Coefficient Of Absolute Risk Aversion Research Articles

Estimating financial risk measures for futures positions: A nonparametric approach

AbstractThis study presents nonparametric estimates of spectral risk measures (SRM) applied to long and short positions in five prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value‐at‐Risk and Expected Shortfall. The SRMs are conditioned on the coefficient of absolute risk aversion, and the latter two are conditioned on the confidence level. Our findings indicate that all risk measures increase dramatically and their estimators deteriorate in precision when their respective conditioning parameter increases. Results also suggest that estimates of SRMs and their precision levels are of comparable orders of magnitude as those of more conventional risk measures. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:689–703, 2010

Economic value of weather forecasting: the role of risk aversion

Extreme meteorological events have increased over the last decades and it is widely accepted that it is due to climate change (IPCC, Climate Change 2007, Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, 2007; Beniston et al., Clim. Change 81:71–95, 2007). Some of these extremes, like drought or frost episodes, largely affect agricultural outputs, and risk management becomes crucial. The goal of this paper it is to analyze farmers’ decisions about risk management, taking into account climatological and meteorological information. We consider a situation in which the farmer, as part of crop management, has available technology to protect the harvest from weather effects. This approach has been used by Murphy et al. (Mon. Weather Rev. 113:801–813, 1985), Katz and Murphy (J. Forecast. 9:75–86, 1990 and Economic Value of Weather and Climate Forecasts, pp. 183–217, Cambridge University Press, Cambridge, 1997) and others in the case when the farmer maximizes the expected returns. In our model, we introduce the attitude towards risk. Thus we can evaluate how the optimal decision is affected by the absolute risk aversion coefficient of Arrow and Pratt, and compute the economic value of the information in this context, while proposing a measure to estimate the amount of money that the farmer is willing to pay for this information in terms of the certainty equivalent.

Interval risk aversion

The conventional measures of absolute and relative risk aversion are appropriate for measuring preferences locally, but because they rely on differential calculus, they cannot accurately capture attitudes towards high-stakes risks involving potentially large changes in wealth. Eisenhauer (2006) has recently proposed an alternative approach which avoids the use of calculus. The present article extends that work in two ways. First, the Pratt–Arrow coefficient of absolute risk aversion is generalized into a measure of interval risk aversion, suitable for analysing preferences over risks of any magnitude, and a corresponding interval measure of relative risk aversion is constructed from preference and risk parameters, without explicit reference to initial wealth or income. Second, the new measures are applied to survey data from the Bank of Italy, to illustrate their empirical applicability to large-scale risk.

Forward hedging under price and production risk of wheat

This paper estimates optimal hedging ratios for a Finnish spring wheat producer under price and yield uncertainty. The contract available for hedging fixes the price and quantity at the time of sowing for a delivery at harvest. Autoregressive models are used to obtain point forecasts for the conditional mean price and price volatility at harvest. Expected yield and yield volatility are estimated from the field experiment data. A range of coefficients of absolute risk aversion are used in the computations. The results suggest that yield volatility is large and it dominates the price volatility in the optimal hedging decisions of the Finnish wheat producers. The point estimate for the price and yield correlation is negative and has a large magnitude. Thus, a negative correlation between the price and the yield, as signalled by the point estimate, will decrease the optimal hedging ratio since the Finnish farmers do not have access to selling put options when they enter in a forward contract.;

Should farmers invest in financial assets as a risk management strategy? Some evidence from New Zealand*

This study explores the potential for risk reduction by New Zealand farmers through the diversification of their farm asset portfolios to include financial investments such as ordinary industrial shares, government bonds and bank bills. Low correlations between rates of return on farm and these financial assets suggest that significant reduction of income variability might follow their inclusion in farmers’ portfolios. Stochastic efficiency analysis is used to analyse alternative portfolios of ordinary shares, government bonds and bank bills and New Zealand farmland, using coefficients of absolute risk aversion derived from a negative exponential utility function. The results suggest that those farmers showing high degrees of risk aversion would gain utility by including financial assets in their portfolios. Deregulation of the New Zealand economy in the 1980s appeared to reduce the potential gains from diversification. Bonds rather than ordinary shares are the main contributors to portfolios which maximise utility for individuals classified as ‘somewhat’ risk averse.

Nonlinear Pricing by Risk-Averse Principals

This paper studies the effects of risk aversion on nonlinear pricing. It first develops a model of risk-averse principal, based on Mussa and Rosen (1978), and finds that the equilibrium allocation increases and approaches the efficient level as the principal's risk aversion increases and tends to infinity. The model is then extended to allow for random participation. It is found that the allocation moves towards the efficient level as the monopolistic principal becomes more risk averse. For the case of duopoly, the cost-based two-part tariff is optimal in the full participation equilibrium and the fixed fee component monotonically decreases to zero when the coefficient of absolute risk aversion of the principals tends to infinity.

Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem

We are concerned with the solvablity of certain nonlinear partial differential equation (PDE), which is derived from the optimal investment problem under the random risk process. The equation describes the evolution of the Arrow-Pratt coefficient of absolute risk aversion with respect to the optimal value function. Employing the fixed point approach combined with the convergence argument we show the existence of solutions.

“Probability of risk aversion” and other applications of derivatives of the certainty equivalent

“Probability of risk” aversion is principally concerned with reactions to scaling up of probabilities of non-zero values of a non-positive random variable by a common factor. Decreasing probability-of-risk aversion is defined and shown to be equivalent to ordinary risk aversion. Implications of this for insurance are pointed out. The sort of scaling involved is the same as that involved in “self-protection,” and it is shown that, for any expenditure on self-protection, say x, a concave utility function will prefer a coinsurance policy, costing x, which leaves probabilities unchanged, but scales down loss amounts by the same proportion as probabilities are scaled under self-protection. Properties of several comparative concepts of decreasing risk aversion are established. Derivatives of the certainty equivalent (CE) are used to elucidate well-known comparative static results in models of expected utility maximization. Finally, the study proves that concavity of the CE implies convexity of the coefficient of absolute risk aversion and examines the role of curvature of the CE in exploring relationships between properties of risk vulnerability, properness, and standardness.

Risk aversion and compliance in markets for pollution control

This paper examines the effects of risk aversion on compliance choices in markets for pollution control. A firm's decision to be compliant or not is independent of its manager's risk preference. However, non-compliant firms with risk-averse managers will have lower violations than otherwise identical firms with risk-neutral managers. The violations of non-compliant firms with risk-averse managers are independent of differences in their profit functions and their initial allocations of permits if and only if their managers’ utility functions exhibit constant absolute risk aversion. However, firm-level characteristics do impact violation choices when managers have coefficients of absolute risk aversion that are increasing or decreasing in profit levels. Finally, in the equilibrium of a market for emissions rights with widespread non-compliance, risk aversion is associated with higher permit prices, better environmental quality, and lower aggregate violations.

Comparing risk attitudes of organic and non-organic farmers with a Bayesian random coefficient model

Organic farming is usually considered to be more risky than conventional farming, but the risk aversion of organic farmers compared with that of conventional farmers has not been studied. Using a non-structural approach to risk estimation, a Bayesian random coefficient model is used to obtain individual Arrow–Pratt coefficients of absolute risk aversion for a sample of Dutch organic and non-organic arable farmers. The model is estimated using Gibbs sampling. The results indicate that organic farmers are significantly less risk averse than their non-organic colleagues.

On Inverse Utility and Third-Order Effects in the Economics of Uncertainty

We prove that the coefficient of absolute prudence is greater than k - times coefficient of absolute risk aversion for the utility function if and only if the coefficient of absolute prudence is (3-k) times the coefficient of absolute risk aversion for the inverse utility function. Moreover this is also equivalent to (k-2)-concavity of the first derivative of the inverse utility function.

A Shortcut Way of Pricing Default Risk Through Zero‐Utility Principle

AbstractPricing the default risk is a hot challenge for every risk manager. The problem is tackled in the framework of the zero‐utility principle. According to Pratt (1964), an approximation of the risk premium should be proportional to the Arrow–Pratt absolute risk aversion coefficient and the variance. Is that still true as a default risk is concerned? The answer appears to be negative, because the variance does not look to be an appropriate tool for asymmetrical risk. On the other hand, fear of ruin coefficient and probability of default are proved to be well‐tailored tools for a preliminary pricing. Bid and ask price approximations are both elicited and a necessary condition for risk exchange set out.

Risk Aversion and Compliance in Markets for Pollution Control

This paper examines the effects of risk aversion on compliance choices in markets for pollution control. A firm's decision to be compliant or not is independent of its manager's risk preference. However, noncompliant firms with risk averse managers will have lower violations than otherwise identical firms with risk neutral managers. The violations of noncompliant firms with risk averse managers are independent of differences in their benefits from emissions and their initial allocations of permits if and only if their managers' utility functions exhibit constant absolute risk aversion. However, firm-level characteristics do impact violation choices when managers have coefficients of absolute risk aversion that are increasing or decreasing in profit levels. Finally, in the equilibrium of a market for emissions rights with widespread noncompliance, risk aversion is associated with higher permit prices, better environmental quality, and lower aggregate violations.

Stochastic efficiency analysis with risk aversion bounds: a simplified approach

A method of stochastic dominance analysis with respect to a function (SDRF) is described and illustrated. The method, called stochastic efficiency with respect to a function (SERF), orders a set of risky alternatives in terms of certainty equivalents for a specified range of attitudes to risk. It can be applied for conforming utility functions with risk attitudes defined by corresponding ranges of absolute, relative or partial risk aversion coefficients. Unlike conventional SDRF, SERF involves comparing each alternative with all the other alternatives simultaneously, not pairwise, and hence can produce a smaller efficient set than that found by simple pairwise SDRF over the same range of risk attitudes. Moreover, the method can be implemented in a simple spreadsheet with no special software needed.

Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions $\!$

This paper investigates the stochastic properties of the first price and second price winning bids in auctions with risk neutral bidders with independent and identically distributed valuations. In such an environment, the winning first price bids second order stochastically dominate the second price winning bids. A key result of this paper is that the ratio of the variance of the winning first price bid to that of the winning second price bid is strictly less than one even as the number of bidders goes to infinity. This suggests that the stochastic dominance of the winning first price bids does not vanish even in the limit. Both the asymptotic and small sample properties of winning bids are investigated. In particular, the small sample results suggest that the identification power of econometric procedures that rely on winning bids can decline rapidly as the number of bidders increases. This paper also includes a systematic evaluation of the difference in certainty equivalents between the two auction formats for several common distributions and number of bidders for the case of auctioneers with constant coefficient of absolute risk aversion. These results are presented in a form that makes it easy to apply them to a specific auction of interest.

Forward hedging under price and production risk of wheat

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An MCDM analysis of agricultural risk aversion

In modelling farm systems it is widely accepted that risk plays a central role. Furthermore, farmers’ risk aversion determines their decisions in both the short and the long run. This paper presents a methodology based on multiple criteria mathematical programming to obtain relative and absolute risk aversion coefficients. We rely on multiattribute utility theory to elicit a separable additive multiattribute utility function and estimate the risk aversion coefficients, and apply this methodology to an irrigated area of Northern Spain. The results show a wide variety of attitudes to risk among farmers, who usually exhibit decreasing absolute risk aversion and constant relative risk aversion.

Non‐parametric estimation of decision makers' risk aversion

AbstractA new non‐parametric method to estimate a decision maker's coefficient of absolute risk aversion from observed economic behaviour is explained. The method uses the expected value‐variance (E‐V) framework and quadratic programming. An empirical illustration is given using Norwegian farm‐level data.

Non-parametric estimation of decision makers’ risk aversion

A new non-parametric method to estimate a decision maker’s coefficient of absolute risk aversion from observed economic behaviour is explained. The method uses the expected value–variance ( E– V) framework and quadratic programming. An empirical illustration is given using Norwegian farm-level data.

Stochastic goal programming: A mean–variance approach

We propose a stochastic goal programming (GP) model leading to a structure of mean–variance minimisation. The solution to the stochastic problem is obtained from a linkage between the standard expected utility theory and a strictly linear, weighted GP model under uncertainty. The approach essentially consists in specifying the expected utility equation corresponding to every goal. Arrow's absolute risk aversion coefficients play their role in the calculation process. Once the model is defined and justified, an illustrative example is developed.