AbstractIn this paper I extend the work of Bernhardt and Donnelly (2019) dealing with Modern explicit tontines, as a way of providing income under a specified bequest motive, from a defined contribution pension pot. A key feature of the present paper is that it relaxes the assumption of fixed proportions invested in tontine and bequest accounts. In making the bequest proportion an additional control function I obtain, hitherto unavailable, closed-form solutions for the fractional consumption rate, wealth, bequest amount, and bequest proportion under a constant relative risk averse utility. I show that the optimal bequest proportion is the product of the optimum fractional consumption rate and an exponentiated bequest parameter. Typical scenarios are explored using UK Office of National Statistics life tables, showing the behaviour of these characteristics under varying degrees of constant relative risk aversion.
AbstractThis article shows how cohort mortality rate projections of mortality models that involve age effects can be improved and extended to extreme old ages. The proposed approach allows insurers to use such mortality models to obtain valuations of financial instruments such as annuities that depend on projections of extreme old age mortality rates.
Keywords:mortality rates, Cairns-Blake-Dowd mortality model, CBDX mortality model, Lee-Carter mortality model, projection, extreme old age.
AbstractThis article shows how mortality models that involve age effects can be fitted to ages beyond the sample range using projections of age effects as replacements for age effects that might not be in the sample. This ‘projected age effect’ approach allows insurers to use age-effect mortality models to obtain valuations of financial instruments such as annuities that depend on projections of extreme old age 𝑞 rates. Illustrative results suggest that the proposed approach provides a good approximation to both 𝑞 rates and term annuity prices. The practical import of this approach is to allow insurers to apply a much wider range of mortality models to such problems than would otherwise be possible.
Key WordsAge-Period-Cohort mortality model, age effect, projection, extreme old age, term annuity
AbstractAn alarming rise in deaths since early 2012 has led to a deterioration of life expectancy in the UK and elsewhere in the world. In the UK several studies sought to implicate austerity as the cause of the increased deaths. However, these studies did not cite other studies which document behaviour of deaths inconsistent with the austerity theory. This short paper presents further evidence which is inconsistent with the austerity theory and poses the possibility that deaths are now falling back to levels expected to apply in the original actuarial forecasts. Possible reasons for the temporary blip in deaths are discussed. This paper uses the direct count of deaths to follow the trends rather than age standardized mortality, because complex trends in age-specific changes in deaths suggest that the process of age standardization may be acting to disguise the underlying causes for the trends.
AbstractSince 2011 ongoing improvements in life expectancy and the mortality rate have been interrupted leading to the failure of actuarial models and higher than expected life insurance pay-outs. This has occurred to varying degrees across all the developed countries. This study presents evidence that deaths follow a curious pattern of on/off switching which can be demonstrated to occur in the 126 countries where monthly deaths data is available for analysis. This on/off switching can be documented to occur from the 1980’s to the present. At switch-on monthly deaths suddenly jump to a new and higher level, remain high for around 12-months, and then suddenly revert to the former baseline where they stay until the next switch-on event arrives. Switch-on can seemingly occur in any month of the year, i.e. factors such as season and temperature can be excluded as causes for the behaviour, with the magnitude of the increase diminishing as the spatial area increases. On average, switch-on occurs around once evert three years. At an international level switch-on appears to cluster in time. Attempts to investigate period and cohort effect using calendar year data will therefore be hindered since a calendar year can contain a mix of on/off behaviour. Artefactual outputs from the method were excluded by analysis of monthly temperature and sunspot numbers.
Key WordsOn/off switching; deaths; actuarial models; period and cohort effects; life insurance costs
SummaryThis article considers whether a collective defined contribution pension scheme (a “CDC scheme”) provides “cover against biometric risk” or “guarantees … a given level of benefits” for the purposes of Article 13(2) of EU Directive 2016/2341 (the “IORP II Directive”) or its predecessor , IORP I Directive 2003/41/EC), Article 15(2). If no such cover and no such guarantee are provided, then a CDC scheme is not required to comply with the technical provisions, buffer and other funding requirements applicable to an IORP which is classified as a “regulatory own fund” in Article 15 of the IORP II Directive. There is a linked, and for current practice, relevant issue: if a pension fund operates a CDC pension scheme that does not qualify as a regulatory own fund IORP, it would be classified as a “special investment fund” for EU VAT Directive purposes with the associated beneficial VAT treatment that is enjoyed by a retail collective investment scheme. Furthermore this VAT treatment is available for all CDC schemes. The article explores this issue by reference to CDC schemes established in The Netherlands and against the background that the UK is planning to introduce legislation permitting CDC schemes to be established in the UK. The article compares some of the Dutch legislation regulating CDC schemes established in The Netherlands with the corresponding position in the UK in relation to the legal form used for a pension scheme, the protection of accrued rights under a pension scheme, the approach to funding defined benefit pension schemes (including, for this purpose, Dutch CDC schemes) and the different approaches to dealing with the insolvency of the employer in relation to a pension scheme (including the difference between the UK legislation for a Pension Protection Fund and The Netherlands not legislating for a pension protection fund). The article also notes that the essence of a CDC scheme is that the benefits are not guaranteed. Instead, the benefits are adjusted in accordance with legally binding rules which provide a mechanism for bringing the value of the target benefits back into line with the value of the assets of the scheme. The employer has no obligation to make any additional deficit repair contributions. The article notes that CDC schemes may also be referred to as Defined Ambition schemes or Target Benefit schemes.
AbstractWe examine the determinants of firms’ defined pension plan de-risking strategy choices, and their impact on firm risk using a unique dataset covering FTSE 100 firms for the period 2009-2017. In particular, we investigate which firm financial and pension fund characteristics influence de-risking strategy choices and their impact on firm risk, proxied with earnings and return volatility, default and credit risk. Results show that de-risking strategies are more likely to be implemented when pensions have a longer investment horizon, indicating a higher level risk exposure due to investment uncertainty. We find that firms with larger pension plans prefer innovative de-risking strategies (buy-in/buy-out and longevity swap), as these reduce the risk more effectively removing various pension fund risk altogether, over the traditional ones (soft and hard freezing). Firms with higher market capitalisation and that are financially unconstrained implement innovative pension de-risking strategies as they have the ability to pay the cash premiums required. We also find that pension de-risking strategies reduce firm risk. Hard freezing and pension buy-ins/buy-outs have the most significant impact in reducing firm risk. In contrast, soft freezing nd longevity swaps tend to have a weaker or no impact on the overall firm risk.
KeywordsPension De-Risking Strategy, Defined-Benefit Pension Plans, Pension Freezing, Pensing Buy-in, Pension Buy-out, Longevity Swap.
AbstractThe paper examines the cointegration between pension assets and economic growth in the presence of structural breaks in 1995 and 1999. The structural breaks are endogenously determined. This paper gives an extensive literature review of the theoretical and empirical framework of pension fund reform in relation to growth. The literature shows pension fund reform has been encouraged with some emerging market economies including South Africa shifting from Pay As You Go (PAYG) to Fully Funded Schemes (FFS). The Zivot Andrews and modified ADF unit root test are used, and empirical evidence suggests no evidence of a unit root. This paper examines the cointegration between pension assets and economic growth in the presence of structural breaks. We find that pension assets have a positive but minimal impact on growth in the presence of structural breaks. The direction of the results is similar for the model with or without structural breaks. The results show that pension reform in South Africa has not contributed to a redistributive growth agenda despite the financial sector sophistication coupled with the strong institutional and regulatory framework.
KeywordsPension Funds Reform, South Africa, structural breaks, PAYG to FFS, ARDL, Zivot Andrews
Persons who have achieved UK state pension age (SPA) may defer their pension and instead receive an extra pension on termination of deferral. We define a scheme to be actuarially fair to a category of deferrer with agreed discount rate, when the expected net present value of pre-tax lifetime receipts is independent of the deferral period. After a review of the literature on deferral and early take-up of state pensions in the UK and other countries, this paper argues that the current UK scheme based upon a uniform accrual rate cannot be actuarially fair. Instead, we propose a scheme where the accrual rate is dependent upon deferral period, gender, SPA, deferrer’s discount rate, degree of pension uprating, and partnership status of the deferrer. Fair accrual rate curves are plotted for various scenarios and compared with the current uniform rates of 10.4% and 5.8% per annum that apply to those who attain SPA before 6 April and after 5 April 2016 respectively. A scheme that is actuarially fair will not be cost neutral to the Exchequer unless the discount rate is the same for both parties. In addition to this asymmetry, adverse selection will impact upon both actuarial fairness and cost to the Exchequer. Expressions are derived for the cost penalty to the Exchequer for attempting to achieve actuarial fairness both with and without an acknowledgement of adverse selection. Similarly, when the objective is to achieve cost neutrality for the Exchequer, expressions for the cost to the deferrer are obtained. Some numerical examples are given for various scenarios. The methodology should be applicable to public pensions in other countries, in order to inform fair policies for both early and postponed take-up of pensions.