精算模型在确定给付养老金计划风险管理中的应用

养老基金的风险管理越来越多地受到各国的关注.捐纳金风险和偿付能力风险是确定给付(DB)养老金计划的主要风险,通过分析和评价确定型模型、随机模型和动态随机控制模型等三类精算模型在评估和控制DB计划风险中的作用,说明养老金计划的决策者能够利用精算模型逐年确定恰当的捐纳金并进行有效的风险管理.     

Impact of Replacing a Defined Benefit Pension with a Defined Contribution Plan or a Cash Balance Plan

Abstract

Four pension plan conversions are examined to determine the impact on retirement benefits of workers. The study was based on interviews with top management, employee surveys, and actuarial analysis of retirement benefits under the old and new pension plans. In general, workers who leave the firm prior to the age of early retirement can expect increased benefits under the new defined contribution and cash balance plans, whereas older, more senior workers can expect to accrue smaller benefits after the plan conversions. Recognizing these potential adverse effects, the employers in our studies provided various types of transition benefits to existing workers or gave employees the choice of remaining in the old defined benefit plan. Employee surveys reveal that younger workers are more supportive of the new pension plans than are older workers. These case studies also indicate that communication by managements with their employees is very important to the successful implementation of plan conversions.     

企业年金确定给付型计划与确定缴费型计划研究

文章对我国企业年金的基本理论和缴费进行分析,比较确定给付型企业年金养老计划与确定缴费型企业年金养老计划的各方面的差异。从养老金的给付情况来看,确定给付计划不但可以保证雇员退休后得到稳定,持久的退休金收入,还可以为其提供健康给付、伤残给付等辅助养老金,充分实现了社会保障的目的。从建立成本的情况来看,确定给付型计划更具有科学性和合理性。     

Measuring Basis Risk in Longevity Hedges

Abstract

In examining basis risk in index longevity hedges, it is important not to ignore the dependence between the population underlying the hedging instrument and the population being hedged. We consider four extensions to the Lee-Carter model that incorporate such dependence: Both populations are jointly driven by the same single time-varying index, the two populations are cointegrated, the populations depend on a common age factor, and there is an augmented common factor model in which a population-specific time-varying index is added to the common factor model with the property that it will tend toward a certain constant level over time. Using data from the female populations of Canada and the United States, we show the augmented common factor model is preferred in terms of both goodness-of-fit and ex post forecasting performance. This model is then used to quantify the basis risk in a longevity hedge of 65-year old Canadian females structured using a portfolio of q-forward contracts predicated on U.S. female population mortality. The hedge effectiveness is estimated at 56% on the basis of longevity value-at-risk and 81.61% on the basis of longevity risk reduction.     

The Impact of Taxes on Corporate Defined Benefit Plan Asset Allocation

This paper investigates the extent to which taxes affect a corporation's decision to allocate its defined benefit plan's assets between equity and bonds. Prior theoretical research shows that if a corporation integrates its financial policy and pension investment policy, differences in tax rates create an arbitrage opportunity. The firm's tax benefits from the arbitrage should be positively related to the percentage of its pension assets allocated to bonds. Consistent with this prediction, but contrary to prior empirical work, this paper finds firms' tax benefits are positively and significantly associated with the percentage of their pension assets invested in bonds.     

风险管理策

风险管理在我国企业中起步较晚,加上受过去传统计划经济和固定经营管理模式的影响,企业不同程度地存在着对其重要性认识不足、措施不当的现象。近年来,国资委要求国有企业开展全面风险管理工作,为企业建立完善有效的风险防控机制提供了契机。     

Portfolio Diversification Effects of Downside Risk

Risk managers use portfolios to diversify away the unpricedrisk of individual securities. In this article we compare thebenefits of portfolio diversification for downside risk in casereturns are normally distributed with the case of fat-taileddistributed returns. The downside risk of a security is decomposedinto a part which is attributable to the market risk, an idiosyncraticpart, and a second independent factor. We show that the fat-tailed-baseddownside risk, measured as value-at-risk (VaR), should declinemore rapidly than the normal-based VaR. This result is confirmedempirically.     

Longevity Risk Management in Singapore's National Pension System

Although annuities are a theoretically appealing way to manage longevity risk, in the real world relatively few consumers purchase them at retirement. To counteract the possibility of retirees outliving their assets, Singapore's Central Provident Fund, a national defined contribution pension scheme, has recently mandated annuitization of workers’ retirement assets. More significantly, the government has entered the insurance market as a public‐sector provider for such annuities. This article evaluates the money's worth of life annuities and discusses the impact of the government mandate and its role as an annuity provider on the insurance market.     

Guaranteeing Defined Contribution Pensions: The Option to Buy Back a Defined Benefit Promise

After a long commitment to defined benefit (DB) pension plans for U.S. public sector employees, many state legislatures have introduced defined contribution (DC) plans for their public employees. In this process, investment risk that was previously borne by state DB plans has now devolved to employees covered by the new DC plans. In light of this trend, some states have introduced a guarantee mechanism to help protect DC plan participants. One such guarantee takes the form of an option permitting DC plan participants to buy back their DB benefit for a price. This article develops a theoretical framework to analyze the option design and illustrate how employee characteristics influence the option's cost. We illustrate the potential impact of a buy‐back option in a pension reform enacted recently by the State of Florida for its public employees. If employees were to exercise the buy‐back option optimally, the market value of this option could represent up to 100 percent of the DC contributions over their work life.     

Measuring Longevity Risk: An Application to the Royal Canadian Mounted Police Pension Plan

An employer that sets up a defined benefit pension plan promises to periodically pay a certain sum to each participant starting at some future date and continuing until death. Although both the future beneficiary and the employer can be asked to finance the plan throughout the beneficiary's career, any shortcoming of funds in the future is often the employer's responsibility. It is therefore essential for the employer to be able to predict with a high degree of confidence the total amount that will be required to cover its future pension obligations. Applying mortality forecasting models to the case of the Royal Canadian Mounted Police pension plan, we illustrate the importance of mortality forecasting to value a pension fund's actuarial liabilities. As future survival rates are uncertain, pensioners may live longer than expected. We find that such longevity risk represents approximately 2.8 percent of the total liability ascribable to retired pensioners (as measured by the relative value at risk at the 95th percentile) and 2.5 percent of the total liabilities ascribable to current regular contributors. Longevity risk compounds the model risk associated with not knowing what is the true mortality model, and we estimate that model risk represents approximately 3.2 percent of total liabilities. The compounded longevity risk therefore represents almost 6 percent of the pension plan's total liabilities.     

经济下行、PPP风险来源与机制设计

自金融危机之后,PPP模式在全球范围内遭到了广泛的质疑,曾经被视为发展公共基础设施建设重要手段的PPP模式沦为各国地方政府沉重的财政负担.为此,我们通过分析经济下行情境下PPP模式在欧盟国家的风险来源,研究了中国现行PPP模式机制设计中的风险识别与分配机制.结果 显示,现阶段物有所值定性评价、地方财政压力测算与风险分配框架受到地方政府强大内生性需求的影响,在经济下行情境中一部分潜在的风险就很容易被忽视:(1)物有所值定性评价结果高度一致,政府官员背景评审专家影响了最终评价结果;(2)地方财政承受能力论证测算以经济繁荣时期的财政增长率为基准,低估了经济下行情境中PPP项目财政支出对于财政预算的压力;(3)风险分配框架不合理,倾向于由政府与社会资本共同承担,将前期风险识别与谈判成本转嫁到了后期再协商阶段.上述发现有助于揭示我国PPP模式推广过程中的机制缺陷,为提高PPP项目抵御未来不确定性的能力,进一步规范中国PPP模式在公共基础设施领域中的应用提供了指引.     

A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions

A method of calculating the downside risk by fitting multivariate nonnormal distributions to financial data is proposed. Firstly, maximum likelihood method by using the random numbers of the Pearson distribution system are introduced. The rates of returns of the stock index are fitted to the multivariate nonnormal distributions by this method. Secondly, the cases of calculating the downside risk by the standard deviation, the percentile of historical simulation method and this method, are compared.     

Securitization of Longevity Risk in Reverse Mortgages

Abstract

The reverse mortgage market has been expanding rapidly in developed economies in recent years. The onset of demographic transition places a rapidly rising number of households in an age window in which reverse mortgages have potential appeal. Increasing prices for residential real estate over the last decade have further stimulated interest.

Reverse mortgages involve various risks from the provider-s perspective that may hinder the further development of these financial products. This paper addresses one method of transferring and financing the risks associated with these products through the form of securitization. Securitization is becoming a popular and attractive alternative form of risk transfer of insurance liabilities. Here we demonstrate how to construct a securitization structure for reverse mortgages similar to the one applied in traditional insurance products.

Specifically, we investigate the merits of developing survivor bonds and survivor swaps for reverse mortgage products. In the case of survivor bonds, for example, we are able to compute premiums, both analytically and numerically through simulations, and to examine how the longevity risk may be transferred to the financial investors. Our numerical calculations provide an indication of the economic benefits derived from developing survivor bonds to securitize the “longevity risk component” of reverse mortgage products. Moreover, some sensitivity analysis of these economic benefits indicates that these survivor bonds provide for a promising tool for investment diversification.     

Securitization of Longevity Risk Using Percentile Tranching

Securitizations that transfer risk to the financial markets are a potential solution to longevity risk in the annuity business. The classical Lee–Carter model is applied to generate the future stochastic survival distribution. A method to design inverse survivor bonds using percentile tranches and to calculate the security prices is presented. The percentile tranche method is a simple and practical way for the issuer to design and price the security. This method can serve to identify the risk–yield relationship, which can provide investors with clear insight regarding the appropriate choice of tranches.     

Effects of Health and Longevity on Financial Risk Tolerance

We investigate the effects of health and life expectancy on tolerance of financial risk. Using a standard life-cycle model, we find that the effects of health and life expectancy on preferences over lifetime-income risk are theoretically ambiguous. However, risk tolerance is independent of health and life expectancy when utility takes one of the standard (harmonic absolute risk aversion) functional forms or when optimal consumption is constant over time. Our empirical results, using data from a stated-preference survey (n=2,795), suggest that financial risk tolerance is positively associated with both health and life expectancy; hence utility is not consistent with standard functional forms.     

A Cautionary Note on Natural Hedging of Longevity Risk

In this article, we examine the so-called natural hedging approach for life insurers to internally manage their longevity risk exposure by adjusting their insurance portfolio. In particular, unlike the existing literature, we also consider a nonparametric mortality forecasting model that avoids the assumption that all mortality rates are driven by the same factor(s).

Our primary finding is that higher order variations in mortality rates may considerably affect the performance of natural hedging. More precisely, although results based on a parametric single factor model—in line with the existing literature—imply that almost all longevity risk can be hedged, results are far less encouraging for the nonparametric mortality model. Our finding is supported by robustness tests based on alternative mortality models.