Pension Fund Dynamics and Gains/Losses Due to Random Rates of Investment Return

A simple model for defined benefit pension plans with independent and identically distributed rates of investment return and a stationary membership is considered. Three methods of adjusting the normal cost as gains or losses arise are compared, and a suitable choice of amortization or spread period is made. We also investigate the evolution in time of the first and second moments of the pension fund and contribution levels.     

Discretionary accounting choices: the case of IAS 19 pension accounting

Based on a sample of 3207 firm-year observations for the years 2005–2013, we investigate how stock-listed companies in France, Germany and the UK use two discretionary choices in their accounting for defined benefit pension plans under International Accounting Standard (IAS) 19 Employee Benefits. We first analyse companies’ decision whether to voluntarily early adopt the equity method of accounting for actuarial gains and losses. Second, we analyse companies’ choice to present pension interest cost and expected return on plan assets, or, in 2013, net pension interest cost, in operating or financial income. Our findings provide evidence that companies’ decisions to early adopt the equity method in 2005, the first year this accounting choice was available, were motivated by short-term effects on equity. Our analyses also indicate that the choice regarding where to present interest cost and expected return on plan assets in the income statement is associated with the resulting effect on Earnings before Interest and Tax. Finally, we document country-specific differences in the use of the discretion provided under IAS 19, suggesting that discretionary pension accounting choices may impede comparability.     

Defined Benefit or Defined Contribution? A Study of Pension Choices

We solve an empirically parameterized life‐cycle model of consumption and pension choices to show how expected earnings growth and risk affect the benefits of final‐salary defined benefit (DB) pension plans, relative to pension plans that are defined contribution (DC) in nature. We use micro data on the pension choices of individuals to provide evidence consistent with the model predictions: (1) individuals who expect a higher growth rate of earnings are more likely to choose DB final‐salary schemes, and (2) individuals who face a higher variance of persistent income shocks are less likely to choose DB final‐salary schemes. We control for cohort and age fixed effects in the empirical analysis.     

An Investigation of the Pay-As-You-Go Financing Method Using a Contingency Fund and Optimal Control Techniques

Abstract

In many countries, aging populations are expected to lead to substantial rises in the cost of public pension systems financed by the pay-as-you-go (PAYGO) method. These systems will need to be adapted to cope with these changes. This paper considers one approach to reform, described in the literature as “parametric” (see, e.g., Disney 2000), and develops a model for adapting the PAYGO method using a contingency fund and optimal control techniques. The solution of the original model is investigated within two different frameworks: a deterministic-continuous one and a stochastic-discrete one. Finally, a case study applied to Greece is discussed, leading to a potentially acceptable proposal of a smooth path for contribution rates and the age of eligibility for the normal retirement pension.     

Multivariate Cox Hidden Markov models with an application to operational risk

ABSTRACT

Modeling multivariate time-series aggregate losses is an important actuarial topic that is very challenging due to the fact that losses can be serially dependent with heterogeneous dependence structures across loss types and business lines. In this paper, we investigate a flexible class of multivariate Cox Hidden Markov Models for the joint arrival process of loss events. Some of the nice properties possessed by this class of models, such as closed-form expressions, thinning properties and model versatility are discussed in details. We provide the expectation-maximization (EM) algorithm for efficient model calibration. Applying the proposed model to an operational risk dataset, we demonstrate that the model offers sufficient flexibility to capture most characteristics of the observed loss frequencies. By modeling the log-transformed loss severities through mixture of Erlang distributions, we can model the aggregate losses. Finally, out-of-sample testing shows that the proposed model is adequate to predict short-term future operational risk losses.     

Learning minimum variance discrete hedging directly from the market

Option hedging is a critical risk management problem in finance. In the Black–Scholes model, it has been recognized that computing a hedging position from the sensitivity of the calibrated model option value function is inadequate in minimizing variance of the option hedge risk, as it fails to capture the model parameter dependence on the underlying price (see e.g. Coleman et al., J. Risk, 2001, 5(6), 63–89; Hull and White, J. Bank. Finance, 2017, 82, 180–190). In this paper, we demonstrate that this issue can exist generally when determining hedging position from the sensitivity of the option function, either calibrated from a parametric model from current option prices or estimated nonparametricaly from historical option prices. Consequently, the sensitivity of the estimated model option function typically does not minimize variance of the hedge risk, even instantaneously. We propose a data-driven approach to directly learn a hedging function from the market data by minimizing variance of the local hedge risk. Using the S&P 500 index daily option data for more than a decade ending in August 2015, we show that the proposed method outperforms the parametric minimum variance hedging method proposed in Hull and White [J. Bank. Finance, 2017, 82, 180–190], as well as minimum variance hedging corrective techniques based on stochastic volatility or local volatility models. Furthermore, we show that the proposed approach achieves significant gain over the implied BS delta hedging for weekly and monthly hedging.     

Do pension buyouts help or hurt employees (retirees)?

This article compares expected pension default losses of employees and retirees before and after pension buyouts. The comparisons are made using a stochastic model calibrated with market data. The analysis shows that the lower protection level provided by the State Guarantee Association relative to that of the Pension Benefit Guaranty Corporation (PBGC) is a critical factor that explains the welfare reduction, or equivalently, larger expected pension default losses, of most retirees who become annuity holders in the buyouts. The analysis also shows that the employee welfare, or equivalently expected pension default gains or losses, depends on the continued PBGC protection and, critically, their employers' postbuyout default risk and pension funding status. Moreover, these employee welfare changes are quite different for the corporations included in this analysis. Our results suggest that welfare improvements depend on the PBGC and state insurance regulators' cooperation in protecting pension participants and supervising buyout insurers.     

Performance Reporting under Fair Value Accounting

Abstract

This paper compares performance measurement under fair value accounting vs. U.S. GAAP accounting. As illustrated in the paper, the main difference between fair value accounting and U.S. GAAP accounting lies in the treatment of gains and losses on both assets and liabilities. Fair value accounting would report all gains and losses on both assets and liabilities in the period in which they arise. U.S. GAAP on the other hand, recognizes gains and losses over the life of the block of business (or at the time of a transaction). When net gains and losses on assets and liabilities are immaterial, the pattern of earnings under both systems can be quite similar. However, If a company is generating significant gains or losses on its net book of business (such as in the case of an asset/liability mismatch), fair value accounting will reveal this much sooner than U.S. GAAP. When the full impact of its actions (including gains and losses) is reported in the current period, management is in a better position to understand how the value of the company is changing and adjust its decisions accordingly. This is one of the main reasons for moving to a fair value system and is expected to be a major benefit if fair value accounting is ultimately adopted.     

Adoption of IAS 19R by Europe's premier listed companies: Corridor approach versus full recognition: Summary of an ACCA research monograph

This report provides a summary of a research monograph sponsored by the Association of Chartered Certified Accountants (ACCA) [Fasshauer, J., Glaum, M., & Street, D. L. (2008). Adoption of IAS 19R by Europe's premier listed companies: Corridor approach versus full recognition. An ACCA research report, London] and is based on our in-depth analysis of the defined benefit pension plan disclosures provided in the year 2005 by companies constituting the premier segments of 20 European exchanges. Most importantly, the study identifies the method these companies selected under International Accounting Standard (IAS) 19 for the recognition of actuarial gains/losses, provides insight into factors affecting the policy choice between the methods allowed under IAS 19 for the recognition of actuarial gains/losses, and assesses the impact on profit and loss (P&L) and the balance sheet of using the new IAS 19 option of full recognition through the Statement of Recognized Gains and Losses (SORIE), in contrast to the traditional corridor approach. We also benchmark key pension assumptions against relevant country or industry averages.As accounting for defined benefit pension plans continues to evolve with the amendment of IAS 19, the recent issuance of SFAS 158 in the U.S., the release of The Financial Reporting of Pensions in Europe, and most notably the release of Preliminary Views on Amendments to IAS 19 Employee Benefits by the IASB, our research provides timely empirical evidence regarding important issues to be addressed in the IASB's current retirement benefits project.     

Modeling a Dynamic Portfolio for Pension Plans in Emerging Markets With Myopic and Nonmyopic Behavior

ABSTRACT

We introduce a dynamic formulation for the problem of portfolio selection of pension funds in the absence of a risk-free asset. In emerging markets, a risk-free asset might be unavailable, and the approaches commonly used may no longer be suitable. We use a parametric approach to combine dynamic programming and Monte Carlo simulation to gain additional flexibility. This approach is general in the sense that optimal asset allocation is tractable for all HARA utility functions in the absence of a risk-free asset. The traditional case composed of several risky assets and one risk-free asset is compared to a case in which the risk-free asset is unavailable.     

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 Effects of Liquidity Shocks on Corporate Investments and Cash Holdings: Evidence from Actuarial Pension Gains/Losses

This paper investigates how anticipated liquidity shocks affect corporate investment and cash holdings by examining the impacts of actuarial pension gains/losses that do not reduce current internal resources but will reduce those available in the future. Using a sample from Japanese manufacturing firms in which pension deficits had a huge impact on the internal resources of sponsoring firms, I show that pension losses significantly decrease the capital expenditures of sponsoring firms. Pension losses also increase corporate cash holdings, suggesting precautionary demands for cash prepared for future pension contributions. Overall, the results indicate that managers consider anticipated liquidity shocks in determining current investment and cash‐saving policies.     

Pension Funding Regulations and Actuarial Gains and Losses

With pervasive pension funding deficits, Korean firms have been under pressure to improve their funding levels. We examine whether firms have incentives to set obligation‐decreasing pension assumptions when they have large pension deficits (pension obligations in excess of plan assets) and when they make insufficient contributions to external pension funds. We find that firms report larger actuarial gains (or smaller actuarial losses) associated with the remeasurement of pension liabilities when their pension funding ratio (the ratio of the fair value of plan assets to defined benefit obligations) is lower and when contributions to plan assets relative to pension service costs are smaller. Next, upon the introduction of a minimum pension funding guideline, we find that the effect of the funding ratio and contributions to pension funds on actuarial gains and losses is more pronounced for firms whose funding ratios are slightly below the minimum funding ratio than it is for firms whose funding ratios exceed or fall short of the minimum by a large margin. Our results indicate that firms opportunistically exercise discretion regarding corporate pension accounting under International Financial Reporting Standards to comply with pension funding regulations, thereby reducing perceived pension deficits.     

Optimal proportional reinsurance with a loss-dependent premium principle

ABSTRACT

Empirical studies suggest that many insurance companies recontract with their clients on premiums by extrapolating past losses: a client is offered a decrease in premium if the monetary amounts of his claims do not exceed some prespecified quantities, otherwise, an increase in premium. In this paper, we formulate the empirical studies and investigate optimal reinsurance problems of a risk-averse insurer by introducing a loss-dependent premium principle, which uses a weighted average of history losses and the expectation of future losses to replace the expectation in the expected premium principle. This premium principle satisfies the bonus-malus and smoothes the insurer's wealth. Explicit expressions for the optimal reinsurance strategies and value functions are derived. If the reinsurer applies the loss-dependent premium principle to continuously adjust his premium, we show that the insurer always needs less reinsurance when he also adopts this premium principle than when he adopts the expected premium principle.     

企业年金缩小企业与机关事业单位职工养老金差距的政策仿真研究——工资异质性的视角

引入工资差异对企业职工企业年金缴费意愿的影响,采用仿真方法测量企业年金对企业与机关事业单位职工养老金差距的影响。首先,根据我国养老制度安排,构建了企业年金基金、基本养老金、退休金预测模型和养老金差距测量指标;其次,选取工资水平从社平工资的0．5倍～5．0倍的14类代表性职工,模拟了基准情境和提高企业年金税收优惠的四种情境——提高雇主缴费的企业所得税免税上限、降低雇主缴费计入个人账户部分的个人所得税税率、降低领取阶段的个人所得税税率、免征个人缴费的个人所得税,并进行了敏感性分析。仿真结果表明,企业年金及其税收优惠政策能够有效缩小企业与机关事业单位职工养老金差距,提高雇主缴费的企业所得税免税上限的作用最显著。企业年金投资收益率提高、企业年金管理费率降低、余寿减少、社平工资增长率提高和工作年限增加都会放大这种作用,反之亦然。工资越高企业职工从企业年金中获益越大,可能扩大企业职工内部养老金差距。     

Developing Mortality Improvement Formulas

Abstract

Longevity improvements have contributed to widespread underfunding of pension plans and losses in insured annuity portfolios. Insurers might reasonably expect some upside from the effect of lower mortality on their life business. Although mortality improvement scales, such as the Society of Actuaries Scale AA, are widely employed in pension and annuity valuation, the derivation of these scales appears heuristic, leading to problems in deriving meaningful measures of uncertainty. We explore the evidence on mortality trends for the Canadian life insurance companies, data, using stochastic models. We use the more credible population data to benchmark the insured lives data. Finally, we derive a practical, model-based formula for actuaries to incorporate mortality improvement and the associated uncertainty into their calculations.     

PAYG pension systems with capital mobility

This paper studies the design of an optimal pension scheme in an OLG and open economy model. The pension scheme provides a flat rate benefit and is based on the PAYG principle. It thus combines inter- and intra-generational redistribution. In this setting a number of symmetric economies are connected by an open and perfect capital market. When this number is very large, we have the small open economy case; when it is reduced to one, we have the case of autarky or perfect coordination. As the number of countries increases, there is more intragenerational redistribution, but less capital accumulation. JEL Code H55 · H87     

The Earnings Implications of Pension Expense

Abstract

Recent challenges to the actuarial pension model and a movement to harmonize international accounting standards both suggest that the current Canadian standards for pension accounting, CICA 3461, may see substantial revision during upcoming years. To understand better the implications of these possible accounting changes, this paper presents the results of a stochastic analysis that quantifies how the volatility of pension expense for a sample of ten Canadian companies sponsoring defined benefit plans will be increased by the adoption of immediate recognition accounting. For certain companies this increase is significant and is shown to have a material earnings impact. The implications of this earnings volatility for the future of defined benefit pension plans are also explored.     

The smoothing of pension expenses: a panel analysis

The main purpose of this paper is to utilize recent developments in panel data techniques to evaluate whether the smoothing of pension expenses is neutral in its long-term effect on reported earnings. Adopting a long-term perspective, the empirical analysis also identifies sources of potential deviations. Results suggest that the current smoothing mechanism tends to induce significant biases in the recognized pension expenses. For a majority of the sample firms, the tendency is to overstate the sponsoring firms’ earnings in the long run. To a large extent, such biases reflect the combination of both ineffective amortization of the deferred gains and losses and questionable latitude in pension rate discretions.