Dynamic portfolio choice with deferred annuities

We derive the optimal life-cycle portfolio choice and consumption pattern for households facing uncertain labor income, risky capital market, and mortality risk. In addition to stocks and bonds, the households have access to deferred annuities. Deferred payout life annuities are financial contracts providing life-long income to the annuitant after a specified period of time conditional on survival. We find that deferred annuities play an important role in household portfolios and generate significant welfare gains. Households with high benefits from state pensions, moderate risk aversion and moderate labor income risk purchase deferred annuities from age 40 and gradually increase their portfolio share. At retirement, deferred annuities account for 78% of total financial wealth. Households with low state pensions and high labor income risk purchase more annuities and earlier. Uncertainty with respect to future mortality rates has the same effect, i.e. household hedge against longevity risks using deferred annuities.     

Will we outlive our money?

Fewer and fewer Americans retire with benefits in the form of life annuities. The author raises key issues regarding the increased importance that uncertainty plays in determining retirement income. The key issues include longevity risk and how savings withdrawals rates will be affected at varying rates of return.     

Endogenous differential mortality,non-contractible effort and non-linear taxation

This paper studies a problem of non-linear taxation when individuals have different longevities resulting from a non-monetary effort (like exercising). We first present the laissez-faire and the first best. Like Becker and Philipson (J. Polit. Econ. 106(3):551–573, 1998), we find that the laissez-faire level of effort is too high compared with the first best, because individuals do not internalize the impact of survival on the return of their savings. We also claim that because of its non-monetary form, effort is not contractible. That is why we modify our framework and assume, for the rest of the paper, that effort is determined by the individual while the social planner only allocates consumptions. It turns out that, under full information, a tax on the return of annuitized savings is desirable for both types. This tax is higher for the low-survival individual. Under asymmetric information, the low-survival individual still faces a tax while the high-survival individual might now face a positive or negative tax on annuities. Interestingly, our results depend on the value of life.     

Mortality Risk and the Value of a Statistical Life: The Dead-Anyway Effect Revis(it)ed

In the expected-utility theory of the monetary value of a statistical life, a well-known result found by Pratt and Zeckhauser [1996] asserts that an individuals’ willingness to pay (WTP) for a marginal reduction in mortality risk increases with the initial level of risk. Their reasoning is based on the so-called “dead-anyway effect” which states that marginal utility of a dollar in the state of death is smaller than in the state of survival. However, this explanation is based on the absence of markets for contingent claims, i.e. annuities and life insurance. This paper reexamines the relationship between WTP and the level of risk under more general circumstances and establishes two main results: first, when insurance markets are perfect, for a risk-averse individual without a bequest motive, marginal WTP for survival does increase with the level of risk but this occurs for a different reason, namely an income effect. Secondly, when the individual has a bequest motive and is endowed with a sufficient amount of wealth from human capital, the effect of initial risk on WTP for survival is reversed: the higher initial risk the lower the value of a statistical life. In the imperfect-markets case we interpret this result as a “constrained-bequest effect”.JEL Classification No.: D8, H43, I18     

Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data

Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status.     

Aggregate external financing and savings waves

US data display aggregate external financing and savings waves. Firms can allocate costly external finance to productive capital, or to liquid assets with low physical returns. If firms raise costly external finance and accumulate liquidity, either the cost of external finance is relatively low or the total return to liquidity accumulation, including its shadow value as future internal funds, is particularly high. We formalize this intuition by estimating a dynamic model of firms׳ financing and savings decisions, and use our model along with firm level data to construct an empirical estimate of the average cost of external finance from 1980 to 2014.     

Partial Hedging for Equity-Linked Products Using Risk-Minimizing Strategies

In this article, we consider the pricing and hedging of equity-indexed annuities (EIAs) using local risk-minimizing strategies as well as evaluating the capital requirement for these products. Since these products involve mortality as well as financial risks, we integrate mortality risk and propose partial hedging strategies that protect the insurer based on risk measures. The framework we present makes use of sequential local risk-minimizing strategies to take into account all intermediate requirements. To demonstrate the flexibility of this framework we present numerical examples featuring point-to-point EIAs with a two-state regime-switching equity model.     

On the Distributional Conditions for a Consumption-oriented Three Moment CAPM

In this paper, we develop sufficient conditions on probability distributions for a three moment (mean, variance, and skewness) consumption-oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying nonincreasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return, and preference for positive skewness. For otherwise arbitrary preferences, we show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption-oriented CAPM.     

Capital Account Liberalization and Aggregate Productivity: The Role of Firm Capital Allocation

We study the effects of capital account liberalization on firm capital allocation and aggregate productivity in 10 Eastern European countries. Using a large firm‐level data set, we show that capital account liberalization decreases the dispersion in the return to capital across firms, particularly in sectors more dependent on external finance. We provide evidence that capital account liberalization improves capital allocation by allowing financially constrained firms to demand more capital and produce at a more efficient level. Finally, using a model of misallocation we document that capital account liberalization increases aggregate productivity through more efficient capital allocation by 10% to 16%.     

Uncertainty on survival probabilities and solvency capital requirement: application to long-term care insurance

In this paper, we focus on uncertainty issues on disabled lives survival probabilities of LTC insurance policyholders and its consequences on solvency capital requirement. Among the risks affecting long-term care portfolios, special attention is addressed to the table risk, i.e. the risk of unanticipated aggregate mortality, arising from the uncertainty in modeling LTC claimants survival law. The table risk can be thought as the risk of systematic deviations referring not only to a parameter risk but, as well, to any other sources leading to a misinterpretation of the life table resulting for example from an evolution of medical techniques or a change in rules of acceptance. In fine, the idea is to introduce the risk of systematic deviations arising from the uncertainty on the disabled lives death probabilities directly. We analyze the consequences of an error of appreciation on the disabled lives survival probabilities in terms of level of reserves and describe a framework in an Own Risk and Solvency Assessment perspective to measure the gap between the risk profile from the standard formula to the risk analysis specific to the organism.     

Human Survival at Older Ages and the Implications for Longevity Bond Pricing

Abstract

Governments are concerned about the future of pension plans, for which increasing longevity is judged to be an important risk to their future viability. We focus on human survival at age 65, the starting age point for many pension products. Using a simple model, we link basic measures of life expectancy to the shape of the human survival function and consider its various forms. The model is then used as the basis for investigating actual survival in England and Wales. We find that life expectancy is increasing at a faster rate than at any time in history, with no evidence of this trend slowing or any upper age limit. With interest growing in the use of longevity bonds as a way to transfer longevity risks from pension providers to the capital markets, we seek to understand how longevity drift affects pension liabilities based on mortality rates at the point of annuitization, versus what actually happens as a cohort ages. The main findings are that longevity bonds are an effective hedge against longevity risk; however, it is not only the oldest old that are driving risk, but also more 65-year-olds reaching less extreme ages such as 80. In addition, we find that the possibility of future inflation and interest rates could be as an important a risk to annuities as longevity itself.     

The fair value of guaranteed annuity options

We discuss the fair valuation of Guaranteed Annuity Options, i.e. options providing the right to convert deferred survival benefits into annuities at fixed conversion rates. The use of doubly stochastic stopping times and of affine processes provides great computational and analytical tractability, while enabling to set up a very general valuation framework. For example, the valuation of options on traditional, unit-linked or indexed annuities is encompassed. Moreover, security and reference fund prices may feature stochastic volatility or discontinuous dynamics. The longevity risk is also taken into account, by letting the evolution of mortality present stochastic dynamics subject not only to random fluctuations but also to systematic deviations.     

AN ANALYSIS OF REGULATED RATES OF RETURN FOR WHOLLY OWNED SUBSIDIARIES

Two methods are used by public utility regulators to set the allowed rate of return to a wholly owned subsidiary: the “independent firm” approach and the “double leverage” approach. Neither approach is consistent with any existing theory of firm valuation. The contribution of this paper is to derive from standard valuation theory a “divisional cost of capital” specification of the allowed rate of return to a wholly owned subsidiary. On the basis of this specification it is shown that the independent firm approach allows shareholders to capture the value created by the interest tax savings on parent debt. It is also reconfirmed that the double leverage approach induces cross-subsidization since it allows each subsidiary to earn the same rate of return on equity regardless of the level of risk specific to the subsidiary.     

Examining the Relationships between Capital,Risk and Efficiency in European Banking

This paper analyses the relationship between capital, risk and efficiency for a large sample of European banks between 1992 and 2000. In contrast to the established US evidence we do not find a positive relationship between inefficiency and bank risk‐taking. Inefficient European banks appear to hold more capital and take on less risk. Empirical evidence is found showing the positive relationship between risk on the level of capital (and liquidity), possibly indicating regulators' preference for capital as a mean of restricting risk‐taking activities. We also find evidence that the financial strength of the corporate sector has a positive influence in reducing bank risk‐taking and capital levels. There are no major differences in the relationships between capital, risk and efficiency for commercial and savings banks although there are for co‐operative banks. In the case of co‐operative banks we do find that capital levels are inversely related to risks and we find that inefficient banks hold lower levels of capital. Some of these relationships also vary depending on whether banks are among the most or least efficient operators.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

A General Semi-Markov Model for Coupled Lifetimes

Joint-life annuities with a high last survivor benefit play an important role in the optimal annuity portfolio for a retired couple. The dependence between coupled lifetimes is crucial for valuing joint-life annuities. Existing bivariate modeling of coupled lifetimes is based on outdated data with limited observation periods and does not take into account mortality improvement. In this article, we propose a transparent and dynamic framework for modeling coupled lifetime dependence caused by both marital status and common mortality improvement factors. Dependence due to marital status is captured by a semi-Markov joint life model. Dependence due to common mortality improvement, which represents the correlation between mortality improvement patterns of coupled lives, is incorporated by a two-population mortality improvement model. The proposed model is applied to pricing the longevity risk in last survivor annuities sold in the United States and the United Kingdom.     

There is a risk-return trade-off after all

This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.     

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.     

The Poisson Log-Bilinear Lee-Carter Model

Abstract

Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. Recent work on the latter has focused on modeling the trend in mortality as a stochastic process. A popular method for modeling death rates is the Lee-Carter model. This methodology has become widely used, and various extensions and modifications have been proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their solvency capital requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company’s financial position, expressing the degree to which the liabilities are covered by the assets.     

The world price of liquidity risk

This paper empirically tests the liquidity-adjusted capital asset pricing model of Acharya and Pedersen (2005) on a global level. Consistent with the model, I find evidence that liquidity risks are priced independently of market risk in international financial markets. That is, a security’s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity, as well as the covariance of its own liquidity with local and global market returns. I also show that the US market is an important driving force of global liquidity risk. Furthermore, I find that the pricing of liquidity risk varies across countries according to geographic, economic, and political environments. The findings show that the systematic dimension of liquidity provides implications for international portfolio diversification.