Hedging Longevity Risk When Interest Rates are Uncertain

Abstract

This paper proposes an asset liability management strategy to hedge the aggregate risk of annuity providers under the assumption that both the interest rate and mortality rate are stochastic. We assume that annuity providers can invest in longevity bonds, long-term coupon bonds, and shortterm zero-coupon bonds to immunize themselves from the risks of the annuity for the equity holders subject to a required profit. We demonstrate that the optimal allocation strategy can lead to the lowest risk under different yield curves and mortality rate assumptions. The longevity bond can also be regarded as an effective hedging vehicle that significantly reduces the aggregate risk of the annuity providers.     

Hedging Housing Risk*

An unusually rich source of data on housing prices in Stockholm is used to analyze the investment implications of housing choices. This empirical analysis derives market-wide price and return series for housing investment during a 13-year period, and it also provides estimates of the individual-specific, idiosyncratic, variation in housing returns. Because the idiosyncratic component follows an autocorrelated process, the analysis of portfolio choice is dependent upon the holding period. We analyze the composition of household investment portfolios containing housing, common stocks, stocks in real estate holding companies, bonds, and t-bills. For short holding periods, the efficient portfolio contains essentially no housing. For longer periods, low-risk portfolios contain 15 to 50 percent housing. These results suggest that there are large potential gains from policies or institutions that would permit households to hedge their lumpy investments in housing. We estimate the potential value of hedges in reducing risk to households, yet yielding the same investment returns. The value is surprisingly large, especially to poorer homeowners.     

盯市风险下的期货套期保值

本文把盯市风险引入传统的期货套期保值框架，论证了在考虑盯市风险的情况下，一个关注每日最大亏损值的套期保值者会显著地减少他的期货头寸。在一个中期的套期保值期内，该套期保值者的期货套期保值头寸约为其现货头寸的80％。盯市风险的影响随着套期保值期的延长而缓慢减弱。如果套期保值者关注的是每日平均亏损值，在一个中期的套期保值期内盯市风险的影响极小。     

Hedging Housing Risk in London

This paper investigates the benefits of allowing households to compensate the portfolio distortion due to their housing consumption through investments in housing price derivatives. Focusing on the London market, we show that a major loss from over-investment in housing is that households are forced to hold a very risky portfolio. However, the strong performance of the London housing market means that little is lost in terms of expected returns. Even households with limited wealth are better off owning their home rather than renting and investing in financial assets, as long as they are willing to face the financial risk involved. In this context, access to housing price derivatives would benefit most poor homeowners looking to limit their risk exposure. It would also benefit wealthier investors looking for the high returns provided by housing investments without the costs of direct ownership of properties. Comparisons with French, Swedish and U.S. data provide a broader perspective on our findings.     

套期保值与金融衍生品风险管理研究

套期保值是企业经营的重要工具,能够锁定企业的经营成本,规避企业的经营风险。但是,如果套期保值运用不当,则会使企业遭受巨额的损失。本文首先对套期保值的原理及其作用进行基本的介绍,然后,结合我国央企巨亏事件,对套期保值巨亏动因进行深入的分析,以揭示套期保值的潜在风险及其认识误区。最后,对我国企业的套期保值风险控制提出若干建议。     

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.     

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.     

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.     

基于死亡率免疫理论的自然对冲有效性评估

为应对长寿风险对年金产品的影响,本文提出分段对冲策略,并以死亡率免疫和死亡率久期规则为理论基础探讨该策略的有效性问题。为避免传统久期匹配方法中参数估计误差的累积和传导,借助WinBUGS软件和贝叶斯Markov Chain Monte Carlo方法,在统一的计算框架下完成了死亡率预测、死亡率久期计算和对冲效果的数值模拟;并以4种分段组合准备金数据的三维图、方差缩减比(VRR)和VaR值为指标进行长寿风险对冲有效性的对比,结果表明低年龄寿险保单和高年龄年金保单组合具有最平滑的三维图,最小的VRR和VaR值,可明显提高长寿风险自然对冲的有效性。     

A Note on Risk Aversion,Prudence and Portfolio Insurance

This paper examines some properties of portfolio insurance that are linked to the risk aversion and the prudence of the investor. We provide explicit conditions to measure portfolio sensitivity to downside risk. We also characterize the degree of portfolio insurance by means of the ratio of absolute prudence to absolute risk aversion.     

Downside Risk Management of a Defined Benefit Plan Considering Longevity Basis Risk

To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies.     

人口老龄化背景下长寿风险管理方法的探讨

伴随着长寿风险的累积,养老保障型产品提供者管理长寿风险的压力逐步凸显,本文主要对比分析了不同长寿风险管理方法,并通过研究Swiss Re死亡率证券和EIB/BNP长寿债券的设计,分析了各类养老基金通过资本市场实现长寿风险转移与对冲管理的可能方式。     

CEO Age,Risk Incentives,and Hedging Strategy

We test whether managerial preferences explain how firms hedge, using hand‐collected data on derivative portfolios in the oil and gas industry. How firms hedge involves choosing between linear contracts and put options, and deciding whether to finance these hedging positions with cash on hand or by selling call options. The likelihood of being a hedger increases with chief executive officer (CEO) age, and near‐retirement CEOs prefer linear hedging instruments. The predictions of the managerial risk incentives theory of hedging strategy, according to which managers with convex compensation schemes avoid hedging strategies that cap upside potential, find no support in the data.     

Mortality-Indexed Annuities Managing Longevity Risk Via Product Design

Abstract

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries. In its aggregate form, the systematic risk of changes to general mortality patterns, it has the potential for causing large cumulative losses for insurers. Since obvious risk management tools, such as (re)insurance or hedging, are less suited for managing an annuity provider’s exposure to this risk, we propose a type of life annuity with benefits contingent on actual mortality experience.

Similar adaptations to conventional product design exist with investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience can be found in German private health insurance. By effectively sharing systematic longevity risk with policyholders, insurers may avoid cumulative losses.

Policyholders also gain in comparison with a comparable conventional annuity product: Using a Monte Carlo simulation, we identify a significant upside potential for policyholders while downside risk is limited.     

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.     

风险厌恶、失望厌恶和期货套期保值

本文考察失望厌恶对期货套期保值的影响。我们把一个不变的绝对风险厌恶（CARA）效用函数放进Gul（1991）的失望厌恶框架之内。它显示出，一个更厌恶失望的套期保值者会比一个厌恶失望程度较低的套期保值者选择一个更接近于最小方差套期保值的最优期货头寸。当套期保值者厌恶风险的程度较低时，失望厌恶的效应更强。对失望很小程度的厌恶会使一个接近于风险中性的套期保值者持有一个截然不同的头寸。此外，一个更厌恶风险或失望的套期保值者会有一个较低的参考点reference point。数字上的结果显示，厌恶失望的套期保值者的参考点往往会低于传统的厌恶损失的套期保值者的参考点。于是，厌恶失望的套期保值者的行动会更加保守，利用机会牟利的行为会少于传统的厌恶损失的套期保值者。