Risk taking in the domain of losses: experiments in several countries

This paper presents an experimental investigation of risk taking in the domain of losses. The experiments were conducted with students in several universities whilst introducing the rudiments of expected utility theory and risk behaviour. The results are partly compatible with expected utility theory, assuming an inflection point in the utility function over losses. They also show similarities in the risk perception of students across different countries, i.e. a useful validation of human behaviour in an international context.     

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship. I. Molchanov supported by Swiss National Science Foundation Grant 200020-109217.     

Sampling distribution of the relative risk aversion estimator: Theory and applications

Brown and Gibbons (1985) developed a theory of relative risk aversion estimation in terms of average market rates of return and the variance of market rates of return. However, the exact sampling distributions of the relative risk aversion estimators have not been derived. The main purpose of this paper is to derive the exact sampling distribution of an appropriate relative risk aversion estimator. First, we have derived theoretically the density of Brown and Gibbons' maximum likelihood estimator. It is shown that the centralt is not appropriate for testing the significance of estimated relative risk aversion distribution. Then we derived the minimum variance unbiased estimator by a linear transformation of the Brown and Gibbons' maximum likelihood estimator. The density function is neither a central nor a noncentralt distribution. The density function of this new distribution has been tabulated. There is an empirical example to illustrate the application of this new sampling distribution.     

Optimal insurance contract and coverage levels under loss aversion utility preference

This study develops an optimal insurance contract endogenously and determines the optimal coverage levels with respect to deductible insurance, upper-limit insurance, and proportional coinsurance, and, by assuming that the insured has an S-shaped loss aversion utility, the insured would retain the enormous losses entirely. The representative optimal insurance form is the truncated deductible insurance, where the insured retains all losses once losses exceed a critical level and adopts a particular deductible otherwise. Additionally, the effects of the optimal coverage levels are also examined with respect to benchmark wealth and loss aversion coefficient. Moreover, the efficiencies among various insurances are compared via numerical analysis by assuming that the loss obeys a uniform or log-normal distribution. In addition to optimal insurance, deductible insurance is the most efficient if the benchmark wealth is small and upper-limit insurance if large. In the case of a uniform distribution that has an upper bound, deductible insurance and optimal insurance coincide if benchmark wealth is small. Conversely, deductible insurance is never optimal for an unbounded loss such as a log-normal distribution.     

Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion

We analyze spectral risk measures with respect to comparative risk aversion following Arrow (1965) and Pratt (1964) for deterministic wealth, and Ross (1981) for stochastic wealth. We argue that the Arrow–Pratt-concept per se well matches with economic intuition in standard financial decision problems, such as willingness to pay for insurance and simple portfolio problems. Different from the literature, we find that the widely-applied spectral Arrow–Pratt-measure is not a consistent measure of Arrow–Pratt-risk aversion. Instead, the difference between the antiderivatives of the corresponding risk spectra is valid. Within the framework of Ross, we show that the popular subclasses of Expected Shortfall, and exponential and power spectral risk measures cannot be completely ordered with respect to Ross-risk aversion. Thus, for all these subclasses, the concept of Ross-risk aversion is not generally compatible with Arrow–Pratt-risk aversion, but induces counter-intuitive comparative statics of its own. Compatibility can be achieved if asset returns are jointly normally distributed. The general lesson is that these restrictions have to be considered before spectral risk measures can be applied for the purpose of optimal decision making and regulatory issues.     

Credit portfolios: What defines risk horizons and risk measurement?

The strong autocorrelation between economic cycles demands that we analyze credit portfolio risk in a multiperiod setup. We embed a standard one-factor model in such a setup. We discuss the calibration of the model to Standard & Poor’s ratings data in detail. But because single-period risk measures cannot capture the cumulative effects of systematic shocks over several periods, we define an alternative risk measure, which we call the time-conditional expected shortfall (TES), to quantify credit portfolio risk over a multiperiod horizon.     

Investors’ preference towards risk: evidence from the Taiwan stock and stock index futures markets

We apply the stochastic dominance (SD) tests proposed by Linton et al. (2005) and Davidson and Duclos (2000) for risk averters and risk seekers to examine investors’ preferences with respect to the Taiwan stock index and its corresponding index futures. We find that there is no first‐order SD relationship between Taiwan spot and futures. However, for second‐ and third‐order SD, we find that spot dominates futures for risk averters whereas futures dominates spot for risk seekers. The implication is that to maximize their expected utilities, risk averters prefer to buy stocks, whereas risk seekers prefer long index futures.     

The usefulness of firm risk disclosures under different firm riskiness,investor-interest,and market conditions: New evidence from Finland

To date, there is only meager research evidence on the usefulness of mandatory annual report risk disclosures to investors. Although it has been argued that corporate disclosure decreases information asymmetry between management and shareholders, we do not know whether investors benefit from high-quality risk reporting in a highly regulated risk disclosure environment. In this paper, we performed association tests to examine whether the quality of firms' mandatory risk disclosures relate to information asymmetry in the Finnish stock markets. In addition, we analyzed whether the usefulness of risk disclosures depends on contingency factors such as firm riskiness, investor interest, and market condition. We demonstrate that the quality of risk disclosure has a direct negative influence on information asymmetry. We also document that risk disclosures are more useful if they are provided by small firms, high tech firms, and firms with low analyst coverage. We also found that momentum in stock markets affects the relevance of firms' risk reports.