Risk-averse Decision Research Articles

AN EXPLICIT OPTION-BASED STRATEGY THAT OUTPERFORMS DOLLAR COST AVERAGING

Dollar cost averaging (DCA) is a widely employed investment strategy in financial markets. At the same time it is also well documented that such gradual policy is sub-optimal from the point of view of risk averse decision makers with a fixed investment horizon T > 0. However, an explicit strategy that would be preferred by all risk averse decision makers did not yet appear in the literature. In this paper, we give a novel proof for the suboptimality of DCA when (log) returns are governed by Lévy processes and we construct a dominating strategy explicitly. The optimal strategy we propose is static and consists in purchasing a suitable portfolio of path-independent options. Next, we discuss a market governed by a Brownian motion in more detail. We show that the dominating strategy amounts to setting up a portfolio of power options. We provide evidence that the relative performance of DCA becomes worse in volatile markets, but also give some motivation to support its use. We also analyse DCA in presence of a minimal guarantee, explore the continuous setting and discuss the (non) uniqueness of the dominating strategy.

One theory for two different risk premia

Generally, in the standard presentation of the expected utility model, the risk premium represents how much a risk-averse decision maker is ready to pay to have a risk eliminated. Here, however, we introduce a different risk premium: how much should a risk (which could be the return on a financial asset) yield to be acceptable to a risk-averse decision maker. Although our risk premium is derived from the Pratt bid price, it should not be confused with it: the Pratt bid price represents the monetary compensation of a risk. The standard risk premium refers to risk-avoidance; our risk premium, however, refers to risk-taking. We then reanalyze the main results concerning risk aversion under expected utility using this risk premium tool and deduce its main properties.

Management Insights

Management Insights

Nitrogen use and the effects of nitrogen taxation under consideration of production and price risks

Production and price risks affect optimal nitrogen use as well as the effects of nitrogen taxation if farmers’ risk aversion is taken into account. We apply a bio-economic model to investigate the influence of risk aversion on nitrogen use in Swiss maize production. Income risks for farmers are expected to increase in the future, for instance, due to higher price variability caused by market liberalization or by higher yield variability caused by climate change. We investigate the influence of changes in these sources of risks on optimal levels of nitrogen use and its influence on the effects of nitrogen taxation. Our empirical analysis for Swiss maize production shows that risk-aversion leads to lower levels of nitrogen application than for risk-neutral farmers. Furthermore, nitrogen taxes lead to higher reductions of nitrogen use if farmers are risk-averse and these farmers face lower abatement costs. Thus, analyses on the effect of nitrogen taxes that are solely based on profit maximizing behavior may underestimate nitrogen reductions and overestimate abatement costs. Taking expected shocks in price and yield variability into account, we find that these differences between risk neutral and risk-averse decision makers will increase further. External influences on production and price risks can thus influence the effects of agricultural policies on farmers’ decision making. Thus, considering farmers’ risk-preferences as well as potential increases in farmers’ income risks can improve agricultural policy making.

Do banks use credit default swaps to hedge or speculate? An agency theoretic perspective

The global financial crisis (GFC) has drawn attention to the increased risk taking of financial institutions, in particular risk taking by banks. Some observers have also suggested that credit default swaps (CDS) have not only contributed to the GFC but to some extent have also exacerbated it. Moreover, it would seem that in many cases the main motivation for banks in using CDS is for trading purposes (Fitch Ratings, 2007, 2010). Given that banks are among the most important sources of finance, and are fraught with extensive public exposure through deposits, risk taking in banks is an important consideration for both regulators and the general public. This paper explores an agency theoretic perspective in analysing the potential motivations for risk taking vs. risk aversion decisions within banks. The paper asserts that the use of CDS for speculative/trading purpose indicates a risk taking motive, whereas the use of CDS for hedging purposes suggests that the overriding motivation is risk aversion. We argue that these dichotomous themes can explain banking strategy in the use of CDS and in turn can also explain the rationale for the phenomenal growth in CDS up until the onset of the GFC.

Mitigating Cotton Revenue Risk Through Irrigation, Insurance, and Hedging

This study focuses on managing cotton production and marketing risks using combinations of irrigation levels, put options (as price insurance), and crop insurance. Stochastic cotton yields and prices are used to simulate a whole-farm financial statement for a 1,000 acre furrow-irrigated cotton farm in the Texas Lower Rio Grande Valley under 16 combinations of risk management strategies. Analyses for risk-averse decision makers indicate that multiple irrigations are preferred. The benefits to purchasing put options increase with yields, as they are more beneficial when higher yields are expected from applying more irrigation applications. Crop insurance is strongly preferred at lower irrigation levels.

Higher-Order Risk Preferences – Consequences for Test and Treatment Thresholds and Optimal Cutoffs

Risikoverhalten hoherer Ordnung umfasst Risikoscheue, das Vorsichtsmotiv und Temperenz. Letzeres bedeutet eine allgemeine Zuruckhaltung, sich Risiken auszusetzten. Wir beschaftigen uns im Aufsatz mit den Wirkungen solcher Risikopraferenzen auf diagnostische und therapeutische Entscheidungen in der Medizin, insbesondere auf die Test- und Behandlungsschwellen und, im Falle von endogenen Tests, auf den optimalen Trennpunkt. Fur risikoscheue Entscheider bedeutet eine Behandlung insofern eine risikomindernde Strategie, als sie den schlechten Gesundheitszustand vermeidet, der eintritt, falls der tatsachlich erkrankte Patient nicht behandelt wird. Im Vergleich zu Risikoneutralitat senkt daher das Vorliegen von Risikoscheue die Test- und Behandlungsschwellen und auch den Trennpunkt. Das Vorsichtsmotiv ist dann von Bedeutung, wenn Komorbiditat im Krankheitsfall auftritt. Es fuhrt zu einer weiteren Reduktion der Schwellen und des Trennpunkts. Temperenz kommt ins Spiel, wenn das Komorbiditatsrisiko linksschief verteilt ist. Sie reduziert die Schwellen und den Trennpunkt noch weiter. Diese Ergebnisse legen es nahe, der Diagnostik im niedrigen Pravalenzbereich - dazu gehoren insbesondere Vorsorgeprogramme beim Brustkrebs und beim Prostatakrebs - eine hohere Bedeutung zuzumessen.

Risk-averse decision making in overbooking problem

Traditional literature studying overbooking problems focuses on risk-neutral decision makers. In this paper, we propose a multi-period overbooking model incorporating risk-aversion and extend well-known structural results (the 3-region policy) under the risk-neutral case to the risk-averse one on the basis of an exponential utility function. We also show that the optimal policy for the risk-neutral decision maker can be obtained by letting the risk-aversion parameter approach to zero under the risk-averse case. Therefore, the extant results under the risk-neutral case can be interpreted as a special case of ours. We also investigate how the optimal policy changes with some cost parameters and the decision maker's degree of risk-aversion. Numerical results suggest that the optimal bounds in the 3-region policy may increase or decrease with the decision maker's degree of risk-aversion.

Monotone strong increases in risk and their comparative statics

We introduce a new concept of the monotone strong increase in risk (MSIR) order that imposes monotonicity restrictions on the ratio of the two cumulative of cumulative distribution functions as a special case of Rothschild–Stiglitz increases in risk that is the subset of the second-degree stochastic dominance criterion. We show that the MSIR order implies that the conditional expectation of a random variable under one cumulative distribution function is greater than or equal to that under another cumulative distribution function. Restricting the payoff function to be linear in the random variable and limiting our analysis to risk-averse decision-makers who are prudent, we obtain appealing comparative statics results for the MSIR shift. This general conclusion can be applied to prevailing economic models having a linear payoff.

Presenting Evidence and Summary Measures to Best Inform Societal Decisions When Comparing Multiple Strategies

Multiple strategy comparisons in health technology assessment (HTA) are becoming increasingly important, with multiple alternative therapeutic actions, combinations of therapies and diagnostic and genetic testing alternatives. Comparison under uncertainty of incremental cost, effects and cost effectiveness across more than two strategies is conceptually and practically very different from that for two strategies, where all evidence can be summarized in a single bivariate distribution on the incremental cost-effectiveness plane. Alternative methods for comparing multiple strategies in HTA have been developed in (i) presenting cost and effects on the cost-disutility plane and (ii) summarizing evidence with multiple strategy cost-effectiveness acceptability (CEA) and expected net loss (ENL) curves and frontiers. However, critical questions remain for the analyst and decision maker of how these techniques can be best employed across multiple strategies to (i) inform clinical and cost inference in presenting evidence, and (ii) summarize evidence of cost effectiveness to inform societal reimbursement decisions where preferences may be risk neutral or somewhat risk averse under the Arrow-Lind theorem. We critically consider how evidence across multiple strategies can be best presented and summarized to inform inference and societal reimbursement decisions, given currently available methods. In the process, we make a number of important original findings. First, in presenting evidence for multiple strategies, the joint distribution of costs and effects on the cost-disutility plane with associated flexible comparators varying across replicates for cost and effect axes ensure full cost and effect inference. Such inference is usually confounded on the cost-effectiveness plane with comparison relative to a fixed origin and axes. Second, in summarizing evidence for risk-neutral societal decision making, ENL curves and frontiers are shown to have advantages over the CEA frontier in directly presenting differences in expected net benefit (ENB). The CEA frontier, while identifying strategies that maximize ENB, only presents their probability of maximizing net benefit (NB) and, hence, fails to explain why strategies maximize ENB at any given threshold value. Third, in summarizing evidence for somewhat risk-averse societal decision making, trade-offs between the strategy maximizing ENB and other potentially optimal strategies with higher probability of maximizing NB should be presented over discrete threshold values where they arise. However, the probabilities informing these trade-offs and associated discrete threshold value regions should be derived from bilateral CEA curves to prevent confounding by other strategies inherent in multiple strategy CEA curves. Based on these findings, a series of recommendations are made for best presenting and summarizing cost-effectiveness evidence for reimbursement decisions when comparing multiple strategies, which are contrasted with advice for comparing two strategies. Implications for joint research and reimbursement decisions are also discussed.

Dual theory of choice with multivariate risks

We propose a multivariate extension of Yaari's dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects using a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the multivariate framework using optimal transportation maps. Finally, risk averse decision makers are characterized within this framework and their local utility functions are derived. Applications to the measurement of multi-attribute inequality are also discussed.

Optimal newsvendor policies for dual-sourcing supply chains: A disruption risk management framework

We propose generic single period (newsvendor-type) inventory models for capturing the trade-off between inventory policies and disruption risks in a dual-sourcing supply chain network both unconstrained and under service level constraints, where both supply channels are susceptible to disruption risks. The models are developed for both risk neutral and risk-averse decision-makers and can be applicable for different types of disruptions related among others to the supply of raw materials, the production process, and the distribution system, as well as security breaches and natural disasters. Analytical closed-form solutions are obtained and interesting managerial insights on the merit of contingency strategies in managing uncertainties and risks in dual-sourcing supply chains are discussed.

Optimal Design of Onshore Natural Gas Pipelines

The optimal design level for onshore natural gas pipelines was explored through a hypothetical example, whereby the pipe wall thickness was assumed to be the sole design parameter. The probability distributions of the life-cycle costs of various candidate designs for the example pipeline were obtained using Monte-Carlo simulation. The life-cycle cost included the cost of failure due to equipment impact and external corrosion, and the cost of periodic maintenance actions for external corrosion. The cost of failure included both the cost of fatality and injury as well as the cost of property damage and value of lost product. The minimum expected life-cycle cost criterion and stochastic dominance rules were employed to determine the optimal design level. The allowable societal risk level was considered as a constraint in the optimal design selection. It was found that the Canadian Standard Association design leads to the minimum expected life-cycle cost and satisfies the allowable societal risk constraint as well. A set of optimal designs for a risk-averse decision maker was identified using the stochastic dominance rules. Both the ASME and CSA designs belong to the optimal design set and meet the allowable societal risk constraint.

Stochastic hydro-economic modeling for optimal management of agricultural groundwater nitrate pollution under hydraulic conductivity uncertainty

In decision-making processes, reliability and risk aversion play a decisive role. This paper presents a framework for stochastic optimization of control strategies for groundwater nitrate pollution from agriculture under hydraulic conductivity uncertainty. The main goal is to analyze the influence of uncertainty in the physical parameters of a heterogeneous groundwater diffuse pollution problem on the results of management strategies, and to introduce methods that integrate uncertainty and reliability in order to obtain strategies of spatial allocation of fertilizer use in agriculture. A hydro-economic modeling approach is used for obtaining the allocation of fertilizer reduction that complies with the maximum permissible concentration in groundwater while minimizes agricultural income losses. The model is based upon nonlinear programming and groundwater flow and mass transport numerical simulation, condensed on a pollutant concentration response matrix. The effects of the hydraulic conductivity uncertainty on the allocation of nitrogen reduction among agriculture pollution sources are analyzed using four formulations: Monte Carlo simulation with pre-assumed parameter field, Monte Carlo optimization, stacking management, and mixed-integer stochastic model with predefined reliability. The formulations were tested in an illustrative example for 100 hydraulic conductivity realizations with different variance. The results show a high probability of not meeting the groundwater quality standards when deriving a policy from just a deterministic analysis. To increase the reliability several realizations can be optimized at the same time. By using a mixed-integer stochastic formulation, the desired reliability level of the strategy can be fixed in advance. The approach allows deriving the trade-offs between the reliability of meeting the standard and the net benefits from agricultural production. In a risk-averse decision making, not only the reliability of meeting the standards counts, but also the probability distribution of the maximum pollutant concentrations. A sensitivity analysis was carried out to assess the influence of the variance of the hydraulic conductivity fields on the strategies. The results show that the larger the variance, the greater the range of maximum nitrate concentrations and the worst case (or maximum value) that could be reached for the same level of reliability.

Optimal investment under operational flexibility, risk aversion, and uncertainty

Traditional real options analysis addresses the problem of investment under uncertainty assuming a risk-neutral decision maker and complete markets. In reality, however, decision makers are often risk averse and markets are incomplete. We confirm that risk aversion lowers the probability of investment and demonstrate how this effect can be mitigated by incorporating operational flexibility in the form of embedded suspension and resumption options. Although such options facilitate investment, we find that the likelihood of investing is still lower compared to the risk-neutral case. Risk aversion also increases the likelihood that the project will be abandoned, although this effect is less pronounced. Finally, we illustrate the impact of risk aversion on the optimal suspension and resumption thresholds and the interaction among risk aversion, volatility, and optimal decision thresholds under complete operational flexibility.

Performance-Reliability-Aided Decision-Making in Multiperson Quadratic Decision Games Against Jamming and Estimation Confrontations

The work presents an attainment of risk-averse cooperative solutions in multi-person, single-objective decision problems for practical situations of the probabilistic (rather than deterministic) nature of performance reliability, its consequences on measuring performance reliability, and the difference between predicting and designing for performance reliability. In particular, some novel research contributions include: (i) closed-loop performance assessment via a performance-information analysis; (ii) cooperative decision selection via a risk-value model; and (iii) risk-averse cooperative decision strategies against confrontations and noncooperation from a malevolent opponent and a stationary environment, respectively.

On the Determination of Cooperative Risk-Value Aware Strategies for Linear Stochastic Multi-Agent Systems

AbstractThe work presents an attainment of risk-value based cooperative solutions for management control of linear stochastic multi-agent systems with distributed observation collections with the following complexities: (1) closed-loop performance robustness ensured by a risk-value model for tradeoffs between performance values and risks and (2) risk-averse decisions and cooperative control policies via local information patterns.

The vigilant parent: Parental role salience affects parents' risk perceptions, risk-aversion, and trust in strangers

Since parenting involves protecting children from various risks and dangers, tendencies towards increased risk perception, risk-averse decision-making, and distrust of strangers may come to be associated with the parental role. Consequently, parents may be more likely to exhibit each of these psychological tendencies when their parental role is situationally salient than when it is not salient. We tested this hypothesis in two studies that manipulated the salience of the parental role in samples of parents and nonparents and measured the effects on participants' risk perceptions, risk-aversion, and trust in strangers. As we hypothesized, parents perceived greater risk (Study 1), made more risk averse choices (Study 1), and trusted strangers less (Study 2) when their parental role was salient than when it was not salient. Implications for understanding psychological adaptations to social roles are discussed.

Sample average approximation of stochastic dominance constrained programs

In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems allows for the modeling of optimization problems where a risk-averse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with the case of multi-variate stochastic dominance under general distributions and nonlinear functions. We introduce the concept of $${\mathcal{C}}$$ -dominance, which generalizes some notions of multi-variate dominance found in the literature. We apply the Sample Average Approximation (SAA) method to this problem, which results in a semi-infinite program, and study asymptotic convergence of optimal values and optimal solutions, as well as the rate of convergence of the feasibility set of the resulting semi-infinite program as the sample size goes to infinity. We develop a finitely convergent method to find an $${\epsilon}$$ -optimal solution of the SAA problem. An important aspect of our contribution is the construction of practical statistical lower and upper bounds for the true optimal objective value. We also show that the bounds are asymptotically tight as the sample size goes to infinity.

Sensitivity Analysis of Risk Tolerance

For a risk-averse decision maker with exponential utility facing a decision between two investments X and Y, there may exist more than one critical value of risk tolerance for which the decision is reversed from one investment to the other. Our main result establishes that if Y is preferred to X by all risk-seeking decision makers, then there is at most one such critical value. We extend this result to linear plus exponential utility functions. The results reduce the input required from a decision maker.