How the provision of inflation information affects pension contributions: A field experiment

Ignoring the effects of inflation in retirement planning can have severe consequences for an individual's future financial well-being. Yet, many pension funds do not communicate inflation-related information, presumably for the fear of reduced contributions once the members understand how low the “real” return on saving for retirement is. As an alternative prediction, the provision of inflation information could increase pension contributions, because it reveals possible pension shortfalls. In cooperation with a major German pension fund, we conduct a field experiment, in which we vary the inflation information provided to the fund members, to explore this important issue. Among all participants, we find mostly positive but insignificant effects of the inflation information on pension contributions. Among those participants who voluntarily changed their pension contributions after the experimental intervention, the provision of inflation information significantly raises the likelihood of increasing pension contributions.     

HARA utility maximization in a Markov-switching bond–stock market

We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor’s risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.     

Dynamic preferences for popular investment strategies in pension funds

In this paper, we characterize dynamic investment strategies that are consistent with the expected utility setting and more generally with the forward utility setting. Two popular dynamic strategies in the pension funds industry are used to illustrate our results: a constant proportion portfolio insurance (CPPI) strategy and a life-cycle strategy. For the CPPI strategy, we are able to infer preferences of the pension fund’s manager from her investment strategy, and to exhibit the specific expected utility maximization that makes this strategy optimal at any given time horizon. In the Black–Scholes market with deterministic parameters, we are able to show that traditional life-cycle funds are not optimal to any expected utility maximizers. We also prove that a CPPI strategy is optimal for a fund manager with HARA utility function, while an investor with a SAHARA utility function will choose a time-decreasing allocation to risky assets in the same spirit as the life-cycle funds strategy. Finally, we suggest how to modify these strategies if the financial market follows a more general diffusion process than in the Black–Scholes market.     

Management of Portfolio Depletion Risk through Optimal Life Cycle Asset Allocation

Members of defined contribution (DC) pension plans must take on additional responsibilities for their investments, compared to participants in defined benefit (DB) pension plans. The transition from DB to DC plans means that more employees are faced with these responsibilities. We explore the extent to which DC plan members can follow financial strategies that have a high chance of resulting in a retirement scenario that is fairly close to that provided by DB plans. Retirees in DC plans typically must fund spending from accumulated savings. This leads to the risk of depleting these savings, that is, portfolio depletion risk. We analyze the management of this risk through life cycle optimal dynamic asset allocation, including the accumulation and decumulation phases. We pose the asset allocation strategy as an optimal stochastic control problem. Several objective functions are tested and compared. We focus on the risk of portfolio depletion at the terminal date, using such measures as conditional value at risk (CVAR) and probability of ruin. A secondary consideration is the median terminal portfolio value. The control problem is solved using a Hamilton-Jacobi-Bellman formulation, based on a parametric model of the financial market. Monte Carlo simulations that use the optimal controls are presented to evaluate the performance metrics. These simulations are based on both the parametric model and bootstrap resampling of 91 years of historical data. The resampling tests suggest that target-based approaches that seek to establish a safety margin of wealth at the end of the decumulation period appear to be superior to strategies that directly attempt to minimize risk measures such as the probability of portfolio depletion or CVAR. The target-based approaches result in a reasonably close approximation to the retirement spending available in a DB plan. There is a small risk of depleting the retiree’s funds, but there is also a good chance of accumulating a buffer that can be used to manage unplanned longevity risk or left as a bequest.     

Portfolio management with stochastic interest rates and inflation ambiguity

We solve, in closed form, a stock-bond-cash portfolio problem of a risk- and ambiguity-averse investor when interest rates and the inflation rate are stochastic. The expected inflation rate is unobservable, but the investor can learn about it from observing realized inflation and stock and bond prices. The investor is ambiguous about the inflation model and prefers a portfolio strategy which is robust to model misspecification. Ambiguity about the inflation dynamics is shown to affect the optimal portfolio fundamentally different than ambiguity about the price dynamics of traded assets, for example the optimal portfolio weights can be increasing in the degree of ambiguity aversion. In a numerical example, the optimal portfolio is significantly affected by the learning about expected inflation and somewhat affected by ambiguity aversion. The welfare loss from ignoring learning or ambiguity can be considerable.     

The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management

In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equities and U.S. Treasury bonds. Our analysis does support 4% as a sustainable withdrawal rate in the pension de-accumulation context (and a somewhat lower rate for an endowment), but only if the investor follows an MV optimal portfolio allocation, not a fixed proportion strategy. Compared with a constant proportion strategy, the MV optimal policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation of wealth and the probability of shortfall. We also explore the effects of suppressing jumps so as to have a pure diffusion process, but assuming a correspondingly larger volatility for the latter process. Surprisingly, it turns out that the MV optimal strategy is more effective when there are large downward jumps compared to having a high volatility diffusion process. Finally, tests based on historical data demonstrate that the MV optimal policy is quite robust to uncertainty about parameter estimates.     

Would emerging market pension funds benefit from international diversification: investigating wealth accumulations for pension participants

In recent years, investment portfolio selection is growing in importance for many emerging market pension funds, as pension reforms replace traditional pay-as-you-go systems with advanced funding systems. Various investment regulations are applied to the funded pensions, particularly in the form of portfolio limits for equities and international assets. With a bootstrap simulation approach, this paper attempts to quantify the impacts on retirement benefits of restricting international assets from the investment portfolios of emerging market pension funds. We find that, on average, over half of the pension portfolios of emerging market countries should be in international assets in order to maximize the expected utility of moderate and conservative pension fund participants. More generally, international assets can play a significant role in the investment portfolios for workers with risk aversion varying from aggressive to conservative. With few exceptions, the entire probability distribution of wealth accumulations at retirement could be shifted higher with the inclusion of international assets.     

金融危机对拉美国家私营养老金的影响及经验启示

2008年爆发的金融危机对全球经济产生了重要影响,也对拉美国家私营养老金制度的发展产生了巨大冲击。文章介绍了拉美国家私营养老金制度的改革路径和养老基金概况,从养老金资产价值、投资收益率、投资组合、雇员、制度覆盖面和缴费密度方面切入,分析了金融危机对拉美私营养老金制度的影响。在现状分析的基础上,得出了要保障私营养老金制度可持续运行的一些经验启示:构建多元化的混合型养老金体系,增强退休和养老金支付的灵活性,积极运用生命周期投资策略,实施多元化和分散化投资,以养老金长期收益作为投资目标,建立社会风险应急储备基金和政府担保机制,以及加强员工退休教育。     

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.     

Asset Pricing and Expected Inflation

This paper provides an equilibrium model in which expected real returns on common stocks are negatively related to expected inflation and money growth. It is shown that the fall in real wealth associated with an increase in expected inflation decreases the real rate of interest and the expected real rate of return of the market portfolio. The expected real rate of return of the market portfolio falls less, for a given increase in expected inflation, when the increase in expected inflation is caused by an increase in money growth rather than by a worsening of the investment opportunity set. The model has empirical implications for the effect of a change in expected inflation on the cross-sectional distribution of asset returns and can help to understand why assets whose return covaries positively with expected inflation may have lower expected returns. The model also agrees with explanations advanced by Fama [5] and Geske and Roll [10] for the negative relation between stock returns and inflation.     

Inflation and the evolution of firm-level liquid assets

This paper shows that inflation has been an important determinant of firm-level liquid asset holdings. Liquid assets as a share of total assets – the cash ratio – for U.S. corporations steadily declined from the 1960s to the early 1980s, and has since steadily increased. Our empirical analysis finds that inflation is a key factor accounting for these changes. We show that these liquid asset holdings are imperfectly hedged against inflation. Hence, changes in inflation alter the real value of a firm’s liquid asset portfolio causing them to readjust these balances.     

Valuation, optimal asset allocation and retirement incentives of pension plans

We provide a framework in which we link the valuation and assetallocation policies of defined benefits plans with the lifetimemarginal productivity schedule of the worker and the pensionplan formula. In turn, we examine the retirement policies thatare implied by the primitives of the model and the value ofpension obligations. Our model provides an explicit valuationformula for a stylized defined benefits plan. The optimal assetallocation policies consist of the replicating portfolio independentof the pension liabilities. We show that the worker with retirewhen the ratio of pension benefits to current wages reachesa critical value which depends on the parameters of the pensionplan and the discount rate. Using numerical techniques we analyzethe feedback effect of retirement policies on the valuationof plans and on the asset allocation decisions.     

On the distribution and estimation of trading costs

This paper investigates the uncertainty about the trading costs associated with a given portfolio strategy. I derive accurate approximations of the ex ante probability distributions of proportional trading costs and portfolio turnover under the conventional assumption of normal asset returns. Based on these approximations, I express the expected trading costs as a function of asset and portfolio characteristics. All else equal, the expected trading costs increase with: i) the deviations of the expected asset returns from the expected portfolio return, ii) the assets' volatility and iii) the portfolio volatility. At the same time, they decrease with the covariance between the assets and the portfolio. Furthermore, I propose novel estimators of the expected turnover and trading costs and show that they offer small bias and low variance, even when the sample size is small. Finally, I incorporate my results into a portfolio selection framework to produce portfolios with low levels of risk and trading costs. Several experiments with real and simulated data confirm the practical value of the results.     

The Impact of DC Pension Systems on Population Dynamics

Abstract

This study investigates the risk inherent in defined contribution (DC) pension plans on an individual and aggregate basis, based on U.S. data. Our aim is to gain insight into the consequences of a DC pension scheme becoming the predominant pillar of retirement income for an entire society. Using the stochastic simulated output of a DC flexible age-of-retirement model, we first determine the optimal investment strategies. We then examine the demographic retirement dynamics of an entire population of DC pension plan participants.

We observe that even for the most risk-averse plan members there is a high level of uncertainty in an individual’s age at retirement. At the aggregate population level, we find that this uncertainty does not get dampened to any great extent by a diversification effect. Instead, the central role played by the market in determining retirement dates results in significant variation in the dependency ratio (the ratio of retirees to workers) over time. In addition, an attempt to ameliorate the outcome by introducing additional realistic features in the DC population modeling did little to dampen this volatility, which suggests that countries dominated by DC schemes of this type may, over time, be exposed to significant risk in the size of its labor force.     

Pension Portfolio Choice and Peer Envy

I examine the effect of envy on the portfolio allocation of workers in a defined contribution (DC) pension plan. If a worker’s DC plan performs better than his co‐worker’s, he may gloat; on the other hand, if his DC plan performs worse, he may feel envy. I model anticipated envy when workers make portfolio allocations, and find that in equilibrium, workers will mimic their co‐worker’s allocation to eliminate the disutility from envy. This portfolio allocation is riskier than that of a worker who does not exhibit envy.     

Portfolio optimisation with jumps: Illustration with a pension accumulation scheme

In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.     

基于前瞻性泰勒规则对中国通货膨胀目标值估计的实证研究

基于状态空间形式的前瞻性泰勒规则,采用卡尔曼滤波估计方法对中国1992～2008年动态通货膨胀目标值进行估计,结果显示中国的通货膨胀预期目标值较实际水平平滑,1998年之后的通货膨胀目标估计值能够较准确反映中国这一时期真实通货膨胀率预期值;中国历年通货膨胀和产出水平的变化随着利率的变化而顺向变动。结论提示今后中国货币政策可采取把灵活而又规范的通货膨胀目标制与泰勒规则结合的操作框架。     

Beliefs and actions: expectations and savings decisions by older Americans

To understand the interaction of savings behavior, pension fund participation and expectations of retirement well being, we ask two questions. Are expected pension benefits a substitute for accumulated savings in replacing preretirement income? Are individuals’ expectations concerning their retirement standard of living realistic based on their accumulated savings and pension plan participation? First-wave data from the Health and Retirement Study (HRS) are analyzed using a probit regression. The results are consistent with the idea that pension benefits are substitutes for saving and that accumulated savings have a significant impact on the expected standard of living but pension plan participation does not.     

Real Stock Returns and Inflation

This paper develops the relation between the real rate of return on the stock market and changes in the price level using a multiperiod economy with production. The observed relation between real ex post stock returns and inflation is shown to be consistent with equilibrium in an economy with rational investors. The relation between expected real returns and expected inflation is shown to depend on the form of the economy's production function and on the form of investor preferences. When the production function exhibits stochastic constant returns to scale, the model explains the negative relation between expected real returns and expected inflation which has frequently been observed in empirical studies.     

Pension benefits, wealth accumulation, and capital market equilibrium: a life cycle hypothesis-based dynamic model

This paper examines the impacts of pension benefits on capital asset pricing in conjunction with wealth accumulation and retirement, and derives and tests a dynamic capital asset pricing model (CAPM) within the framework of a life cycle hypothesis-based dynamic model. The life cycle hypothesis-based dynamic model maximizes the expected utility of the individual's lifetime wealth in a continuous time process. An optimal solution of the individual's wealth path, incorporating the ages of retirement and death, is obtained and, based on the optimal wealth path, an analysis of comparative dynamics is pursued. The dynamic CAPM is then derived from the optimal wealth path; simulation and nonparametric tests are undertaken to evaluate the performance of the dynamic CAPM as compared to the traditional model which does not consider the impacts of pension benefits and the static model that incorporates the effects of pension benefits. The test results suggest that the proposed dynamic CAPM closely states the expected rate of return for a capital asset; that the new dynamic CAPM is preferable over the static model that is preferable over the traditional model; and that the three models considered are statistically distinguishable from one another.