Solvency II reporting: How to interpret funds’ aggregate solvency capital requirement figures

Depending on the current risk exposure of an insurance company, the impact of buying an additional unit of a fund on an insurer’s overall Solvency II capital charges, i.e., the Solvency Capital Requirement (SCR), will differ. We call this impact the fund’s SCR contribution and show in which boundaries it lies if only the fund’s aggregate sub-SCR figures are known but not the risk exposures of the insurance company buying the fund. The upper bound of this range, the worst-case SCR contribution, can be used as a conservative measure to assess funds’ Solvency II risk contributions or to assign them to different Solvency II risk categories. We believe that providing funds’ worst-case SCR contributions can be useful information to insurance companies when screening from a broad investment universe.     

Valuation of intergenerational transfers in funded collective pension schemes

This paper applies contingent claim analysis to value pension contracts for real-life collective pension plans with intergenerational risk sharing and offering DB-like benefits. We rewrite the balance sheet of such a pension fund as an aggregate of embedded generational options. This implies that a pension fund is a zero-sum game in value terms, so any policy change inevitably leads to value transfers between generations. We explore intergenerational value transfers that may arise from a plan redesign or from changes in funding policy and risk sharing rules. We develop a stochastic framework which accounts for time-varying investment opportunities and computes the embedded generational options. Changes in the values of the generational options enable us to evaluate the impact of policy modifications in the pension contract with respect to intergenerational transfers and redistribution. We find that a switch to a less risky asset mix is beneficial to elderly members at the expense of younger members who lose value. A reallocation of risk bearing from a plan with flexible contributions and fixed benefits to a plan with fixed contributions and flexible benefits leads to value redistribution from older plan members to younger ones.     

Optimal investment for a pension fund under inflation risk

This paper investigates an optimal investment problem faced by a defined contribution (DC) pension fund manager under inflationary risk. It is assumed that a representative member of a DC pension plan contributes a fixed share of his salary to the pension fund during the finite time horizon [0, T]. The pension contributions are invested continuously in a risk-free bond, an index bond and a stock. The objective is to maximize the expected utility of terminal value of the pension fund. By solving this investment problem we present a way to deal with the optimization problem, in case there is a (positive) endowment (or contribution), using the martingale method.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

A note on statistical models for individual hedge fund returns

In recent years, a large number of research papers and monographs on the analysis of hedge fund returns have been published. Typically, the authors of these studies implicitly or explicitly treat monthly returns of hedge funds as independent and identically distributed observations. The Hedge Fund Index might be able to serve that role. But the returns of an individual hedge fund are not like that. They behave autoregressively depending on the time periods. This stochastic behavior should be modeled as a combined/regime switching stochastic process of two processes: i.i.d. process and autoregressive process. This paper first depicts the autoregressiveness of hedge fund returns. Then we introduce our statistical model for returns of an individual hedge fund and then, with our retrospective view, we perform several data analyses for individual hedge funds’ return data.     

Dynamic asset allocation for varied financial markets under regime switching framework

Asset allocation among diverse financial markets is essential for investors especially under situations such as the financial crisis of 2008. Portfolio optimization is the most developed method to examine the optimal decision for asset allocation. We employ the hidden Markov model to identify regimes in varied financial markets; a regime switching model gives multiple distributions and this information can convert the static mean–variance model into an optimization problem under uncertainty, which is the case for unobservable market regimes. We construct a stochastic program to optimize portfolios under the regime switching framework and use scenario generation to mathematically formulate the optimization problem. In addition, we build a simple example for a pension fund and examine the behavior of the optimal solution over time by using a rolling-horizon simulation. We conclude that the regime information helps portfolios avoid risk during left-tail events.     

Effective models for reactive flow under a dominant Péclet number and order one Damköhler number: Numerical simulations

The paper is devoted to the longitudinal dispersion of a soluble substance released in a steady laminar flow through a slit channel with heterogeneous reaction at the outer wall. The reactive transport happens in the presence of a dominant Péclet number and order one Damköhler number. In particular, these Péclet numbers correspond to Taylor’s dispersion regime. An effective model for the enhanced diffusion in this context was derived recently. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. In the present paper, we show through numerical simulations the efficiency of this new model. In particular, using Taylor’s ‘historical’ parameters, we illustrate that our derived contributions are important and that using them is necessary in order to simulate correctly the reactive flows. We emphasize three main points. First, we show how the effective diffusion is enhanced by chemical effects at dispersive times. Second, our model captures an intermediate regime where the diffusion is anomalous and the distribution is asymmetric. Third, we show how the chemical effects also slow down the average speed of the front.     

Markowitz’s mean-variance asset-liability management with regime switching: A continuous-time model

This paper considers an asset-liability management (ALM) problem under a continuous-time Markov regime-switching model. By adopting the techniques of [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model. SIAM J. Control Optim. 42, 1466-1482], we investigate the feasibility, obtain the optimal strategy, delineate the efficient frontier, and establish the associated mutual fund theorem.     

Markowitz’s mean-variance asset-liability management with regime switching: A continuous-time model

This paper considers an asset-liability management (ALM) problem under a continuous-time Markov regime-switching model. By adopting the techniques of [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model. SIAM J. Control Optim. 42, 1466–1482], we investigate the feasibility, obtain the optimal strategy, delineate the efficient frontier, and establish the associated mutual fund theorem.     

一直在努力?——基金管理者买卖行为的有效性分析

通过构建收益缺口-基金的净资产收益与投资组合收益之差,探讨了我国证券市场中开放式基金管理者的买卖行为及其对基金业绩的影响.研究结果表明,在2004至2007年中,基金月收益缺口的均值显著大于零,表明基金管理者的努力总体上能增加基金的价值;投资者若模拟基金的股票构成进行投资,在熊市中,其平均回报小于基金的收益,但在牛市中,却显著地大于基金的收益,这一差异对配置型基金更明显.同时,基金收益缺口的大小与基金的类型和规模显著相关.     

赎回风险约束的开放式基金管理费研究

从赎回风险的视角研究开放式基金的管理费.以赎回风险为内生变量构建了基金管理人的动态投资决策模型,利用动态优化的Bellman原理得到了最优管理费.进一步分析发现:一是基金管理费与基金管理人的投资能力正相关,即基金管理人的投资能力越强,收取的基金管理费越多;二是基金管理费与投资者的赎回率负相关,即投资者的赎回率越大,基金管理费越少.而且选取中国股票型开放式基金的数据构建VAR计量经济模型,检验基金管理人的投资能力与投资者的赎回风险对基金管理费的影响,实证结果支持理论模型的结论.     

基金契约中代理问题存在性研究

基金投资与基金经理之间的关系是一种委托一代理关系，这种委托一代理关系集中体现在基金契约中。为了激励基金经理能按照最大化基金投资的效用行动，减少代理问题，人们设计了各种类型的基金契约。本以一个最常用的线性基金契约为例，讨论分析了其中代理问题的存在性。     

Optimal management and inflation protection for defined contribution pension plans

Due to the increasing risk of inflation and diminishing pension benefits, insurance companies have started selling inflation-linked products. Selling such products the insurance company takes over some or all of the inflation risk from their customers. On the other side financial derivatives which are linked to inflation such as inflation linked bonds are traded on financial markets and appear to be of increasing popularity. The insurance company can use these products to hedge its own inflation risk. In this article we study how to optimally manage a pension fund taking positions in a money market account, a stock and an inflation linked bond, while financing investments through a continuous stochastic income stream such as the plan member’s contributions. We use the martingale method in order to compute an analytic expression for the optimal strategy and express it in terms of observable market variables.     

基金经理过度自信对基金收益与风险的影响研究

本文扩展了以前的研究范围，考察了基金经理过度自信对基金收益与风险的影响。与以前研究不同的是。我们在模型中引进了基金经理的能力这一参数，并假设基金经理从接收到的信号中提取信息的多少依赖于其能力的大小。我们发现。过度自信导致基金经理交易较多数量的风险资产。结果使得基金获得了较高的收益。但同时基金的风险也较高。从不同的角度。我们进一步证实了以前的研究结论。     

基金投资行为与投资绩效实证研究

本文主要研究2000年末到2004年6月国内基金投资行为与投资绩效。我们将基金交易行为分为:新进入、完全退出和对仓位进行调整3类,并分别研究其投资行为。研究结果显示,我国基金交易频率很高,近90%的基金采用动量投资策略,基金新进入股票时动量效应最强。价值型基金更易采取动量投资策略,高动量组收益高于低动量组收益。     

中证开放式基金指数和GARCH-M模型

基于开放式基金指数周收益率时间序列的非正态性和厚尾特性,以中证开放式基金指数为例,运用GARCH-M模型进行研究,系统地分析我国不同类型的开放式基金的投资风险.实证分析表明:GARCH-M模型对中证开放式基金指数周收益率的拟合效果较好,并为预测我国开放式基金的投资风险提供了科学依据.     

“高水位”法下私募基金经理的激励与风险选择

私募基金契约本质上是一种复杂的委托—代理关系。本文基于现行私募基金行业标准的“2-20”合同,在委托代理框架下,结合前景理论,讨论了“高水位”法对基金经理的激励效应及其导致的冒险行为。研究发现,在高水位激励下产生“承诺升级”现象,当基金经理在评估期对基金业绩超过“高水位”持乐观信念时,经理倾向采用保守型投资策略;反之其倾向激进的投资策略。由此提出“2-20”合同改进：业绩激励乘数随着基金经理的差异信念而时变,同时纳入对基金风险范围的约束,以防范代理投资过程中的过度冒险问题。     

Linear response in the nonequilibrium zero range process

We explore a number of explicit response formulæ around the boundary driven zero range process to changes in the exit and entrance rates. In such a nonequilibrium regime kinetic (and not only thermodynamic) aspects make a difference in the response. Apart from a number of formal approaches, we illustrate a general decomposition of the linear response into entropic and frenetic contributions, the latter being realized from changes in the dynamical activity at the boundaries. In particular in this way one obtains nonlinear modifications to the Green–Kubo relation. We end by bringing some general remarks about the situation where that nonequilibrium response remains given by the (equilibrium) Kubo formula such as for the density profile in the boundary driven Lorentz gas.     

风险内生的委托代理模型研究

证券投资基金的委托代理关系与一般的委托代理关系不同,在一般的委托代理关系中,产出的风险是外生的,而基金产出的风险是内生的,即风险是由基金管理人来选择的.在模型假设的背景下,在不考虑基金管理人的努力成本时,基金委托代理关系中不存在道德风险问题.如果考虑基金管理人的努力成本,当其行为不可观测时,基金投资者无法通过契约参数的变化来影响基金管理人的努力水平,但此时投资组合的风险水平将低于基金管理人行为可观测时的情况.实证研究证实了基金收益分享比例与基金管理人努力程度无关的模型推论.     

Valuation of risk-based premium of DB pension plan with terminations

This paper concentrates on the premium valuation of pension insurance provided by the Pension Benefit Guaranty Corporation (PBGC). The PBGC provides a defined benefit pension sponsor with coverage in case that the pension fund fails to make pension payments as promised or that the plan sponsor does not stay in business any more. In practice, both the pension fund and the sponsor assets play a critical role in fulfilling the commitment of pension payments, and thereby it is not reasonable to isolate the risk of distress termination of the sponsor assets from that of the premature termination of the pension fund. Different from previous works in which the premature termination of the pension fund and the distress termination of the sponsor assets are analyzed separately, our model examines the situation in which retirees suffer the risk of two types of terminations at the same time. We evaluate the risk-based fair premium under the framework that the pension fund and the sponsor assets are correlated and subject to the risk of the involuntary termination (i.e., premature termination) and the distress termination, respectively. In this framework, we manage to obtain closed-form pricing formulas. Our model is more practical because of the realistic design of termination schemes. Numerical simulations are also carried out to demonstrate our findings. Our numerical experiments validate that a variable rate premium is more appropriate for the PBGC to implement.