Regret theory and the banking firm: The optimal bank interest margin

This paper examines the optimal bank interest margin, i.e., the spread between the loan rate and the deposit rate of a bank, when the bank is not only risk-averse but also regret-averse. Regret-averse preferences are characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that the presence of regret aversion raises or lowers the optimal bank interest margin than the one chosen by the purely risk-averse bank, depending on whether the probability of default is below or above a threshold value, respectively. Regret aversion as such makes the bank less prudent and more prone to risk-taking when the probability of default is high, thereby adversely affecting the stability of the banking system.     

Production and insurance under regret aversion

This paper examines the behavior of a regret-averse producer facing revenue risk. To insure against the revenue risk, the producer can purchase a coinsurance contract with an endogenously chosen coinsurance rate. Regret-averse preferences are characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that the regret-averse producer never fully insures against the revenue risk even though the coinsurance contract is actuarially fair. When the producer is sufficiently regret averse and the loss probability is high, we further show that the regret-averse producer chooses not to purchase the actuarially fair coinsurance contract. Even when purchasing the actuarially fair coinsurance contract is optimal, we derive sufficient conditions under which the regret-averse producer reduces the optimal output level as compared to that without the coinsurance contract. These results are distinct from those under pure risk aversion, thereby making the consideration of regret aversion crucial.     

Production and hedging decisions under regret aversion

In this paper, we investigate regret-averse firms' production and hedging behaviors. We first show that the separation theorem is still alive under regret aversion by proving that regret aversion is independent of the level of optimal production. On the other hand, we find that the full-hedging theorem does not always hold under regret aversion as the regret-averse firms take hedged positions different from those of risk-averse firms in some situations. With more regret aversion, regret-averse firms will hold smaller optimal hedging positions in an unbiased futures market. Furthermore, contrary to the conventional expectations, we show that banning firms from forward trading affects their production level in both directions.     

Fixed versus variable rate loans under regret aversion

This paper examines the optimal mix of fixed and variable rate loans of a competitive bank facing funding cost uncertainty, where the bank is not only risk averse but also regret averse. Regret aversion is characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that a negative spread between fixed and variable rate loans is a necessary but not sufficient condition for the dominance of variable rate loans over fixed rate loans. If the bank optimally extends both fixed and variable rate loans, the total amount of loans depends neither on the bank's regret aversion nor on the funding cost uncertainty. The bank, however, optimally lends less should it be forced to assume the entire funding cost uncertainty by exclusively extending fixed rate loans. Finally, using a two-state example, we show that the bank optimally extends more (less) fixed rate loans than in the case of pure risk aversion if the high (low) marginal cost of funds is more likely to prevail. Regret aversion as such plays a crucial role in determining the bank's optimal choice between fixed and variable rate loans.     

Optimal bank interest margins under capital regulation in a call-option utility framework

This paper examines the optimal bank interest margin under capital regulation when the bank's preference admits an additive call-option representation including both the like of higher equity return and the dislike of higher equity risk. In the call-option utility maximization, an increase in the capital requirement results in an increased amount of loans held by a bank at a reduced margin when loan quality is in distress. We also show that the impact on the bank interest margin from an increase in the capital requirement which ignores the dislike, that we call such behavior call-option equity maximization, leads to significant underestimation. Our results cast doubt on the effectiveness of capital regulation to exert a risk-reducing and return-increasing effect on the bank in particular where loan quality becomes worse, thereby adversely affecting the stability of the banking system.     

The relevance of supply shocks for inflation: the spanish case

A retrenchment in crossborder credit is under way, the product of both market forces and political pressure on international banks to lend at home (Economist, 2009). In addition, banks, particularly the largest, have also dramatically expanded their retail banking operations over the past few years (Hirtle and Stiroh, 2007). Our goal, in this article, is to study the effects of default risk on equity returns through bank interest margin management under a renewed focus on domestic retail banking, a trend often attributed to the stability of banking activities. Specifically, this article explores the determinants of optimal bank interest margins based on an option-based firm-theoretical model with multiple sources of structural breaks due to political pressure. The model demonstrates how capital regulation and political pressure on foreign lending return and risk conditions jointly determine the optimal bank interest margin decision. We show that a more stringent capital requirement is linked with lower equity return, but higher default risk of the bank in the return to domestic retail banking. An increased focus on the political pressure on foreign lending return is linked with higher equity return and default risk of the bank. It is also showed that an increased focus on the political pressure on foreign lending risk decreases the bank's equity return and default risk. We conclude that the return to domestic retail banking may be a relatively stable activity when the political pressure decision impacts only the expected risk of the bank's foreign lending and not the return.     

Intertemporal elasticity of substitution and risk aversion: are they related empirically?

This article examines the relationship between two types of preference: preference of intertemporal choices and preference towards risk. In the simplest form of the constant relative risk aversion utility function, the intertemporal elasticity of substitution (IES) and risk aversion have an inverse relationship. However, there is no empirical evidence that suggests this inverse relationship holds. We examine the relationship between risk aversion and IES using household consumption data from the Consumer Expenditure Survey during 1996–2010. Multiple risk domains are selected to represent risk preference, and for each domain, we consider some households to be more risk averse than others. We separately estimate IES for the more risk-averse and less risk-averse households. We find that the IES estimates are generally smaller for the more risk-averse households than for the less risk-averse households and that the difference is statistically significant in the majority of the financial domains. This finding supports the inverse relationship between the two parameters, although considerable heterogeneity is found across domains.     

Regret theory and the competitive firm

This paper examines the production decision of the competitive firm under uncertainty when the firm is not only risk averse but also regret averse. Regret-averse preferences are characterized by a modified utility function that includes disutility from having chosen ex-post suboptimal alternatives. The extent of regret depends on the difference between the actual profit and the maximum profit attained by making the optimal production decision had the firm observed the true realization of the random output price. If the firm is not too regret averse, we show that the conventional result that the optimal output level under uncertainty is less than that under certainty holds. Using a simple binary model wherein the random output price can take on either a low value or a high value with positive probability, we show the possibility that the firm may optimally produce more, not less, under uncertainty than under certainty, particularly when the firm is sufficiently regret averse and the low output price is very likely to prevail.     

The Impact of Regret on Exports

We examine optimal production and export decisions of a firm facing exchange rate uncertainty, where the firm's management is not only risk averse but also regret averse, i.e., is characterized by a utility function that includes disutility from having chosen ex post suboptimal alternatives. Experimental and empirical results support the view that managers tend to be regret averse. Under regret aversion a negative risk premium need not preclude the firm from exporting which would be the case if the firm were only risk averse. Exporting creates an implicit hedge against the possibility of regret when the realized spot exchange rate turns out to be high. The regret‐averse firm as such has a greater ex ante incentive to export than the purely risk averse firm. Finally, we use a two‐state example to illustrate that the firm optimally exports more (less) to the foreign country than in the case of pure risk aversion if the low (high) spot exchange rate is more likely to prevail. Regret aversion as such plays a crucial role in determining the firm's optimal allocation between domestic sales and foreign exports.     

Status,Risk-Taking and Intertemporal Substitution in an Endogenous Growth Model

This paper examines intertemporal risk-taking in a stochastically growing economy with externalities in human capital accumulation where agents have preferences for social status. In order to isolate the effects of status concerns on long-run expected growth, the analysis is embedded in a non-expected utility setting, which disentangles the effects from risk aversion and intertemporal substitution. We examine the interaction between status desire and risk, risk aversion and intertemporal substitution. The externalities generated by the status game are able to correct the allocative distortions from the knowledge spillovers.Acknowledgement The author would like to thank an anonymous referee for his valuable comments.     

How does equity capital cost affect bank performance during a financial crisis?

This article theoretically examines how equity capital cost affects return performance and safety of a bank and how this effect varies across a financial crisis comparing to a normal time when the bank manager’s performance reveals the like of higher equity return and the dislike of higher equity risk. We derive two main results. First, an increase in the bank’s equity capital cost from an increase of the interest rate of the Federal funds results in a reduced loan risk-taking at an increased optimal bank interest margin, implying better bank performance. Second, by ignoring the dislike, we find that the better performance is reinforced during a financial crisis but is reduced during a normal time. Financial crises and the dislike preference as such contribute a relatively low return and the stability of banking activities.     

Anticipated regret as an explanation of uncertainty aversion

The paper provides a psychological explanation of uncertainty aversion based on the fear of regret. We capture an agent’s regret using a reference-dependent utility function in which the agent’s utility depends on the performance of his chosen option relative to the performance of the option that would have been best ex post. An uncertain option is represented as a compound lottery. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries.     

ROBUST MONETARY POLICY UNDER UNCERTAINTY ABOUT CENTRAL BANK PREFERENCES

In this paper, we study the impact of central bank opacity on macroeconomic performances in a new Keynesian framework with model uncertainty using robust control techniques. We identify a new source of central bank opacity, which refers to the lack of information about the central bank's preference for robustness in the sense of Hansen and Sargent . We find closed‐form solutions for the robust control problem, analysing the impact of the lack of transparency about the central bank's preferences for robustness. We show that an increased transparency about the central bank's preference for robustness makes monetary policy respond less aggressively to cost‐push shocks, thus reducing the inflation and output gap variability. As a consequence, inflation and output gap are less volatile than under central bank opacity about its preference for robustness.     

Fixed versus variable rate loans under state-dependent preferences

This paper examines the optimal mix of fixed and variable rate loans of a competitive bank facing uncertain funding costs. The bank's preferences are state-dependent in that the utility function depends on a state variable. We show that the optimal amount of loans extended by the bank depends neither on the state-dependent preferences of the bank, nor on the joint distribution of the marginal cost of funds and the state variable. The bank, however, optimally lends less should it be forced to assume all interest rate risk by exclusively extending fixed rate loans. We show further that a non-positive spread between fixed and variable rate loans is no longer a necessary and sufficient condition for the bank to refrain from extending fixed rate loans should the marginal cost of funds be correlated with the state variable in the sense of expectation dependence. State-dependent preferences as such play a pivotal role in determining the bank's optimal choice between fixed and variable rate loans.     

Greater downside risk aversion in the large

In this paper, we advance a definition of greater downside risk aversion that applies to both large and small changes in risk preference, and thereby complements the results for small changes reported previously. We show that a downside risk-averse transformation of a utility function results in a function that is more downside risk averse in the same manner that a risk-averse transformation increases risk aversion. Our demonstration is conducted first by using the compensated approach introduced by Diamond and Stiglitz [P. Diamond, J. Stiglitz, Increases in risk and in risk aversion, J. Econ. Theory 8 (1974) 337-360] and then by using an adaptation of the risk premium approach taken by Pratt [J. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964) 122-136].     

Time Horizon and the Discount Rate

We consider an economy à la Lucas (1978, Econometrica46 , 1429-1446) with a risk-averse representative agent. The exogenous growth rate of the economy follows a random walk. We characterize the set of utility functions for which it is efficient to discount more distant cash flows at a lower rate. The benchmark result is that, when the growth rate is almost surely nonnegative, the yield curve is decreasing if and only if relative risk aversion is decreasing with wealth. Relaxing the assumption on the absence of recession requires more restrictions on preferences, such as increasing relative prudence. Journal of Economic Literature Classification Numbers: D81, D91, Q25, Q28.     

Background risk in generalized expected utility theory

Summary. In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion. Received: August 10, 2001; revised version: June 18, 2002 RID="*" ID="*"I thank Simon Grant and an anonymous referee for helpful comments and criticism. This research was supported by an Australian Research Council Senior Fellowship and Australian Research Council Large Grant A79800678.     

SIMULTANEOUS MEASUREMENT OF TIME AND RISK PREFERENCES: STATED PREFERENCE DISCRETE CHOICE MODELING ANALYSIS DEPENDING ON SMOKING BEHAVIOR*

Measuring time and risk preferences and relating them to economic behaviors are important topics in behavioral economics. We developed a new method to simultaneously measure the rate of time preference and the coefficient of risk aversion. Analyzing the individual‐level relationships between preference parameters and cigarette smoking, we conclude that current smokers are more impatient and risk‐prone than nonsmokers. Heavy smokers are the most impatient and risk‐prone, whereas ex‐smokers are the most patient and risk‐averse. Among nonsmokers, neither age‐related nor gender‐related differences were found. On the other hand, risk and time preferences are significantly different according to age and gender for smokers.     

Invariant risk attitudes

Concepts of constant absolute risk aversion and constant relative risk aversion have proved useful in the analysis of choice under uncertainty, but are quite restrictive, particularly when they are imposed jointly. A generalization of constant risk aversion, referred to as invariant risk aversion is developed. Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant index of riskiness. The best-known index with such properties is the standard deviation. The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences.     

Loss aversion and social security: a general equilibrium approach

Introducing an intertemporal model of loss aversion, I study the role of social security in determining intergenerational redistribution when consumers have reference-dependent preferences with loss aversion. Using a unified social security model in which different social security plans are specified via different degrees of fundedness, I examine the effect of the transition from a less funded system to a more funded one on savings, consumption, and capital accumulation for an OLG production economy. A general equilibrium analysis shows that the direction of intertemporal equilibrium is dependent on how the total savings responds to the interest rate change, but the effect of the payroll tax on capital accumulation is ambiguous. By deriving closed-form solutions, I find that an increase in fundedness intensity unambiguously increases capital accumulation in steady states, while the tax effects on consumption and savings are not conclusive. Moreover, simulation exercises show that when consumers are prone to over-consume because they care more about the contemporaneous gain utility, the fully funded system may help the individuals smooth out their lifecycle consumption.