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.     

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.     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

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.     

On the theory of the competitive firm with a utility function defined on profits and regret

In this paper we analyze the optimal output determined by a competitive firm facing uncertain demand. We analyze the effect of introducing uncertainty and the effect of increasing uncertainty on the optimal output, under the assumption that the utility function of the firm depends both on profits and on regret. We show that if the firm is more risk averse to profits than to regret (in a sense described below), both effects tend to decrease the optimal output. Similar effects of introducing uncertainty and of increased uncertainty were previously shown by Sandmo (1971) to exist in the case where utility is defined on profits only. Thus, this paper provides conditions under which the above results hold true, even when utility is defined on regret and on profits.     

Risk and regret aversions on optimal bank interest margin under capital regulation

This paper examines the bank's optimal loan rate (and thus the bank's interest margin) under more stringent capital regulation when the bank is not only risk-averse but also regret-averse. Risk-averse preferences are characterized by an option-based utility function that includes disutility from the dislike of bank equity risk. Regret-averse preferences feature an option-based utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that an increase in bank capital requirement results in an increased margin under risk aversion dominating regret aversion, whereas it results in a reduced margin under regret aversion dominating risk aversion. The former holds when risk aversion domination stems from increasing risk-averse preference, but not from decreasing regret-averse preference, while the latter holds when regret aversion domination results from either decreasing risk-averse or increasing regret-averse preference. Risk aversion, as such, makes the bank more prudent and less prone to risk-taking, while regret aversion, as such, makes the bank less prudent and more prone to risk-taking.     

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.     

The cyclicality of bank regulation in a general economic framework

This article utilizes a representative agent model to address how the regulation policies for banks should respond to the general economic condition. With the consideration of a self-fulfilling deposit insurance facility with sufficient bank reserve to meet the expected need of liquidity shock, our model suggests a counter-cyclical capital adequacy requirement in a competitive loan market. The exception might occur when the moral hazard problem becomes very unwieldy and the representative individual is rather risk averse. With regard to the closure policy, we find that it is closely related to the individual’s degree of risk aversion. A counter-cyclical closure policy is recommended when the individual is highly risk averse. Otherwise, a pro-cyclical closure policy is preferred.     

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.     

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.     

Optimal sequential contract with a risk‐averse supplier

We study optimal contracts in environments where a risk‐averse supplier discovers cost information privately and gradually over time: the supplier is privately informed about its cost uncertainty at the time of contracting and discovers the realization of cost condition privately after contracting and before production. We show that both the buyer and the supplier prefer more cost uncertainty when the supplier is not very risk‐averse but less cost uncertainty when the supplier is sufficiently risk‐averse. However, the buyer always prefers to contract before the cost uncertainty resolves regardless of the supplier's degree of risk aversion. The nature of the optimal contract also depends on the supplier's risk preference. A separating contract is optimal when the supplier is not very risk‐averse; however, a pooling contract, which offers the same contract terms regardless of the cost uncertainty, can be optimal when the supplier becomes sufficiently risk‐averse. Moreover, the optimal production schedule is often characterized by “inflexible rules.”     

PRICE CONSTRAINTS,FORWARD MARKETS AND THE COMPETITIVE FIRM UNDER PRICE UNCERTAINTY*

This article proposes a model of the competitive firm simultaneously facing price constraints and forward markets under price uncertainty. The incorporation of a forward market is shown to be very important because a risk-averse firm will set its production decision to the forward price regardless of its attitude toward risk. In addition, we show that risk aversion is a sufficient condition for a decrease in risk to reduce the amount hedged when risk is reduced through a mean-preserving price squeeze.     

Multiple variable factors,demand uncertainty,and the cooperative firm

It has been shown that the risk averse, cooperative firm producing its output with labor as the only variable input and selling this output in a competitive market will produce more than the cooperative firm operating under condition of certainty. This letter proves that this result may not apply to the case of the cooperative firm facing a stochastic demand and/or employing more than one variable input.     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Regret aversion and opportunity dependence

This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage's minimax regret, and a smooth model of regret aversion.     

INEQUALITY AVERSION CAUSES EQUAL OR UNEQUAL DIVISION IN ALTERNATING‐OFFER BARGAINING

A solution to Rubinstein (1982)'s open‐ended, alternating‐offer bargaining problem for two equally patient bargainers who exhibit similar degrees of inequality aversion is presented. Inequality‐averse bargainers may experience envy if they are worse off, and guilt if they are better off, but they still reach agreement in the first period under complete information. If the guilt felt is strong, then the inequality‐averse bargainers split a pie of size one equally regardless of their degree of envy. If the guilt experienced is weak, then the agreed split is tilted away from the Rubinstein division towards a more unequal split whenever the degree of envy is smaller than the discounted degree of guilt. Envy and weak guilt have opposite effects on the equilibrium division of the pie, and envy has a greater marginal impact than weak guilt. Equally inequality‐averse bargainers agree on the Rubinstein division if the degree of envy equals the discounted degree of guilt. As both bargainers' sensation of inequality aversion diminishes, the bargaining outcome converges to the Rubinstein division.     

BACKGROUND RISK AND THE THEORY OF THE COMPETITIVE FIRM UNDER UNCERTAINTY*

This paper examines the optimal production decision of a firm under output price risk á la Sandmo when the firm also faces a dependent background risk. It is shown that standard risk aversion plus a non-negative association between the output price risk and the background risk are sufficient to ensure a reduction in the firms optimal output upon introduction of the background risk. The paper investigates the impact of a deterministic transformation of the background risk on the firms optimal production decision. It is shown that decreasing absolute risk aversion in Ross' sense is among the sufficient conditions that generate an unambiguous negative comparative static result.     

Conjectural variations,risk aversion and price-cost margins

Summary We have shown that introduction of random conjectural variations and risk aversion into an oligopoly model leads to results in line with those derived earlier for competitive and monopolistic firms. In particular, a risk-averse firm has smaller output and higher expected price-cost margin than a risk-neutral firm. For a specific form of conjectural variations we have shown that under risk aversion the firm-level expected price-cost margins depend on the market structure, measured in terms of the Herfindahl index of the rest of the firms in the industry, as well as on the expected degree of correlation between the competitors' reactions.     

Operational and financial hedging for exporting firms

This paper examines the interaction between operational and financial hedging in the context of an internationally competitive but domestically monopolistic firm under exchange rate uncertainty. Operational hedging is modeled by letting the firm make its export decision after it has observed the true realization of the then prevailing spot exchange rate. Financial hedging, on the other hand, is modeled by allowing the firm to trade fairly priced exotic derivatives that are tailor-made for the firm's hedging need. We show that both operational and financial hedging unambiguously entice the firm into producing more. We further derive sufficient conditions under which operational hedging dominates (is dominated by) financial hedging in terms of promoting the firm's optimal output.     

On the theory of the competitive labor-managed firm under price uncertainty

The short-run behavior of a labor-managed firm under competitive assumptions and price uncertainty is analyzed assuming risk aversion. It is compared with its behavior under certainty and the behavior of a capitalist-managed firm under price uncertainty. It is shown that a risk-averse labor-managed firm employs more labor than a risk-neutral labor-managed firm. Generally, uncertainty is seen to have greater impact on the behavior of a labor-managed firm than on the behavior of a capitalist-managed firm. Except under constant risk aversion, the behavior of a labor-managed firm under price uncertainty is less predictable than that of a capitalist-managed firm.