chosen by |
| By: | George Samartzis; Nikitas Pittis |
| Abstract: | We derive a closed-form expression capturing the degree of Relative Risk Aversion (RRA) of investors for non-"fair" lotteries. We argue that our formula is superior to earlier methods that have been proposed, as it is a function of only three variables. Namely, the Treasury yields, the returns and the market capitalization of a specific market index. Our formula, is tested on CAC 40, EURO, S&P 500 and STOXX 600, with respect to the market capitalization of each index, for different time periods. We deduce that the investors in these markets exhibit Decreasing Absolute Risk Aversion (DARA) through all the different time periods that we consider, while the degree of RRA has altered between being constant, decreasing or increasing. Furthermore, we propose a simple and intuitive way to measure the degree to which a wrong assumption with respect to the utility function of an investor will affect the structure of his portfolio. Our method is built on a two asset portfolio framework. Namely, a portfolio consisting of one risky and one risk-free asset. Applying our method, the empirical findings indicate that the weight invested in the risky asset varies substantially even among utility functions with similar characteristics. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.03604&r=upt |
| By: | Gaudecker, Hans-Martin von (University of Bonn); Wogrolly, Axel (Private Sector); Zimpelmann, Christian (IZA) |
| Abstract: | This paper analyzes the stability and distribution of ambiguity attitudes using a broad population sample. Using high-powered incentives, we collected six waves of data on ambiguity attitudes about financial markets – our main application – and climate change. Estimating a structural stochastic choice model, we obtain three individual-level parameters: Ambiguity aversion, likelihood insensitivity, and the magnitude of decision errors. These parameters are very heterogeneous in the population. At the same time, they are stable over time and largely stable across domains. We summarize heterogeneity in these three dimensions using a discrete classification approach with four types. Each group makes up 20-30% of the sample. One group comes close to the behavior of expected utility maximizers. Two types are characterized by high likelihood insensitivity; one of them is ambiguity averse and the other ambiguity seeking. Members of the final group have large error parameters; robust conclusions about their ambiguity attitudes are difficult. Observed characteristics vary between groups in plausible ways. Ambiguity types predict risky asset holdings in the expected fashion, even after controlling for many covariates. |
| Keywords: | ambiguity attitudes, temporal stability, domain specificity, socio-demographic factors, cluster analysis, household portfolio choice |
| JEL: | D81 G41 C38 D14 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15712&r=upt |
| By: | Ferraz, Eduardo; Mantilla, Cesar |
| Abstract: | We use a three-period model adopting a recursive definition of consumption to explore the optimal delegation that a present self, aware that her near-future self is present-biased but better informed, will make to protect her far-future self against income shocks. The model captures the present self's trade-off between using commitment mechanisms, restricting the near-future self's agency through illiquid savings, and profiting from the near-future self's better information about future shocks. Our main result states that agents with higher risk aversion can cover better against utility losses from time-inconsistent consumption through the commitment mechanism. Given the evidence of women being more risk-averse than men, this result provides the micro-foundation for the gender gap in adopting financial commitment devices, especially among single individuals. |
| Date: | 2022–09–10 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:xbsn8&r=upt |
| By: | Fabian R. Pieroth; Martin Bichler |
| Abstract: | Game theory largely rests on the availability of cardinal utility functions. In contrast, only ordinal preferences are elicited in fields such as matching under preferences. The literature focuses on mechanisms with simple dominant strategies. However, many real-world applications do not have dominant strategies, so intensities between preferences matter when participants determine their strategies. Even though precise information about cardinal utilities is unavailable, some data about the likelihood of utility functions is typically accessible. We propose to use Bayesian games to formalize uncertainty about decision-makers utilities by viewing them as a collection of normal-form games where uncertainty about types persist in all game stages. Instead of searching for the Bayes-Nash equilibrium, we consider the question of how uncertainty in utilities is reflected in uncertainty of strategic play. We introduce $\alpha$-Rank-collections as a solution concept that extends $\alpha$-Rank, a new solution concept for normal-form games, to Bayesian games. This allows us to analyze the strategic play in, for example, (non-strategyproof) matching markets, for which we do not have appropriate solution concepts so far. $\alpha$-Rank-collections characterize a range of strategy-profiles emerging from replicator dynamics of the game rather than equilibrium point. We prove that $\alpha$-Rank-collections are invariant to positive affine transformations, and that they are efficient to approximate. An instance of the Boston mechanism is used to illustrate the new solution concept. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.10317&r=upt |
| By: | Jacob K Goeree |
| Abstract: | I introduce a concave function of allocations and prices -- the economy's potential -- which measures the difference between utilitarian social welfare and its dual. I show that Walrasian equilibria correspond to roots of the potential: allocations maximize weighted utility and prices minimize weighted indirect utility. Walrasian prices are "utility clearing" in the sense that the utilities consumers expect at Walrasian prices are just feasible. I discuss the implications of this simple duality for equilibrium existence, the welfare theorems, and the interpretation of Walrasian prices. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.14437&r=upt |
| By: | James Alm (Tulane University); Matthias Kasper (University of Vienna) |
| Abstract: | ‘Behavioural economics’, or the application of methods and evidence from other social sciences to economics, has increased greatly in significance and use in the last two decades. In this paper we discuss the basic elements of behavioural economics. We then assess the applications of behavioural economics to the analysis of tax compliance. Our central conclusion is that many, perhaps most, of the recent insights on what motivates tax compliance have flowed directly from behavioural economics. We conclude with suggestions on – and predictions of – directions in which future applications should prove useful. |
| Keywords: | Behavioural economics; tax compliance; expected utility theory; non-expected utility theory; social interactions theory |
| JEL: | C9 H26 H83 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:tul:wpaper:2207&r=upt |
| By: | Drobner, Christoph (Technical University of Munich); Goerg, Sebastian J. (Technische Universität München) |
| Abstract: | We study belief updating about relative performance in an ego-relevant task. Manipulating the perceived ego-relevance of the task, we show that subjects update their beliefs optimistically because they derive direct utility flows from holding positive beliefs. This finding provides a behavioral explanation why and how overconfidence can evolve in the presence of objective information. Moreover, we document that subjects, who received more bad signals, downplay the ego-relevance of the task. Taken together, these findings suggest that subjects use two alternative strategies to protect their ego when presented with objective information. |
| Keywords: | motivated beliefs, optimistic belief updating, overconfidence, direct belief utility, Bayes' rule, ex-post rationalization |
| JEL: | C91 D83 D84 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15682&r=upt |
| By: | Jing Peng; Pengyu Wei; Zuo Quan Xu |
| Abstract: | This paper studies a continuous-time optimal portfolio selection problem in the complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor concerns about the terminal relative growth rate (log-return) instead of absolute capital value. This model can be regarded as an extension of the classical growth optimal problem to the behavioral framework. It leads to a new type of M-shaped utility maximization problem under nonlinear Choquet expectation. Due to the presence of probability distortion, the classical stochastic control methods are not applicable. By the martingale method, concavification and quantile optimization techniques, we derive the closed-form optimal growth rate. We find that the benchmark growth rate has a significant impact on investment behaviors. Compared to Zhang et al where the same preference measure is applied to the terminal relative wealth, we find a new phenomenon when the investor's risk tolerance level is high and the market states are bad. In addition, our optimal wealth in every scenario is less sensitive to the pricing kernel and thus more stable than theirs. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.05402&r=upt |
| By: | Banghua Zhu; Stephen Bates; Zhuoran Yang; Yixin Wang; Jiantao Jiao; Michael I. Jordan |
| Abstract: | We study the hidden-action principal-agent problem in an online setting. In each round, the principal posts a contract that specifies the payment to the agent based on each outcome. The agent then makes a strategic choice of action that maximizes her own utility, but the action is not directly observable by the principal. The principal observes the outcome and receives utility from the agent's choice of action. Based on past observations, the principal dynamically adjusts the contracts with the goal of maximizing her utility. We introduce an online learning algorithm and provide an upper bound on its Stackelberg regret. We show that when the contract space is $[0,1]^m$, the Stackelberg regret is upper bounded by $\widetilde O(\sqrt{m} \cdot T^{1-C/m})$, and lower bounded by $\Omega(T^{1-1/(m+2)})$. This result shows that exponential-in-$m$ samples are both sufficient and necessary to learn a near-optimal contract, resolving an open problem on the hardness of online contract design. When contracts are restricted to some subset $\mathcal{F} \subset [0,1]^m$, we define an intrinsic dimension of $\mathcal{F}$ that depends on the covering number of the spherical code in the space and bound the regret in terms of this intrinsic dimension. When $\mathcal{F}$ is the family of linear contracts, the Stackelberg regret grows exactly as $\Theta(T^{2/3})$. The contract design problem is challenging because the utility function is discontinuous. Bounding the discretization error in this setting has been an open problem. In this paper, we identify a limited set of directions in which the utility function is continuous, allowing us to design a new discretization method and bound its error. This approach enables the first upper bound with no restrictions on the contract and action space. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.05732&r=upt |
| By: | Barile, Lory (Department of Economics, University of Warwick); Cullis, John (Department of Economics, University of Bath); Philip Jones (Department of Economics, University of Bath) |
| Abstract: | This paper begins by listing three uncomfortable implications of the standard expected utility model of individual decision-making concerning participation in fiscal crimes : that tax evasion and benefit fraud can be treated identically; fiscal crimes should be endemic; and that all individuals, depending on parameter values, should be either honest or dishonest. Levitt and List’s (2007) utility function relating to decisions with a moral dimension is adapted to offer insight into these implications involving an individuals optimal honesty and moral hinterland. Predictions are developed that include moral costs as a determinant of dishonest intentions and are tested with reference to some 2,942 questionnaire responses to a 2016 national (UK) survey. This paper offers insight into the way moral costs inform perceptions of the intrinsic value of doing the right thing thereby providing a richer analysis of fiscal crimes. The account has particular relevance for policy prescriptions that involve aspects of shame. |
| Keywords: | benefit fraud ; tax evasion ; optimal honesty ; moral costs JEL Codes: D01 ; H2 ; K42 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1435&r=upt |
| By: | Semyon Malamud (Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute); Neng Wang (Columbia University - Columbia Business School, Finance; National Bureau of Economic Research (NBER); Asian Bureau of Finance and Economic Research (ABFER)); Yuan Zhang (Shanghai University of Finance and Economics) |
| Abstract: | “Buy Now, Pay Later” (BNPL) and other forms of consumer credit create a wedge between consumption and payments. We introduce this wedge into a standard consumption-based asset pricing model (CCAPM). In equilibrium, the pricing kernel equals the marginal utility of consumption divided by the return on the annuity with BNPL duration. When this duration is stochastic and co-moves with market risk, the BNPLCCAPM pricing kernel can jointly price size- and book-to-market-sorted stock portfolios and maturity-sorted bond portfolios. |
| Keywords: | asset pricing, yield curve, buy-now-pay-later, consumer credit, financial frictions, credit frictions |
| JEL: | D11 D50 D51 D53 E21 E51 G12 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2285&r=upt |
| By: | Tal Alon; Paul D\"utting; Yingkai Li; Inbal Talgam-Cohen |
| Abstract: | We study a generalization of both the classic single-dimensional mechanism design problem, and the hidden-action principal-agent problem of contract theory. In this setting, the principal seeks to incentivize an agent with a private Bayesian type to take a costly action. The goal is to design an incentive compatible menu of contracts which maximizes the expected revenue. Our main result concerns linear contracts, the most commonly-used contract form in practice. We establish that in Bayesian settings, under natural small-tail conditions, linear contracts provide an $O(1)$-approximation to the optimal, possibly randomized menu of contracts. This constant approximation result can also be established via a smoothed-analysis style argument. We thus obtain a strong worst-case approximation justification of linear contracts. These positive findings stand out against two sets of results, which highlight the challenges of obtaining (near-)optimal contracts with private types. First, we show that the combination of private type and hidden action makes the incentive compatibility constraints less tractable: the agent's utility has to be convex (as without hidden action), but it also has to satisfy additional curvature constraints. Second, we show that the optimal menu of contracts can be complex and/or exhibit undesirable properties - such as non-monotonicity of the revenue in the type distribution. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.06850&r=upt |
| By: | Daniel E. Rigobon; Ronnie Sircar |
| Abstract: | We formulate a model of the banking system in which banks control both their supply of liquidity, through cash holdings, and their exposures to risky interbank loans. The value of interbank loans jumps when banks suffer liquidity shortages, which can be caused by the arrival of large enough liquidity shocks. In two distinct settings, we compute the unique optimal allocations of capital. In the first, banks seek only to maximize their own utility -- in a decentralized manner. Second, a central planner aims to maximize the sum of all banks' utilities. Both of the resulting financial networks exhibit a `core-periphery' structure. However, the optimal allocations differ -- decentralized banks are more susceptible to liquidity shortages, while the planner ensures that banks with more debt hold greater liquidity. We characterize the behavior of the planner's optimal allocation as the size of the system grows. Surprisingly, the `price of anarchy' is of constant order. Finally, we derive capitalization requirements that cause the decentralized system to achieve the planner's level of risk. In doing so, we find that systemically important banks must face the greatest losses when they suffer liquidity crises -- ensuring that they are incentivized to avoid such crises. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.12404&r=upt |
| By: | Michał Krawczyk (University of Warsaw, Faculty of Economic Sciences); Joanna Rachubik (University of Warsaw, Faculty of Economic Sciences,) |
| Abstract: | The representativeness heuristic (RH) proposes that people expect even a small sample to have similar characteristics to its parent population. One domain in which it appears to operate is the preference for combinations of numbers on lottery tickets: most players seem to avoid very characteristic, “unrepresentative” combinations, e.g., only containing very low numbers. Likewise, many players may avoid betting on a recently drawn combination because it would seem particularly improbable to be drawn again. We confirm both of these tendencies in a lab experiment and corroborate their external validity in two field experiments. However, we only find a weak link between these two choices: the same people do not necessarily exhibit the two biases. In this sense, there is little consistent manifestation of the RH across different tasks at the individual level. Nevertheless, there are some links related to rationality across the two choices – people who are willing to forgo a monetary payment to get the preferred ticket in one task are also willing to do it in the other. We find such preferences to be related to the misperception of probabilities and providing intuitive, incorrect answers in the Cognitive Reflection Test. |
| Keywords: | Decision making under risk, Lottery choice, Perception of randomness, Number preferences in lotteries, Representativeness heuristic |
| JEL: | C93 D01 D81 D91 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2021-24&r=upt |
| By: | Constantin Charles; Cary D. Frydman; Mete Kilic |
| Abstract: | We show theoretically that the weak transmission of beliefs to actions induces a strong bias in basic asset pricing tests. In particular, expected returns can appear to decline in risk when investors weakly transmit their payoff expectations into willingness to pay. We experimentally test this prediction and find that subjects exhibit an extremely weak transmission of beliefs to actions, which generates a negative risk-return relation. We argue that the weak transmission is due to cognitive noise and demonstrate that cognitive noise causally affects the risk-return relation. Our results highlight the importance of incorporating weak transmission into belief-based asset pricing models. |
| Keywords: | investor behavior, cognitive noise, portfolio choice |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10067&r=upt |