Optimal reinsurance under general law-invariant risk measures

In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided.     

Winners and losers: German equity mutual funds

We investigate the performance of winners and losers for German equity mutual funds (1990–2009), using empirical order statistics. When using gross returns and the Fama–French three-factor model, the number of statistically significant positive alpha funds is zero but increases markedly when market timing variables are added. However, when using a ‘total performance’ measure (which incorporates both alpha and the contribution of market timing), the number of statistically significant winner funds falls to zero. The latter is consistent with the bias in estimated alphas in the presence of market timing. We also find that many poorly performing funds are unskilled rather than unlucky.     

On Mixed and Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented.     

General convex order on risk aggregation

Using a general notion of convex order, we derive general lower bounds for risk measures of aggregated positions under dependence uncertainty, and this in arbitrary dimensions and for heterogeneous models. We also prove sharpness of the bounds obtained when each marginal distribution has a decreasing density. The main result answers a long-standing open question and yields an insight in optimal dependence structures. A numerical algorithm provides bounds for quantities of interest in risk management. Furthermore, our numerical results suggest that the bounds obtained in this paper are generally sharp for a broader class of models.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.     

A performance measure for mutual funds using the Connor-Korajczyk methodology: An empirical study

This article examines the performance of a sample of bond, stock, and balanced funds. Close attention is paid to the bond versus equity composition of the mutual funds and how this asset composition affects the performance measure. This research includes the period from January 1977 through March 1984. The results of the analysis show that none of these mutual funds categories has outperformed the market. Fund managers in this sample are unable to predict security prices consistently to warrant the associated costs. In addition, the “goodness of fit” varied significantly between the types of funds examined.     

Circuit Breakers and the Tail Index of Equity Returns

Using the tail index of returns on U.S. equities as a summarymeasure of extreme behavior, we examine changes in the equitymarkets surrounding the development of program trading for portfolioinsurance, the crash of 1987, and the subsequent introductionof circuit breakers and other changes in market architecture.Recently-developed tests for the null of constancy of the tailindex, versus the alternative of a change at an unknown date,permit inference on changes in extreme behavior over a longtime period while allowing for second-moment dependence in thereturn data. We find strong evidence of a decrease in the tailindex (increase in the probability of extreme events) aroundthe beginning of large-scale program trading, and weaker, butstill substantial, evidence of further significant change inthe tail index following the introduction of circuit breakers.Point estimates of the tail index suggest that the tail indexmay have roughly regained pre-program trading levels. More generally,the results tend to suggest that long samples of U.S. equityreturns should not be treated as samples from a single distributionfunction, particularly in examining extremes.     

Comparisons of aggregate claim numbers and amounts: a study of heterogeneity

In this paper, we investigate how the heterogeneity among occurrence probabilities and claim severities affects the aggregate claim numbers and aggregate claim amount for an insurance portfolio. We show that higher heterogeneity (and dependence) among occurrence probabilities results in both smaller aggregate claim numbers and aggregate claim amount in the sense of the mean residual lifetime order. We also prove that as the heterogeneity among the claims increases, the aggregate claim amount increases in the sense of the usual stochastic order when the vector of occurrence probabilities is left tail weakly stochastic arrangement increasing. These theoretical findings are applied to (i) study ordering properties of convolutions of binomial random variables, (ii) provide upper bounds for the mean residual lifetime functions of the aggregate claim numbers and amount, and (iii) compare stop-loss premiums and risk capital of different insurance portfolios.     

Active management, fund size, and bond mutual fund returns

Conventional wisdom holds that bonds are relatively homogenous investments compared to equities. Consequently, factors that explain variation in returns among bond mutual funds may differ in magnitude from those for equity mutual funds. In this study, a time-series cross-sectional analysis is employed to investigate the relationship between a bond fund's risk-adjusted return and specific fund attributes. Results indicate that a bond fund's past performance does not predict future performance and that bond fund managers are generally ineffective at increasing risk-adjusted returns. However, unlike equity mutual funds, bond mutual funds do appear to enjoy economies of scale.     

Stochastic orders in dynamic reinsurance markets

We consider a dynamic reinsurance market, where the traded risk process is driven by a compound Poisson process and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the minimal martingale measure and the minimal entropy martingale measure are determined, and some comparison results for prices under different martingale measures are provided. This leads to a simple stochastic ordering result for the optimal martingale measures. Moreover, these optimal martingale measures are compared with other martingale measures that have been suggested in the literature on dynamic reinsurance markets.Received: March 2004, Mathematics Subject Classification (2000): 62P05, 60J75, 60G44JEL Classification: G10     

Country and industry concentration and the performance of international mutual funds

We examine the relation between country and industry portfolio concentration and performance using a data set of international equity mutual funds. When sorted by concentration measures, funds in the most concentrated quintile outperform those in the most diversified quintile by 0.16% and 0.30% monthly in country and industry dimensions, respectively. Further analysis shows that the superior performance of concentrated funds is largely driven by industry rather than country concentration, suggesting the existence of global industry private information. Finally, we show that industry-concentrated funds rotate top-holding industries less frequently than their diversified counterparts, and that the industries these funds purchase subsequently outperform the industries they sell.     

Market structure and diversification of mutual funds

This study characterizes a systematic relationship between the diversification incentives and the market structure of the mutual funds industry with investors differentiated by their attitude towards risk. With sufficiently low competition the subgame perfect portfolio equilibrium exhibits maximal risk differentiation. With intensified competition intermediate funds, i.e., those attracting investors with intermediate attitudes towards risk, select diversified portfolios. Finally, we offer a general characterization of how imperfect competition between risk-differentiated funds will generate an equilibrium relationship between risk and expected returns.     

Update rules for convex risk measures

In the first part of the paper we investigate the properties that describe the intertemporal structure of dynamic convex risk measures. The usual backward approach to dynamic risk assessment leads to strong and weak versions of time consistency. As an alternative, we introduce a forward approach of consecutivity. In the second part we discuss the problem of how to update a convex risk measure when new information arrives. We analyse to what extent the above properties are appropriate update criteria.     

投连险与基金信息披露的比较分析

与国际通行做法相比,我国投连险投资账户多履行了一个资产组合管理职能,这就使得投连险投资账户与基金具有了一定的可比性。本文基于投连险与基金信息披露的比较视角,指出了我国投连险信息披露存在的问题,并从保险公司、监管部门、社会力量三个方面提出了相应的对策。     

Information sharing between mutual funds and auditors

This paper examines whether there is information sharing between mutual funds and their auditors about the auditors’ other listed firm clients. Using data from the Chinese market, we find that mutual funds earn higher profits from trading in firms that share the same auditors. The effects are more pronounced when firms have a more opaque information environment and when the audit partners for the fund and the partners for the listed firm share school ties. The evidence is consistent with information flowing from auditors to mutual funds, providing mutual funds with an information advantage in firms that share the same auditors. Our findings are robust to the use of audit-firm mergers and acquisitions (M&As) as exogenous shocks and several other robustness checks. We further find that auditors benefit by charging higher audit fees for mutual fund clients and by improving their audit quality for listed firm clients. Our study provides evidence of bi-directional information sharing between two important market intermediaries.     

Convex risk measures for the aggregation of multiple information sources and applications in insurance

We propose a novel class of convex risk measures, based on the concept of the Fréchet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty.     

Limited attention and portfolio choice: The impact of attention allocation on mutual fund performance

This study proposes that the performance of mutual fund managers is linked to how efficiently they allocate attention across assets in their investment set. Motivated by existing models of optimal portfolio choice and rational inattention, we posit that the efficiency of attention allocation increases when a manager chooses larger (smaller) active positions in assets that need more (less) information acquisition effort to resolve uncertainty about future payoffs. We show that the efficiency of attention allocation has a significantly positive impact on future fund performance. Efficient attention allocation has a lesser impact on performance as the total demands on a manager's limited attention increase.