Using Four‐Moment Tail Risk to Examine Financial and Commodity Instrument Diversification

We consider the effect of higher moments on diversification, since most assets possess a potential for tail losses. In particular, we examine higher‐moment Value‐at‐Risk measures for individual instruments and diversified portfolios. We find that a naïve futures portfolio is consistently superior to common stock indexes. As few as ten randomly chosen instruments diversify away 85% of the unsystematic four‐moment tail risk. We also compare the two‐ and four‐moment tail risks for different size portfolios. Finally, the tail risk for naïve portfolios varies much less over time than other portfolios.     

Market Price of Insurance Risk Implied by Catastrophe Derivatives

Abstract

Insurance derivatives facilitate the trading of insurance risks on capital markets, such as catastrophe derivatives that were traded on the Chicago Board of Trade. Simultaneously, insurance risks are traded through reinsurance portfolios. In this paper we make inferences about the market price of risk implied by the information embedded in the prices of these two assets.     

Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market

This paper studies the modelling of large diversified portfolios in a financial market with jump-diffusion risks. The portfolios considered include three categories: equal money-weighted portfolios, risk-minimizing portfolios and market indices. Reduced-form dynamics driven jointly by one Brownian motion and one Poisson process are derived for the asymptotics of such portfolios. We prove that derivatives written on a portfolio can be priced by treating the asymptotic dynamics as the underlying process if the number of assets in the portfolio is sufficiently large. Analytical and Monte Carlo value-at-risk can be computed for the portfolios based on their asymptotic dynamics.     

The Impact of Institutional Ownership on the Reinsurance Decision

Risk management has a central role in corporate America. Insurance companies frequently manage risk by purchasing reinsurance because it reduces the downside risk (i.e., bankruptcy risk) of an insurer. Because reinsurance is costly, Mayers and Smith (1990, Journal of Business , 63: 19-40) argue that reinsurance purchases should be negatively associated with the diversification of the owners' portfolios. Further, institutional owners play a significant role in equity markets yet we know little about their effect on firm behavior. The purpose of this study is to examine empirically the influence of institutional ownership on reinsurance for a sample of widely held property-liability insurers. We hypothesize that insurers with higher levels of institutional ownership purchase less reinsurance. Using a sample of 45 publicly traded property-liability insurers from 1995 to 1997, we demonstrate that the utilization of reinsurance decreases as the level of institutional ownership increases. This suggests that the diversification of the owners' portfolios is a determinant of the insurers' reinsurance decisions.     

Law of large numbers and large deviations for dependent risks

We analyse the mathematical structure of models for large risk portfolios, especially for credit risk models. These risk portfolios are modelled using a multivariate mixture model for the dependence structure between the risks. The dependence structures are characterized by latent variables Θ, which play the role of systematic risks. We show that, depending on the choice of the distribution of Θ, there are different asymptotic behaviours for the aggregated risk portfolio, namely law of large numbers/central limit theorem behaviour and large deviation behaviour.     

Fast simulations in credit risk

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.     

Securitization, Insurance, and Reinsurance

This article considers strengths and weaknesses of reinsurance and securitization in managing insurable risks. Traditional reinsurance operates efficiently in managing relatively small, uncorrelated risks and in facilitating efficient information sharing between cedants and reinsurers. However, when the magnitude of potential losses and the correlation of risks increase, the efficiency of the reinsurance model breaks down, and the cost of capital may become uneconomical. At this juncture, securitization has a role to play by passing the risks along to broader capital markets. Securitization also serves as a complement for reinsurance in other ways such as facilitating regulatory arbitrage and collateralizing low-frequency risks.     

Optimal Risk Financing in Large Corporations through Insurance Captives

A captive is an insurance or reinsurance company established by a parent group to finance its own risks. Captives mix internal risk pooling between the business units of the parent group and risk transfer towards the reinsurance market. We analyse captives from an optimal insurance contract perspective. The paper characterises the vertical contractual chain that links firstly business units to insurance captives or to “fronters” through insurance contracts, secondly fronters to reinsurance captives through the cession of risks and thirdly insurance or reinsurance captives to reinsurers through cessions or retrocessions. In particular, the risk cession by fronters to a reinsurance captive trades off the benefits derived from recouped premiums and from the risk-sharing advantage of an “umbrella reinsurance policy”, against the risks that result from the captive liabilities.     

ON INDUSTRY MOMENTUM STRATEGIES

In this article, we investigate industry momentum strategies. We find that industry portfolios that outperformed in the previous month generate on average significantly higher returns in the holding period than those that underperformed. Plain and risk-managed strategies using this short-run industry momentum are not subject to optionality effects. Also, the tail risks of these strategies are uncorrelated with traditional industry momentum strategies. The spread associated with the risk-managed strategy both meets necessary conditions as a risk factor and is significantly priced in the cross-section of U.S. industry portfolios.     

Can tail risk explain size,book‐to‐market,momentum, and idiosyncratic volatility anomalies?

We examine the impact of tail risk on the return dynamics of size, book‐to‐market ratio, momentum and idiosyncratic volatility sorted portfolios. Our time‐series analyses document significant portfolio return exposures to aggregate tail risk. In particular, portfolios that contain small, value, high idiosyncratic volatility and low momentum stocks exhibit negative and statistically significant tail risk betas. Our cross‐sectional analyses at the individual stock level suggest that tail risk helps in explaining the four pricing anomalies, particularly size and idiosyncratic volatility anomalies.     

ESG,time horizons,risks and stock returns

Investment time horizon is an important part of significance of ESG factors. This research examines the role of ESG factors in returns and risks in short- and medium-term investment periods. It compares (a) the returns and risks of ESG portfolios between before scoring and after scoring, and (b) the returns and risks between ESG portfolios and their peers.The main results suggest that after scoring most short-term ESG portfolios have similar returns, but lower risks than before scoring. The returns of ESG portfolios are similar to those of nonESG portfolios for both short- and medium-term. There are more ESG portfolios, whose risks are different from nonESG portfolios, in the short-term investment than in the medium-term.ESG factors therefore play a greater role in risks than in returns, and in the short-term than in the medium-term. Additionally, the role of ESG factors in risks varies from industry to industry.     

Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle

In this article, an optimal reinsurance problem is formulated from the perspective of an insurer, with the objective of minimizing the risk-adjusted value of its liability where the valuation is carried out by a cost-of-capital approach and the capital at risk is calculated by either the value-at-risk (VaR) or conditional value-at-risk (CVaR). In our reinsurance arrangement, we also assume that both insurer and reinsurer are obligated to pay more for a larger realization of loss as a way of reducing ex post moral hazard. A key contribution of this article is to expand the research on optimal reinsurance by deriving explicit optimal reinsurance solutions under an economic premium principle. It is a rather general class of premium principles that includes many weighted premium principles as special cases. The advantage of adopting such a premium principle is that the resulting reinsurance premium depends not only on the risk ceded but also on a market economic factor that reflects the market environment or the risk the reinsurer is facing. This feature appears to be more consistent with the reinsurance market. We show that the optimal reinsurance policies are piecewise linear under both VaR and CVaR risk measures. While the structures of optimal reinsurance solutions are the same for both risk measures, we also formally show that there are some significant differences, particularly on the managing tail risk. Because of the integration of the market factor (via the reinsurance pricing) into the optimal reinsurance model, some new insights on the optimal reinsurance design could be gleaned, which would otherwise be impossible for many of the existing models. For example, the market factor has a nontrivial effect on the optimal reinsurance, which is greatly influenced by the changes of the joint distribution of the market factor and the loss. Finally, under an additional assumption that the market factor and the loss have a copula with quadratic sections, we demonstrate that the optimal reinsurance policies admit relatively simple forms to foster the applicability of our theoretical results, and a numerical example is presented to further highlight our results.     

A Model of Shadow Banking

We present a model of shadow banking in which banks originate and trade loans, assemble them into diversified portfolios, and finance these portfolios externally with riskless debt. In this model: outside investor wealth drives the demand for riskless debt and indirectly for securitization, bank assets and leverage move together, banks become interconnected through markets, and banks increase their exposure to systematic risk as they reduce idiosyncratic risk through diversification. The shadow banking system is stable and welfare improving under rational expectations, but vulnerable to crises and liquidity dry‐ups when investors neglect tail risks.     

Long-term asset tail risks in developed and emerging markets

A power law typically governs the tail decay of financial returns but the constancy of the so-called tail index which dictates the tail decay remains relatively unexplored. We study the finite sample properties of some recently proposed endogenous tests for structural change in the tail index. Given that the finite sample critical values strongly depend on the tail parameters of the return distribution we propose a bootstrap-based version of the structural change test. Our empirical application spans developed and emerging financial asset returns. Somewhat surprisingly, emerging stock market tails are not more inclined to structural change than their developed counterparts. Emerging currency tails, on the contrary, do exhibit structural shifts in contrast to developed currencies. Our results suggest that extreme value theory (EVT) applications in hedging tail risks can assume stationary tail behavior over long time spans provided one considers portfolios that solely consist of stocks or bonds.     

Reinsurance decisions in life insurance: An empirical test of the risk–return criterion

Recent studies have analyzed optimal reinsurance contracts within the framework of profit maximization and/or risk minimization. This type of framework, however, does not consider reinsurance as a tool for capital management and financing. In the present paper, we consider different proportional reinsurance contracts used in life insurance (viz., quota-share, surplus, and combinations of quota-share and surplus) while taking into account the insurer's capital constraints. The objective is to determine how different reinsurance transactions affect the risk/reward profile of the insurer and whether factors, such as claims severity, premiums, and insurer's risk appetite, influence the choice of a proportional reinsurance coverage. We compare each reinsurance structure based on actual insurance company data, using the risk–return criterion. This criterion determines the type of reinsurance that enables insurer to retain the largest underwriting profits and/or minimize the risk of the retained claims while keeping the insurer's risk appetite constant, assuming a given capital constraint. The results of this study confirm that the choice of reinsurance arrangement depends on many factors, including risk retention levels, premiums, and the variance of the sum insured values (and therefore claims). As such, under heterogeneous insurance portfolio single type of reinsurance arrangement cannot maximize insurer's returns and/or minimize the risk, therefore a combination of different reinsurance coverages should be employed. Hence, future research on optimal risk management choices should consider heterogeneous portfolios while determining the effects of different financial and risk management tools on companies' risk–return profiles.     

U.S. Reinsurance Prices, Financial Quality, and Global Capacity

The puzzle of underwriting cycles and insurance crises in property‐liability insurance has led to numerous economic hypotheses and analyses, yet no single theory seems capable of explaining all of its aspects. Reinsurance is hypothesized to be a potential factor in observed cycles in the primary market; despite this, few underwriting cycle studies focus on reinsurance. The purpose of this research is to investigate determinants of reinsurance prices in the U.S. Nonproportional reinsurance is highlighted, since it is designed to cover the tail of the loss distribution and is considered to be relatively riskier than proportional reinsurance as a result. Separate samples of professional U.S. reinsurers for property and for casualty are studied, based upon the reinsurers' writings of property versus casualty nonproportional reinsurance. The sample period is 1991–1995. The results support both the capacity constraint hypothesis and the risky debt hypothesis, and this is the first research to support both. A major innovation in this study is the use of capacity variables that are broken down by major region of the world.     

Does Reinsurance Need Reinsurers?

The reinsurance market is the secondary market for insurance risks. It has a very specific organization. Direct insurers rarely trade risks with each other. Rather, they cede part of their primary risks to specialized professional reinsurers who have no primary business. This article offers a model of equilibrium in reinsurance and capital markets in which professional reinsurers arise endogenously. Their role is to monitor primary insurers credibly, so that insurers can raise capital more easily. In equilibrium, the financial structure of primary insurers consists of a mix of reinsurance and outside capital. The comparative statics yield empirical predictions which are broadly in line with a number of stylized facts from the reinsurance market.     

Rückversicherungen und Alternative Risikotransfers: Ein theoretischer Vergleich

This paper analyses the economic potential of alternative risk transfers (ART) in comparison with classic reinsurance. The particular question discussed is whether ARTs operate as complements or substitutes to reinsurance. We obtain that ARTs are equivalent to reinsurance with respect to their ability to allocate risks optimally. This might be induced by risk aversion of the primary insurer, costs of bankruptcy, solvability regulation, progressive taxes or agency costs. As a consequence, ARTs have to be considered as strong competitors of reinsurance in the standard business of risk transfers. However, ART are dominated by reinsurance with respect to the risk management services which the latter provides.     

Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution

Abstract

Estimation of the tail index parameter of a single-parameter Pareto model has wide application in actuarial and other sciences. Here we examine various estimators from the standpoint of two competing criteria: efficiency and robustness against upper outliers. With the maximum likelihood estimator (MLE) being efficient but nonrobust, we desire alternative estimators that retain a relatively high degree of efficiency while also being adequately robust. A new generalized median type estimator is introduced and compared with the MLE and several well-established estimators associated with the methods of moments, trimming, least squares, quantiles, and percentile matching. The method of moments and least squares estimators are found to be relatively deficient with respect to both criteria and should become disfavored, while the trimmed mean and generalized median estimators tend to dominate the other competitors. The generalized median type performs best overall. These findings provide a basis for revision and updating of prevailing viewpoints. Other topics discussed are applications to robust estimation of upper quantiles, tail probabilities, and actuarial quantities, such as stop-loss and excess-of-loss reinsurance premiums that arise concerning solvency of portfolios. Robust parametric methods are compared with empirical nonparametric methods, which are typically nonrobust.     

Chancen und Herausforderungen der Rückversicherung in der gesetzlichen Krankenversicherung

In 2009 a so-called morbidity orientated risk structure equalization scheme was installed for the German statutory health insurance in order to minimize structural differences between different providers with respect to revenue and expenditures. Even with this mechanism some risks to the individual health insurance providers remain. Reinsurance could be a way to mitigate these risks, but so far only very few contracts have been signed. Moreover the existing reinsurance contracts only focus on the periphery of the statutory health insurance system such as travel health insurance. In this article we therefore analyse existing risks for individual health insurance providers and evaluate their (re-)insurability. Hereafter the potential for reinsurance solutions in the German statutory health insurance itself as well as in newer forms of healthcare provision (e.g. integrated health care and managed care) is discussed. We find that reinsurance may be a reasonable solution for many of the risks in the statutory health insurance scheme. But as research in this area is very young further analysis of the nature of risks is necessary.