Higher-order Risk Research Articles

Precautionary risk-reduction and saving decisions: Two sides of the same coin?

We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are Nth-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are Nth-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.

Exploring Downside Co-Skewness and Upside Co-Kurtosis: Implications for Asset Pricing Models

This study examines how the investors' preferences for downside co-skewness and upside co-kurtosis may influence the asset pricing. We analyze data from 2000 to 2021, encompassing 2874 companies listed on the Shanghai Stock Exchange. Our methodology includes both time series and cross-sectional analyses, employing the Fama-Macbeth approach. Our findings reveal that the estimated values for downside co-skewness and upside co-kurtosis contribute to a significant premium, one that remains unexplained by traditional market factors such as size, value, profitability, and investment. Furthermore, when these higher-order co-moments are incorporated into the Capital Asset Pricing Model (CAPM), they demonstrate significant explanatory power in understanding the variations in stock returns. This augmented CAPM, with downside co-skewness and upside co-kurtosis, exhibits a superior goodness-of-fit compared to conventional asset pricing models. This suggests a crucial link between these higher-order risk factors and stock valuation, offering new insights into the complexities of investor behavior and market dynamics.

Higher-order risk preferences and livelihood choices of farmers from West Bengal, India

Higher-order risk preferences and livelihood choices of farmers from West Bengal, India

Publisher Correction: An alternative representation of the C-CAPM with higher-order risks

Publisher Correction: An alternative representation of the C-CAPM with higher-order risks

An alternative representation of the C-CAPM with higher-order risks

An alternative representation of the C-CAPM with higher-order risks

Higher-Order Risk Premium and Return Spillovers between Commodity and Stock Markets

Higher-Order Risk Premium and Return Spillovers between Commodity and Stock Markets

Higher order risk attitudes: new model insights and heterogeneity of preferences

It is now well established that higher-order risk preferences play a crucial role in determining the risky choices of decision makers in a wide range of important areas such as economics, finance and health. While influential theories of risky choice in those fields can explain attitudes to second order risk, the implications of these models for higher order risk preferences is still to be developed. This paper addresses that gap for the Markowitz (J Political Econ, 60:151–58, 1952) (M) model of utility which embodies reference-dependent utility, loss aversion and was seemingly the first model to explain the fourfold attitude to risk. In this paper, we set out new properties of the M model for higher order preferences, such as higher-order risky choice reversals, that can help explain experimental evidence not readily reconcilable with other models of risky choice. A second contribution of the paper is to empirically examine the heterogeneity of preference functionals describing second as well as higher order risky choices using hierarchical Bayesian estimation methods. Our analysis of the risky choices revealed in three prominent studies provides support for the M model as a useful complement to other leading models of risky choice such as cumulative prospect theory (CPT). In addition, we set up a new experiment whose design is shown to have satisfactory discriminatory power between the M and CPT specifications, and our results based on the Bayes factor confirm the heterogeneity of preference functionals across decision makers, and that the CPT specification is more prevalent.

Option-based intermediary leverage

We introduce a new proxy for the health of financial intermediaries-the Leverage Bearing Capacity (LBC). LBC is the leverage of a fictitious intermediary that targets a fixed level of risk and rebalances its capital structure on an ongoing basis. Our measure is based on market values, incorporates off-balance sheet activities, is available at any frequency, and inherently captures higher-order risks. We analyze the dynamics of LBC in event studies and demonstrate that it is closely linked to financial sector uncertainty. Building on an intermediary asset pricing model, we validate that LBC proxies the marginal wealth of intermediaries. Empirically, it explains the expected returns across several asset classes and subsumes the explanatory power of existing measures of intermediaries’ health, financial uncertainty, higher-order risks, and common risk factors.

On the consistency of the individual behavior when facing higher-order risk attitudes

We propose and analyze three procedures to elicit participants’ behavior regarding their higher-order risk attitudes. Our procedures relax the rigidity of having to choose among only two alternatives (as usual in the literature), and allow for choosing a third or even a fourth alternative. This way, the remaining choices for the two original alternatives carry lower levels of noise, i.e., lower randomness in behavior from the subjects without a strong preference in the binary setting, that are forced to choose among only two alternatives. Although the proposed procedures only filter out a small proportion of the choices, the effect on the consistency of the individual behavior across moments is highly significant.

Equivalent Risk Indicators: VaR, TCE, and Beyond

While a lot of research concentrates on the respective merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on the equivalence between such indicators. Further, TCE, despite its merits, may not be the most accurate indicator to take into account the nature of probability distribution tails. In this paper, we introduce a new risk indicator that extends TCE to take into account higher-order risks. We compare the quantiles of this indicator to the quantiles of VaR in a simple Pareto framework, and then in a generalized Pareto framework. We also examine equivalence results between the quantiles of high-order TCEs.

The Reflection Effect for Higher-Order Risk Preferences

Abstract Higher-order risk preferences are important determinants of economic behavior. We apply insights from behavioral economics: we measure higher-order risk preferences for pure gains and losses. We find a reflection effect not only for second-order risk preferences, as did Kahneman and Tversky (1979), but also for higher-order risk preferences: we find risk aversion, prudence and intemperance for gains and much more risk-loving preferences, imprudence and temperance for losses. These findings are at odds with a universal preference for combining good with bad or good with good, which previous results suggest may underlie higher-order risk preferences.

Optimal portfolio choice for higher-order risk averters

The effects of higher-order risk aversion on optimal cross-sectional portfolio choice are investigated using portfolio optimization with Stochastic Dominance constraints. Tractable sufficient conditions for higher-degree dominance are introduced that take the form of a system of linear inequalities. Existing studies of active equity industry rotation are extended from lower degrees to higher degrees of dominance. Fourth-degree dominance assumes that investors are ‘prudent’ and ‘temperate’ and therefore like skewness and dislike kurtosis. Using this dominance criterion leads to superior out-of-sample investment performance, by allowing for more concentration in recent winner industries which tend to show persistent positive abnormal returns and a favorable higher-order risk profile due to the industry-level price momentum effect.

Framing effects on the strength of higher-order risk preferences

This study provides the first experimental evidence on whether framing affects elicited intensity of prudence. The framing effect is not significant at the aggregate level, but a closer look shows that more than 70% of subjects are influenced by framing.

Multivariate risk preferences in the quality-adjusted life year model.

The interest in multivariate and higher‐order risk preferences has increased. A growing body of literature has demonstrated the relevance and impact of these preferences, but for health the evidence is lacking. We measure multivariate and higher‐order risk preferences for quality of life (QoL) and longevity, the two attributes of the Quality‐Adjusted Life Year (QALY) model. We observe preferences for a positive correlation between these attributes and for pooling together a fixed loss in one of the attributes and a mean‐zero risk in the other, and for pooling together mean‐zero risks in QoL and longevity. The findings indicate that higher‐order risk preferences are stronger for health than for money. Furthermore, we test if preferences for a risky treatment for a disease affecting only QoL, depend on life expectancy. We find no such a relation, but there is a positive relation between riskiness of a comorbidity affecting life expectancy and risk aversion for a QoL treatment. We therefore observe no definitive deviation from the QALY model, although the model is more robust when expected longevity is high. Our findings suggest that the current practice of cost‐effectiveness analysis should be generalized to account for risk aversion in QoL and longevity, and higher‐order preferences.

Willingness to take financial risks and insurance holdings: A European survey

We investigate the relationship between self-reported willingness to take financial risks and ownership of life insurance and long-term care insurance. For a representative sample of individuals aged 50+ from 14 countries and controlling for demographic and socioeconomic determinants of insurance demand, we find a positive link between willingness to take financial risks and ownership of both long-term care insurance and life insurance. The link is stronger for whole life insurance compared to term life insurance and long-term care insurance. Two robustness tests that (i) use risky asset ownership instead of willingness to take financial risks and (ii) focus on specific demographic and socioeconomic groups confirm the results for life insurance, while the results for long-term care insurance are less clear. Our empirical results cannot be explained by the classical expected utility framework and thus support recent research indicating that alternative models (e.g., higher-order risk attitudes or prospect theory) are needed to explain insurance demand.

Experiencing risk: Higher-order risk attitudes in description- and experience-based decisions.

Risky decisions are often characterized by (a) imprecision about consequences and their likelihoods that can be reduced by information collection, and by (b) unavoidable background risk. This article addresses both aspects by eliciting risk attitude, prudence, and temperance in decisions from description and decisions from experience. The results reveal a novel description-experience gap for prudence and replicate the known gap for risky decisions. While widespread prudence has been observed in decisions form description, we find no evidence of prudent decision making from experience. In decisions from experience people are strongly influenced by the sampled mean, while skewness plays a smaller role than in decisions from description. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Higher Order Risk Preferences in the Koszegi-Rabin

Higher Order Risk Preferences in the Koszegi-Rabin

Supplemental Material for Experiencing Risk: Higher-Order Risk Attitudes in Description- and Experience-Based Decisions

Supplemental Material for Experiencing Risk: Higher-Order Risk Attitudes in Description- and Experience-Based Decisions

Higher-Order Risk–Returns to Education

In the traditional human capital framework, education is often considered as an investment, rather than consumption, while consumption is not necessarily precluded. Whether education is an investment is empirically unclear and relatively under-explored. We shed light on this issue by estimating the risk–return trade-off in the context of education. If education is indeed an investment, risk could play an important role in individual educational decisions just as with risky assets. As portfolio theory predicts, there could be a trade-off between returns to education and risks concerning those returns: higher risks are generally associated with higher returns. We contribute to the literature by proposing various measures of risk based on the entire distribution of returns to education recovered by our nonparametric models. Our results confirm a trade-off between returns and variance. We also found statistically significant impacts for the higher moments: skewness and kurtosis. Interestingly, we found the relationship between mean returns and variance to be linear, and the relationship between expected returns and higher-moments (skewness and kurtosis) is non-linear.

Enabling Warp Speed Using the Hypervelocity Innovation Model: A Blue Print for Drug Development in Pandemics.

Pharmaceutical R&D is organized around prioritized investments, delivering on assets with the greatest return of investments Linear sequencing of trials and financial risks are determinants of speed in an enterprise There is less flexibility in leveraging expertise around priorities that are thrust on the system by external forces This commentary provides an insight into enabling warp speed using a hypervelocity mindset for mobilizing resources and scientific creativity, for accelerated timelines in response to pandemics