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.     

Iterated VaR or CTE measures: A false good idea?

The purpose of this paper is twofold. Firstly, we consider different risk measures in order to determine the solvency capital requirement of a pension fund. Secondly, we illustrate the impact of the time horizon of long-term guarantee products on these capital. We consider a financial market modelled by a common Black–Scholes–Merton model. We neglect the mortality and underwriting risks by assuming that the pension fund is fully hedged against these risks, which allows us to keep understandable and tractable formulæ (the longevity risk will be a part of future researches). A portfolio is built in this market according to different strategies and the pension fund offers a fixed guaranteed rate on a certain time horizon. We begin with well-known static risk measures (value at risk and conditional tail expectation measures) and then we consider their natural dynamic generalization. In order to be time consistent, we consider their iterated versions by a backward iterations scheme. Within the dynamic setting, we show that solvency capital can be expensive and that attention must be paid to the safety level considered.     

Long-term optimal portfolios with floor

Long-term risk-sensitive portfolio optimization is studied with floor constraint. A simple rule to characterize its solution is mentioned under a general setting. Following this rule, optimal portfolios are constructed in several ways, using the optimal portfolio without floor constraint, combined with ideas of dynamic portfolio insurance, such as CPPI (constant proportion portfolio insurance), OBPI (option-based portfolio insurance), and DFP (dynamic fund protection). In addition, examples are presented with explicit computations of solutions.     

Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds

Polynomial goal programming (PGP) is a flexible method that allows investor preferences for different moments of the return distribution of financial assets to be included in the portfolio optimization. The method is intuitive and particularly suitable for incorporating investor preferences in higher moments of the return distribution. However, until now, PGP has not been able to meet its full potential because it requires quantification of “real” preference parameters towards those moments. To date, the chosen preference parameters have been selected somewhat “arbitrarily”. Our goal is to calculate implied sets of preference parameters using investors’ choices of and the importance they attribute to risk and performance measures. We use three groups of institutional investors—pension funds, insurance companies, and endowments—and derive implied sets of preference parameters in the context of a hedge fund portfolio optimization. To determine “real” preferences for the higher moments of the portfolio return distribution, we first fit implied preference parameters so that the PGP optimal portfolio is identical to the desired hedge fund portfolio. With the obtained economically justified sets of preference parameters, the well-established PGP framework can be employed more efficiently to derive allocations that satisfy institutional investor expectations for hedge fund investments. Furthermore, the implied preference parameters enable fund of hedge fund managers and other investment managers to derive optimal portfolio allocations based on specific investor expectations. Moreover, the importance of individual moments, as well as their marginal rates of substitution, can be assessed.     

An analysis of risk-taking behavior for public defined benefit pension plans

This paper presents the first comprehensive study on the determinants of public pension fund investment risk and reports several new important findings. Unlike private pension plans, public funds undertake more risk if they are underfunded and have lower investment returns in the previous years, consistent with the risk transfer hypothesis. Furthermore, pension funds in states facing fiscal constraints allocate more assets to equity and have higher betas. There also appears to be a herding effect in that CalPERS equity allocation or beta is mimicked by other pension funds. Finally, our results suggest that government accounting standards strongly affect pension fund risk, as higher return assumptions (used to discount pension liabilities) are associated with higher equity allocation and portfolio beta.     

The market of dynamic hybrid products in Germany: concept, risk-return profiles, and market overview

This article analyzes dynamic hybrid products along with their diverse characteristics and contract variations that are currently available in the German market. Dynamic hybrid products are innovative life insurance contracts combining features of traditional participating life insurance with those of unit-linked policies. This approach is thereby implemented by a mathematical algorithm based on a constant proportion portfolio insurance strategy that periodically reallocates funds (e.g. once per month or day) between the policy reserve stock (with an interest rate guarantee), a guarantee fund and/or equity fund. In this paper, we contribute to the literature by examining the concepts and key features of available dynamic hybrid products with particular focus on the embedded options, which allows the identification of key contract characteristics associated with them. In addition, risk-return profiles are studied and compared, which is of high relevance for regulators and policyholders. Our results show that these strongly vary, depending on the individual rebalancing mechanism and the type and amount of embedded options.     

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。     

Investor sophistication and risk taking

Using investment policy data of 857 Dutch pension funds during 1999–2006, we develop three indicators of investor sophistication. The indicators show that pension funds’ strategic portfolio choices are often based on coarse and less sophisticated approaches. First, most pension funds round strategic asset allocations to the nearest multiple of 5%, similar to age heaping in demographic and historical studies. Second, many pension funds invest little or nothing in alternative, more complex asset classes, resulting in limited asset diversification. Third, many pension funds favor regional investments and as such do not fully employ the opportunities of international risk diversification. Our indicators are correlated with pension fund size, in line with the expectation that smaller pension funds are generally less sophisticated than large pension funds. Using the indicators for investor sophistication, we show that less sophisticated pension funds tend to opt for investment strategies with less risk.     

Portfolio selection with a drawdown constraint

When identifying optimal portfolios, practitioners often impose a drawdown constraint. This constraint is even explicit in some money management contracts such as the one recently involving Merrill Lynch’ management of Unilever’s pension fund. In this setting, we provide a characterization of optimal portfolios using mean–variance analysis. In the absence of a benchmark, we find that while the constraint typically decreases the optimal portfolio’s standard deviation, the constrained optimal portfolio can be notably mean–variance inefficient. In the presence of a benchmark such as in the Merrill Lynch–Unilever contract, we find that the constraint increases the optimal portfolio’s standard deviation and tracking error volatility. Thus, the constraint negatively affects a portfolio manager’s ability to track a benchmark.     

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.     

Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

We study optimal insurance, consumption, and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing constant absolute risk aversion utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance decision is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses life insurance and investment portfolio choice to hedge stochastic wage risk.     

Pension Fund Manager Tournaments and Attitudes Towards Corporate Characteristics

Abstract:  This paper explores the relationship between the tournament incentives of pension fund managers and the characteristics of equities they choose to hold. Using a comprehensive data set on pension fund portfolio holdings, we determine the intensity of fund manager tournaments by sorting pension funds into portfolios based on the number of concurrent managers each pension fund employs. We then investigate which corporate characteristics are preferred by each of these portfolios by estimating share selection models that include a range of corporate characteristics that are expected to shape the returns to investment in stocks over the short and long run. We find that the intensity of the tournament faced by fund managers plays a significant role in shaping preferences over corporate characteristics. Managers facing more intense tournaments exhibit significantly weaker preferences for attributes associated with long run payoffs, such as social performance and growth potential, and significantly stronger preferences for short term attributes, such as operational efficiency, when compared to managers that face weak or no tournament incentives.     

新形势下基本养老保险城乡一体化路径初探

研究城乡基本养老保险制度的一体化有助于从社会保障待遇层面缩小城乡差距。当今形式下的基本养老保险政策正向着一体化的方向发展。本文着重从理论与实际两个方面分析当前中国基本养老保险制度的现状与问题,以国内养老保险有特色地区的养老保险模式为视角,总结基本养老保险制度合轨的困境所在。在解决困境的基础上,结合各地区养老保险特色,提出基本养老保险制度合轨的政策建议:提出公式"个人负担指数"=个人收入结余*M%/当地人均可支配收入,通过计算出可承受的缴费负担,来选定缴费档次,从而确定可选择的标准档次;通过增加基金投资种类,选取适当的基金投资组合方式来完善养老保险基金机制;建立统一专门的养老保险监管机构,并逐步建立并实施养老保险网上管理;通过推行"社保卡",建立"人手一户"的社会保障账户,来扩大基本养老保险适用的人群。通过这四方面的制度设计来逐步实现新农保、城镇居民基本养老保险与职工基本养老保险在制度上的合轨,从而实现真正意义上的城乡居民养老保险的全覆盖。     

Timing and selectivity in Portuguese mutual fund performance

We extend the international evidence on timing and selectivity skills of fund managers by applying the Henriksson and Merton [Henriksson, R., Merton, R., 1981. On market timing and investment performance. II. Statistical procedures for evaluating forecasting skills. J. Bus. 54, 513–533] model to Portuguese based mutual funds investing in local, European and International equity.

The results show that managers do not exhibit selectivity and timing abilities, and there is even some evidence of negative timing. Furthermore, we observe a distance effect on stock selection performance, since fund managers that invest locally seem to perform better that those who invest in foreign markets. However, this effect is reverted with respect to market timing skills of fund managers, suggesting that International fund managers are more focused in market timing strategies.     

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.     

Optimal consumption,portfolio and life insurance rules for an uncertain lived individual in a continuous time model

A continuous time model for optimal consumption, portfolio and life insurance rules, for an investor with an arbitrary but known distribution of lifetime, is derived as a generalization of the model by Merton (1971). The classic Tobin-Markowitz separation theorem obtains with the mutual funds being identical to those obtained under the assumption of certain lifetime. The investor is found to have a ‘human capital’ component of wealth, which is independent of his preferences and risky market opportunities and represents the certainty equivalent of his future net (wage) earnings. Explicit solutions, which are linear in wealth, are found for the investor with constant relative risk aversion.     

Minimizing the lifetime ruin under borrowing and short-selling constraints

In this paper, the optimal investment strategies for minimizing the probability of lifetime ruin under borrowing and short-selling constraints are found. The investment portfolio consists of multiple risky investments and a riskless investment. The investor withdraws money from the portfolio at a constant rate proportional to the portfolio value. In order to find the results, an auxiliary market is constructed, and the techniques of stochastic optimal control are used. Via this method, we show how the application of stochastic optimal control is possible for minimizing the probability of lifetime ruin problem defined under an auxiliary market.     

风险分散与中国混合型基本养老保险制度改革研究

本文从参保人养老投资风险分散角度研究混合型基本养老保险制度设计。通过构建一个两期消费模型,综合考虑参保人所面临的人口结构、工资增长率、养老基金投资等风险因素,本文研究了混合型基本养老保险制度中现收现付制与基金积累制的最优比例,并利用中国数据进行了测算与敏感性分析。研究发现:引入小规模个人账户基金积累制可以分散人口老龄化给现收现付制所带来的风险,中国实行混合型基本养老保险制度有其合理性;但如果要维持40%～45%的养老金替代率水平,中国基本养老保险制度的财务可持续性会面临较大挑战。     

The optimal asset allocation of the main types of pension funds: a unified framework

The existing literature deals with the optimal investment strategy of defined benefit (DB) or defined contribution (DC) pension plans. This article’s objective is to compare the optimal policies of different types of pension plans. This is done by first defining an original framework, which is based on the distinction between the nature of the guarantee—which can be internal or external—offered by or to a pension fund. This framework allows to establish links between optimization programs of DC, DB and targeted money purchase schemes. The case of an internal guarantee appears as a standard portfolio insurer’s problem. The second kind of guarantee, not analyzed in the literature yet with regard to the resulting optimal policy, is characterized by the existence of an option in the final wealth definition. Four funds are present in the internal guarantee optimal allocation: the speculative component, the preference independent guarantee- and contribution-hedge terms and the preference dependent state variable-hedge fund. The external guarantee program, solved with an original method using the principles of standard options theory, yields an optimal policy incorporating the delta of the option embodied in the final wealth definition. The conclusion is that the resulting optimal portfolio policy becomes riskier.

Optimal Control of DC Pension Plan Management under Two Incentive Schemes

Since the late 1990s, a performance fee arrangement has been approved as a managerial incentive in direction contribution (DC) pension plan management to motivate managers. However, the fact that managers may take undue risk for the larger performance fees and thus reduce members’ utility has been a subject of debate. As such, this study investigates the optimal risk-taking policies of DC pension fund managers under both the single management fee scheme and a mixed scheme with a lower management fee, as well as an additional performance fee. The analytical solutions are derived by using the duality method and concavification techniques in a singular optimization problem. The results show the complex risk-taking structures of fund managers and recognize the win-win situation of implementing performance-based incentives in DC pension plan management. Under the setting of geometric Brownian motion asset price dynamics and constant relative risk aversion utility, the optimal risk investment proportion shows a peak-valley pattern under the mixed scheme. Further, the manager gambles for gain when fund wealth is low and time to maturity is short. As opposed to the existing literature, this study found that the risk-taking policy is more conservative when fund wealth is relatively large. Furthermore, the utilities of the manager and members could both be improved by appropriately choosing the performance fee rate.