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A large strand of research has identified when (i) a single risk is undesirable and (ii) two independent risks aggravate each other. We extend this line of inquiry by establishing when (iii) mutual aggravation is greater for greater risks. This natural property of greater mutual aggravation explains recent experimental findings on higher-order risk preferences, and can guide managerial behavior when risks in the decision environment become more severe. History: Accepted by Han Bleichrodt, decision analysis. Funding: S. Ebert gratefully acknowledges financial support from the Dutch Research Foundation (NWO) [VENI Grant 451-14-007]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2017.2746. Keywords: mixed risk aversion * mutual aggravation * risk apportionment * stochastic dominance * utility premium * prudence, 1. Introduction This note elaborates on Kimball's (1993) seminal notion of 'mutual aggravation of risks,' which refers to situations in which the presence of one risk increases sensitivity to the [...]

Disruptive events that halt production can have severe business consequences if not appropriately managed. Business interruption (BI) insurance offers firms a financial mechanism for managing their exposure to disruption risk. Firms can also avail of operational measures to manage the risk. In this paper, we explore the relationship between BI insurance and operational measures. We model a manufacturing firm that can purchase BI insurance, invest in inventory, and avail of emergency sourcing. Allowing the insurance premium to depend on the firm's insurance and operational decisions, we characterize the optimal insurance deductible and coverage limit as well as the optimal inventory level. We prove that insurance and operational measures are not always substitutes, and we establish conditions under which they can be complements; that is, insurance can increase the marginal value of inventory and can increase the overall value of emergency sourcing. We also find that the value of insurance is higher for those firms less able to absorb financially significant disruptions. As disruptions become longer but rarer, the value of emergency sourcing increases, and the value of inventory and the value of insurance increase before eventually decreasing. Key words: disruptions; inventory; insurance History: Received December 1, 2010; accepted January 11, 2012, by Martin Lariviere, operations management. Published online in Articles in Advance June 5, 2012., 1. Introduction The purpose of business interruption (BI) insurance is to protect against losses incurred when a firm cannot operate normally because of a disruption to one of its facilities. [...]

This paper investigates how firms manage risk by examining the relationship between financial and operational hedging using a sample of bank holding companies. Risk management theory holds that capital market imperfections make cash flow volatility costly. I investigate whether financial firms consider this cost or focus exclusively on managing tradable exposures. After documenting that acquisitions provide operational hedging by reducing potentially costly volatility, I find that postacquisition financial hedging declines even after controlling for the specific underlying risks. In addition, the decrease in financial hedging is related to the acquisition's level of operational hedging. Larger increases in operational hedging are followed by larger declines in financial hedging. These results indicate that firms in this sample manage aggregate risk, not just tradable exposures, and that operational hedging can substitute for financial hedging. Key words: finance; corporater finance; financial institutions; banks; risk management History: Received July 31, 2007; accepted July 7, 2009, by John Birge, focused issue editor. Published online in Articles in Advance September 28, 2009., 1. Introduction This study is motivated by the widespread challenge of risk management--a challenge highlighted for both financial and nonfinancial firms during the 2008 credit crisis. Both theoretical and empirical [...]

Dynamic, intensity-based point process models are widely used to measure and price the correlated default risk in portfolios of credit-sensitive assets such as loans and corporate bonds. Monte Carlo simulation is an important tool for performing computations in these models. This paper develops, analyzes, and evaluates two simulation algorithms for intensity-based point process models. The algorithms extend the conventional thinning scheme to the case where the event intensity is unbounded, a feature common to many standard model formulations. Numerical results illustrate the performance of the algorithms for a familiar top-down model and a novel bottom-up model of correlated default risk. Key words: simulation; probability; stochastic model applications; financial institutions; banks History: Received September 14, 2010; accepted June 2, 2011, by Assaf Zeevi, stochastic models and simulation. Published online in Articles in Advance September 20, 2011., 1. Introduction Correlated default risk plays an important role in financial markets. Intensity-based point process models are widely used to measure and value correlated default risk. At the center of [...]

This paper introduces a parameter-free method for measuring the weighting functions of prospect theory and rank-dependent utility. These weighting functions capture risk attitudes, subjective beliefs, and ambiguity attitudes. Our method, called the midweight method, is based on a convenient way to obtain midpoints in the weighting function scale. It can be used both for risk (known probabilities) and for uncertainty (unknown probabilities). The resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity, i.e., the difference between uncertainty and risk. Compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity, our method is more efficient and can accommodate violations of expected utility under risk. An experiment demonstrates the tractability of our method, yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods, as predicted by Ellsberg. Key words: prospect theory; ambiguity; probability weighting; pessimism History: Received March 11, 2009; accepted September 14, 2010, by George Wu, decision analysis., 1. Introduction Decision under risk relates to cases where known statistical probabilities are available for random events. Since Keynes (1921) and Knight (1921), it has been understood that such probabilities [...]

Many of the options available to decision makers, such as college majors and romantic partners, can become unavailable if sufficient effort is not invested in them (taking classes, sending flowers). The question asked in this work is whether a threat of disappearance changes the way people value such options. In four experiments using 'door games,' we demonstrate that options that threaten to disappear cause decision makers to invest more effort and money in keeping these options open, even when the options themselves seem to be of little interest. This general tendency is shown to be resilient to information about the outcomes, to increased experience, and to the saliency of the cost. The last experiment provides initial evidence that the mechanism underlying the tendency to keep doors open is a type of aversion to loss rather than a desire for flexibility. Key words: options; aversion to loss; search, Introduction Imagine a student who is uncertain about whether he wants to become a computer programmer or a poet. If he wants to keep both options available, he has to [...]

The risk-pooling effect has been documented to benefit inventory systems by reducing the need for safety stock and consequently lowering costs such as inventory holding and shortage penalty. In this paper, we propose a new approach, called 'demand reshape,' to take advantage of the risk-pooling effect. It is demonstrated that a company can improve its profit by encouraging some of its customers, who intended to purchase one product to switch to another. The effectiveness of this approach is evaluated in various scenarios and found to be very promising. (Demand Reshape; Risk Pooling; Consolidation; Multiproduct; Substitution), 1. Introduction Variability of products' demand frequently attracts managers' attention because of its costly implications. By carrying high inventory levels, firms may satisfy customers' orders and materialize high revenue in [...]

Economic forces shape the behavior of individuals and institutions. Forces affecting individual behavior are attitudes about payoffs (gains and losses) and beliefs about outcomes (risk and ambiguity). Under risk, the likelihoods of alternative outcomes are fully known. Under ambiguity, these likelihoods are unknown. In our experiment, payoffs and outcomes were manipulated independently during a classical choice task as brain activity was measured with positron emission tomography (PET). Here, we show that attitudes about payoffs and beliefs about the likelihood of outcomes exhibit interaction effects both behaviorally and neurally. Participants are risk averse in gains and risk-seeking in losses; they are ambiguity-seeking in neither gains nor losses. Two neural substrates for choice surfaced in the interaction between attitudes and beliefs: a dorsomedial neocortical system and a ventromedial system. This finding reveals that the brain does not honor a prevalent assumption of economics--the independence of th e evaluations of payoffs and outcomes. The demonstration of a relationship between brain activity and observed economic choice attests to the feasibility of a neuroeconomic decision science., Introduction A gamble with known payoffs with a well-defined probability distribution is termed 'risky' (Ellsberg 1961, Knight 1921). In contrast, a gamble with known payoffs with probabilities that are not [...]

Two studies were performed to determine if cross-situational differences in choice behavior should be defined in the expected utility framework as variabilities in risk attitude or as variabilities in the perception of the relative riskiness of choice options as facilitated by risk-return interpretations of utility functions. In particular, they aimed to prove that the ability of situational variables to influence people's risk choices does not automatically mean that stable individual differences in risk preference are not measurable. The studies proved that a definition of risk aversion and risk seeking as the preference for options perceived to be of greater or less risk offers the cross-situational stability to the risk preference of a person that more conventional definitions have failed to capture.

The differences in observed risk taking behavior among companies in the petroleum exploration industry and its effects on firm performance are examined. The study focuses on changes in corporate risk propensity based on changes in firm size and the relationships between firm-level risk-taking behavior and alternative dimensions of firm performance, such as ex post risk and return measures. A decision theoretic model is developed as a tool for quantifying risk propensity as an 'implied' utility function. A new risk propensity measured called 'Risk Tolerance Ratio' is also introduced. This measure controls for company size and facilitates the differentiation among companies based on relative risk propensity. Application on the ex ante risk propensity model indicates the importance of risk-taking behavior and that firm performance is significantly affected by decisions about corporate risk policy.

A generally accepted outcome in the theory of production under price risk is that the availability of forward cover results in the determination of production based on the known, quoted forward or futures price instead of on expectations of future prices. However, in practice, a natural hedge may be available because primary production usually involves joint or substitutable products. Additionally, costs are highly changeable and may be linked with output prices. A study is conducted that examines the demand for market-based hedging instruments associated to the aforementioned natural hedges and the potential application of storage for hedging. The results of the studies as well as implications for future research are discussed.

Hedging policies are analyzed for a company that generates an unpredictable foreign currency cash flow. The study demonstrates that, in perfect capital markets, the contractual value of the corporation's foreign currency liabilities alone completely shapes the profile of cash flows that accumulate for the firm's shareholders in different states. This finding suggests that the contractual value of foreign currency liabilities determines the optimality of hedging policies, and not the seniority structure of domestic and foreign currency debts. The results also show that the companies that attempt to reduce the probability of bankruptcy are less likely to go bankrupt when there is some degree of uncertainty in the exchange rates than when uncertainty is completely absent.

A variety of alternative and opposing techniques for the valuation of risky projects have emerged in both academic and professional circles. A study was conducted to determine their effectiveness by comparing and contrasting three of such approaches. The three methods studied were risk-adjusted discount-rate analysis, option pricing analysis and decision analysis. The examination showed how the proper application of option pricing and decision analysis methods can result in consistent outcomes. The study also revealed how to effectively integrate option pricing and decision analysis techniques. The investigation also demonstrated that option pricing techniques can be employed for the simplification of decision analyses when certain risks can be hedged. Decision analysis techniques were also shown to be applicable in extending option pricing techniques to problems having incomplete securities markets.

The impact of risk and risk aversion in the single-period inventory problem, otherwise known as the newsboy problem, is investigated. The newsboy problem, when applied to a manufacturing context, is demonstrated in such areas as plant capacity, overbooking and target production levels. For the study, comparative-static effects of changes in the different price and cost measures are identified and related to the risk aversion of the newsboy. Moreover, the examination look on the impact of adding random background wealth and riskiness of newspaper demand. Results show that most of the comparative effects are largely vague although certain simple restrictions on preferences and risk increases are discovered to result in qualitatively deterministic outcomes.

Shareholders control the compensation contract and monitor management performance according to the size of their stake in a company. Shareholders with larger investments have a stake in the profits of the firm, thereby encouraging them to monitor management closely and make incentives for better performance. However, large shareholders increase the idiosyncratic firm risk that they bear as they increase their stakes. A model is developed that describes the equilibriation of these factors as a result of social surplus maximization. The results indicate that a highly concentrated ownership structure results in an increased incentive toward management monitoring and incentives. In a competitive environment, only a diffuse ownership equilibrium results given investors who are all price takers.

A model of portfolio choice is used to examine the effects of multivariate risks such as uncertain wealth, uncertain prices of goods and other risky attributes. Conditions under which portfolio choices can be separated from consumption decisions are derived. The optimal portfolio is affected by other risks unless the appropriate restrictions hold on investors' preferences or on the probability distribution of risks. This requires generalizing the usual measures of risk aversion. With one risky asset, matrix measures of risk aversion are used to generalize the effects of risk aversion and wealth on the optimal portfolio. With two risky assets, the choices made by two investors will coincide if and only if their generalized risk-aversion measures are the same. The effect of risk aversion on the level of investment on the riskier asset is then characterized.

An analysis of corporate strategic management was conducted to examine mean-variance relationships and to counter previous research findings which have suggested that negative associations exist between the levels of risk and return. The current analysis suggests that the existence of negative associations between the levels of return and risk in mean-variance terms is not verifiable. This suggestion infers that findings obtained by using variance and mean of return are specific to the information and time period analyzed and may not be generalizable. In addition, because mean and variance are mathematically connected, enhancing the system with more equations will not generate the data necessary to establish validity of statements addressing the mean-variance relationship. An empirical example of the US airline industry is presented to supplement analytic proofs.

The linear plus exponential utility function has received increasing attention of late as a particularly attractive family for evaluating additive gambles for wealth. In addition to its ability to reflect increasing appreciation for money, risk aversion, and decreasing risk aversion, it is consistent with a risk-return representation in which return is measured by expected value. In this paper we present a new condition, strong one-switch, that characterizes the linear plus exponential family., 1. Introduction You have been presented with an opportunity to benefit from one of two gambles, A or B. But you do not need to choose either A or B. [...]

Managerial flexibility has value in the context of uncertain R&D projects, as management can repeatedly gather information about uncertain project and market characteristics and, based on this information, change its course of action. This value is now well accepted and referred to as 'real option value.' We introduce, in addition to the familiar real option of abandonment, the option of corrective action that management can take during the project. The intuition from options pricing theory is that higher uncertainty in project payoffs increases the real option value of managerial decision flexibility. However, R&D managers face uncertainty not only in payoffs, but also from many other sources. We identify five example types of R&D uncertainty, in market payoffs, project budgets, product performance, market requirements, and project schedules. How do they influence the value from managerial flexibility? We find that if uncertainty is resolved or costs/revenues occur after all decisions have been made, more variability may 'smear out' contingencies and thus reduce the value of flexibility. In addition, variability may reduce the probability of flexibility ever being exercised, which also reduces its value. This result runs counter to established option pricing theory intuition and contributes to a better risk management in R&D projects. Our model builds intuition for R&D managers as to when it is and when it is not worthwhile to delay commitments--for example, by postponing a design freeze, thus maintaining flexibility in R&D projects., 1. Introduction and Literature Overview Most investment decisions (and R&D projects in particular) are characterized by irreversibility and uncertainty about their future rewards: Once money is spent, it cannot be [...]

Research on Stein and Rubenstein's covariance formula is described. The formula was generalized to include cases where both variables are functions of multivariate normal random variables. Implicit functions of multivariate normal random variables or nonpolynomials of multivariate normal random variables can be solved with the formula. The research included an application of the formula to the estimation of real systematic risk.

Existing studies have demonstrated that the Sharpe measure and its risk proxy can be determined by sample size, the investment horizon, and market conditions. These conclusions can be generalized to incorporate the performance measures of Treynor and Jenson. It has also been established that estimates of ex-ante Treynor's measures are biased, actually creating biased ranking, and a possible bias linked to the cumulative average residual technique used in market testing may be produced by the relationship between the estimated Jenson's measure and its estimated risk measure. Also discussed are the indications of Friend's and Blume's positive empirical relationships.

Current performance-based fee contracts are analyzed using option pricing theory. Performance-based fee contracts are examined because they may induce portfolio managers to adopt adverse risk management practices for the portfolios in their care. Contract parameters for inducing proper risk incentives are presented for various classes of investment strategies. When rewards for good performance are outweighed by penalties for bad performance adverse risk incentives are avoided in buy-and-hold and rebalancing strategies.

Four hypotheses of discount rate behavior are examined using an intertemporal choice experiment with a 4X4X4 factorial design which manipulates the scenario, time delay, and cash flow. The results support an implicit risk hypothesis and reject the classical hypothesis that discount rates are uniform across time delays, scenarios, and sums of cash flow.

A study was conducted to analyze the choices of decision makers when faced with multiple plays of a gamble or investment. Three repeated gambles that were similar from a normative perspective were developed. The gambles supported differences in the magnitude of single trial losses. Workers' decision to invest their retirement savings in stocks were examined. Results indicated that decision makers are sensitive to the amount to lose on a single trial and display myopic loss aversion. Findings also revealed that the way that information is given can significantly influence choices. In addition, it was shown that workers invest more of their retirement savings in stocks if they are shown long-term rates of return.

A study was conducted to analyze errors in decision making processes related to capital investments and planning situations. Extensions to conventional decision and risk analysis procedures were determined that take into account borrowing and lending opportunities without straining evaluation frameworks. Different preferences were then utilized to analyze uncertainties resolved in various periods. In addition, H. Raiffa's wildcatter problem was analyzed utilizing standard decision and risk analysis methods to characterize subsequent definitions and results. Results indicated that errors caused by considering background borrowing and lending decisions can be significant during substantial project risks and long delays in solving uncertainties.