Pension plan solvency and extreme market movements: a regime switching approach

We develop and test a new approach to assess defined benefit (DB) pension plan solvency risk in the presence of extreme market movements. Our method captures both the ‘fat-tailed’ nature of asset returns and their correlation with discount rate changes. We show that the standard assumption of constant discount rates leads to dramatic underestimation of future projections of pension plan solvency risk. Failing to incorporate leptokurtosis into asset returns also leads to downward biased estimates of risk, but this is less pronounced than the time-varying discount rate effect. Further modifying the model to capture the correlation between asset returns and the discount rate provides additional improvements in the projection of future pension plan solvency. This reduces the perceived future risk of underfunding because of the negative correlation between interest rate changes and asset returns. These results have important implications for those with responsibility for balancing risk against expected return when seeking to improve the current poor funding positions of DB pension schemes.     

A Termination Rule for Pension Guarantee Funds

A termination rule based on a critical funding ratio is proposed for a pension guarantee fund (PGF) that considers closing an underfunded pension plan. This ratio is determined by solving an expected utility maximization problem on behalf of plan beneficiaries subject to two constraints designed to preserve the PGF's viability. The first is an upper bound on the PGF's annual intervention probability; the second, a restriction on the expected shortfall of an underfunded pension plan that is not closed. Both too low and too high critical funding ratios hurt beneficiaries’ interests, depending on their degree of risk aversion.     

An Examination of ERR and Asset Allocation in Public Pension Plans

In this paper, we examine the usefulness of expected rates of return (ERR) for public pension plans. Specifically, we test the correlation between the expected rate of return on plan assets and asset allocation. We also examine the predictive power of ERR on the actual returns of the pension assets. We find that the correlation between expected return and the percentage of assets that are equity securities is relatively weak. Further, we find that the percentage of assets that are equity securities is a much better predictor of actual returns than the disclosed expected return in public pension plans. These results provide evidence to support SFAS No. 87 , which requires the disclosure of plan assets and against recently promulgated SFAS No. 132 , which eliminates this disclosure requirement. The evidence also supports GASB 25'sStatement of Net Plan Assets .     

Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends

Abstract

In this paper asset and liability values are modeled by geometric Brownian motions. In the first part of the paper we consider a pension plan sponsor with the funding objective that the pension asset value is to be within a band that is proportional to the pension liability value. Whenever the asset value is about to fall below the lower barrier or boundary of the band, the sponsor will provide sufficient funds to prevent this from happening. If, on the other hand, the asset value is about to exceed the upper barrier of the band, the assets are reduced by the potential overflow and returned to the sponsor. This paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In particular we are interested in situations where these two expected values are equal. In the second part of the paper the refunds at the upper barrier are interpreted as the dividends paid to the shareholders of a company according to a barrier strategy. However, if the (modified) asset value ever falls to the liability value, which is the lower barrier, “ruin” takes place, and no more dividends can be paid. We derive an explicit expression for the expected discounted dividends before ruin. From this we find an explicit expression for the proportionality constant of the upper barrier that maximizes the expected discounted dividends. If the initial asset value is the optimal upper barrier, there is a particularly simple and intriguing expression for the expected discounted dividends, which can be interpreted as the present value of a deterministic perpetuity with exponentially growing payments.     

Determinants of the Pension Curtailment Decisions of UK Firms

Abstract:  During the last ten years of regulatory change, many UK companies have curtailed their defined benefit pension scheme. We test three competing explanations of UK corporate pension curtailments: integration, separation and risk management. We predict and find an association between the use of managerial discretion over changes in UK firms' expected rate of return on pension assets (ERR) assumptions, and subsequent decisions to curtail future defined benefit pension obligations. These findings are consistent with a risk management-based explanation, even after controlling for other factors identified by prior literature as significant in explaining pension benefit reductions. We also find that curtailments and the risk management of ERR assumptions are associated with subsequent corporate restructuring decisions. The findings support the view that pension curtailment decisions are driven by the failure to adapt to new economic and regulatory pressures and that they are ultimately determined by strategic corporate risk management considerations.     

Pension funds with a minimum guarantee: a stochastic control approach

In this paper we propose and study a continuous-time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits, and the level of wealth is constrained to stay above a “solvency level.” The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. We concentrate the analysis on the effect of the solvency constraint, analyzing in particular what happens when the fund wealth reaches the allowed minimum value represented by the solvency level.     

Portfolio Optimization under Solvency Constraints: A Dynamical Approach

We develop portfolio optimization problems for a nonlife insurance company seeking to find the minimum capital required that simultaneously satisfies solvency and portfolio performance constraints. Motivated by standard insurance regulations, we consider solvency capital requirements based on three criteria: ruin probability, conditional Value-at-Risk, and expected policyholder deficit ratio. We propose a novel semiparametric formulation for each problem and explore the advantages of implementing this methodology over other potential approaches. When liabilities follow a Lognormal distribution, we provide sufficient conditions for convexity for each problem. Using different expected return on capital target levels, we construct efficient frontiers when portfolio assets are modeled with a special class of multivariate GARCH models. We find that the correlation between asset returns plays an important role in the behavior of the optimal capital required and the portfolio structure. The stability and out-of-sample performance of our optimal solutions are empirically tested with respect to both the solvency requirement and portfolio performance, through a double rolling window estimation exercise.     

Valuation of Contingent Pension Liabilities and Guarantees Under Sponsor Default Risk

This article analyzes the relationship between a pension fund with contingently indexed defined benefit liabilities and its sponsor, using contingent claims analysis. As pension funds generally choose to run a mismatch risk, future surpluses and deficits will occur. Surpluses are divided between beneficiaries and sponsor through contingent indexation of the benefits and refunding. Covering a deficit at the pension fund level is a function of the sponsor's financial ability to do so. This article suggests that this system creates an asymmetric allocation of the residual risk between sponsor and beneficiaries. The optimal investment policy for the pension fund in this context can be found by reverse engineering option valuation formulas. The main conclusion is that sponsor default risk negatively impacts the optimum risk profile and thereby the market value of contingent pension liabilities.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

The Pension Protection Fund*

We develop a model of the Pension Protection Fund (PPF), a defined benefit pension guarantee system for the UK, based on an analogy between pension liabilities and corporate debt obligations. We show that the PPF is likely to face many years of low claims interspersed irregularly with periods of very large claims. There is a significant chance that these claims will be so large that the PPF will default on its liabilities, leaving the government with no option but to bail it out. The cause of this problem is the double impact of a fall in equity prices on the PPF: it makes sponsor firms more likely to default and it makes defaulted plans more likely to be underfunded. We use our model to derive a fair premium for PPF insurance under different circumstances, to estimate the extent of cross‐subsidies in the PPF between strong and weak sponsors, and to show that risk‐rated premiums are unlikely to have a substantial effect on either the size or the lumpiness of claims. We argue that for the PPF to operate effectively, it should be introduced in tandem with strong minimum funding requirements and a lower level of benefit guarantee than at present.     

偿付能力、生命周期与养老金动态调整策略

本文从生命周期的角度,把养老保险基金的偿付能力作为内生变量,直接引入到养老金调整模型,使之能够自我反馈信息和修正预测偏差,并能根据偿付能力的变化对养老金进行动态调整,最终使养老保障能力与偿付能力实现了内在统一。情景分析表明:(1)在人口出生率和经济增速持续放缓的趋势下,如果不优化当前的养老金调整模式,偿付能力不足的程度将持续加剧;(2)与现行政策和现有模型相比,基于偿付能力构建的调整模型,能有效缓解偿付能力不足的程度,而且降低了养老金大幅波动的风险;(3)结合生命周期理论来调整养老金,不仅偿付能力的提升效果优于其它模式,而且延长了参保人员应对风险的时间,更加符合风险承受能力变化的生命周期特征,提高了抵抗风险的能力;(4)在制定延迟退休年龄等政策时,要综合考虑调整模式、养老金增长率和人口出生率等多方面因素,养老保险基金才可能持久地保持充足的偿付能力。     

Institutional Investor Ownership and Corporate Pension Transparency

We examine the association between institutional ownership and defined benefit (DB) pension decisions. We find that institutional ownership is negatively associated with pension underfunding, opportunistic increases in the expected rate of return assumption in the presence of underfunding, and significant ownership of the firm's own stock in the DB plan portfolio. Furthermore, these relations are stronger when institutional ownership is concentrated, when institutions are nontransient investors, or when institutions are relatively large. These results suggest that institutional investors are monitoring firm pension decisions, particularly those institutions with stronger monitoring incentives or resources.     

Managerial Self-Interest, Pension Financial Slack and Corporate Pension Funding

This paper examines the impact of managerial self-interest on corporate pension funding decisions. It is postulated that managers with no ownership stake in the firm will have incentives to maintain financial slack in the form of excess pension funding. Pension funding slack may be viewed as a managerial perquisite that decreases the probability of necessary future debt financing. Such a strategy may increase the value of undiversified human capital to the detriment of maximizing shareholder wealth. As managerial ownership increases, the incentives to consume such a perquisite will decrease since the interests of managers and shareholders become more aligned. The results presented in this study strongly support this proposition.     

Accounting of the German Statutory Pension Scheme: Balance Sheet,Cross‐Sectional Internal Rate of Return and Implicit Tax Rate

We present a framework for accounting of the German statutory pension scheme and calculate a balance sheet for the period 2005–14. Estimating a funding ratio of about 90 per cent, we present some policy recommendations in order to restore balancing of assets and liabilities. Extending and applying the methodology proposed by Settergren and Mikula (2005), we additionally estimate the aggregate cross‐sectional internal rate of return of the German pension scheme over this period. We are able to show that these internal rates of return are mainly financed by increasing contributions and by increasing unfunded liabilities. Additionally, our analysis reveals that from an expenditure perspective, the major part of the internal rate of return results from changing longevity rather than other changes. We also estimate the implicit tax rates from a cross‐sectional perspective and find that they can mainly be interpreted as an ‘implicit wealth tax’ on pension wealth. Finally, we analyse the impact of demographic change on the balance sheet employing a population projection. While the pure demographic effect leads to a decreasing funding ratio during population ageing, the automatic balancing mechanisms of the German pension scheme lead to a significant overfunding in the long run from the accounting perspective adopted in the Swedish pension system.     

Estimating portfolio risk for tail risk protection strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, copula‐GARCH and dynamic generalized autoregressive score models. Utilizing a loss function that overcomes the lack of elicitability for expected shortfall, we propose a novel expected shortfall (and value‐at‐risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modeling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts, given the defensive portfolio insurance mechanics.     

Pension plan accounting estimates and the freezing of defined benefit pension plans

This study provides evidence that, when “hard” freezing their defined benefit pension plans, employers select downward biased accounting assumptions to exaggerate the economic burden of their benefit plans. Downward biased expected rates of return and discount rates allow managers to increase reported pension expenses and, for discount rates, allow managers to increase reported pension liabilities. We find that prior to the Sarbanes-Oxley Act, both rates are downward biased when firms freeze their plans, whereas after SOX the bias is lower. This finding is consistent with managers opportunistically biasing pension estimates to obtain labor concessions during periods of reduced regulatory scrutiny.     

Pension return assumptions and shareholder-employee risk-shifting

Firm managers of defined-benefit (DB) pension plan sponsors reveal their primary motives — risk-shifting or risk-management — through their assumed expected rates of return (ERRs) on the plan assets. Managers with risk-shifting motives choose high ERRs to exploit flexible internal financing from employees via pension underfunding. Those with risk-management motives choose low ERRs to reduce future cash-flow uncertainty by improving the pension funding status. We examine if ERRs predict the firms’ future cash-flow allocation between pension funding and corporate investments, in a Japanese sample that mitigates the selection bias concern for US DB plan sponsors. Using dynamic panel regressions that control for lagged dependent variables, firms’ business prospects, and unobserved fixed effects, we show that higher ERRs precede higher capital investments, R&D expenses, and net pension obligations while revealing managerial aggression, especially among firms with high external financing costs. Higher ERRs predict higher market-to-book ratios for the firms with larger R&Ds and/or underfunding, suggesting that the risk-shifting channel of internal financing with high ERRs can help alleviate underinvestment problems.     

Additional evidence on transparency and bank financial performance

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book‐to‐market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E‐GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.     

降低企业基本养老保险政策缴费率能促进年金发展吗?北大核心

构建有效的多层次养老保障体系是积极应对我国人口老龄化的重要举措。本文基于税收调查数据,利用政策缴费率的差异,识别企业基本养老保险缴费负担对企业年金发展的影响。研究发现,企业基本养老保险缴费负担抑制了企业年金发展,其中政策缴费率每提高1个百分点,企业建立年金的概率会下降0.29个百分点,年金缴费率会减少0.06个百分点。使用上市公司数据进行分析,基本结论依然成立。进一步分析表明,基本养老保险会通过利润分享渠道、缴费能力渠道和缴费动机渠道影响企业年金发展。此外,企业基本养老保险对年金的影响,在企业产品定价能力较弱或小规模企业中更大,也会随地区经济增速的差异而不同,且仅在非国有企业中显著存在。依据本文估计的结果可以推算,企业基本养老保险政策缴费率降低4个百分点,能使年金覆盖率增加1.2个百分点,这同目前5.7%的覆盖率相比,是一个较大幅度的提升,但也应注意到6.9%的覆盖率依然偏低,年金发展需要更为积极的支持政策。     

Income Drawdown Schemes for a Defined-Contribution Pension Plan

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined-contribution personal pension plan. The optimal asset allocation is defined so that it minimizes the expected loss of the pensioner as measured by the performance of the pension fund against a benchmark. Two benchmarks are considered: a risk-free investment and the price of an annuity. The fair-value income drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitization is recommended if the expected fair-value drawdown rate falls below the annuity rate available at retirement. As an illustration, the annuitization age is calculated for a Gompertz mortality distribution function and a power law loss function.