Modelling the cohort effect in CBD models using a piecewise linear approach

This paper discusses a new pattern of mortality model which is built on the form and knowledge of the two-factor mortality model named after its designers Cairns, Blake and Dowd (2006). This model – the CBD model – is widely used and has been extended by the authors in a number of ways, including by the use of a cohort effect. In this paper, we propose a range of new parsimonious approaches to model the cohort effect. Instead of adding a cohort factor to an age-period model we model the effect by building discontinuities into the pattern of rates within each year. The fit of the resulting models is close to that available from the best of the CBD derivatives

Tax-Efficient Pension Choices in the UK

ABSTRACTThe special tax treatment of United Kingdom pensions means that the decision on how to use pension assets is particularly involved. In particular, the ability to take up to 25% of pension assets as a tax-free cash lump sum at retirement, offers retirees opportunities to enhance their pension above that possible through the purchase of a compulsory purchase annuity (“CPA”). The tax-free cash lump sum can be used to buy a tax-efficient purchased life annuity (“PLA”), or in a phased retirement strategy. Income withdrawal can also be used to defer the purchase of an annuity until age 75 and, potentially, to generate a higher income. In this paper I compare the options available to retirees using stochastic modelling. I compare the expected excess pension and expected shortfall, both relative to the alternative risk-free pension available, to assess the various options. I find that if the maximum amount of tax-free cash is available to be used to enhance retirement income, then phased retirement offers the best risk/reward trade off. The advantage is greatest for higher-rate tax payers. As the level of tax-free cash falls, income withdrawal becomes more attractive to those wishing to take greater risks.</jats:p

The Missing Link - Economic Exposure and Pension Plan Risk

The funding position of a defined benefit pension plan is often closely linked to the performance of the sponsoring company's business. For example, a plan sponsor whose financial health is dependent on high oil prices may struggle during periods of oil price weakness. If the pension plan’s assets perform poorly at this time, the ability of the sponsor to address any funding requirement could be restricted precisely when the need for funding is heightened. In this paper, we propose an approach to dealing with joint plan and sponsor risk that can provide protection against extreme adverse events for the sponsor. In particular, adopt a strategy of minimising a portfolio’s expected losses in the event of an assumed drop of x% in the oil price. Our methodology relies on an asset allocation framework which takes into account the impact of serial correlation in asset returns, as well as the negative skewness and leptokurtosis resulting from the non-normal shape of marginal distributions of historical asset returns. We also make use of copulas to measure the dependence between asset class returns

The Cost and Value of Defined Benefit Pension Schemes, and the Implications for Defined Contribution Pension Provision

Over the last twenty years, the extent of defined benefit provision has declined substantially in the United Kingdom. Whilst most of the focus has been on deficits relating to past benefit accrual, a more important consideration is the increasing cost of future benefit accrual. In particular, I look at how the cost of pensions has changed relative to the cost of non-pensions earnings. I also look at the main components of the change in pensions cost – those relating to benefits payable, discount rates and longevity – to analyse their relative importance. I find that the cost of employing a member of defined benefit pension scheme has outpaced the cost of employing someone in a defined contribution arrangement by 1.1% of earnings per annum from 1995 to 2015. As at March 2015, the total cost of accrual was 25.4% of earnings. The average impact of interest rate changes on the change in the cost of accrual is 0.9% per annum. This is significantly more than the average impact of longevity improvements, which is 0.2% per annum. Both of these have added to the total cost. However, benefit changes marginally offset these increases, by around 0.05% per annum on average. Looking only at changes in interest rates, the estimated cost of accrual has risen to 36.7% of earnings as at September 2016. If the current 2.5% LPI increases to pensions in payment were removed and replaced with conditional indexation, the cost of accrual for the employer would fall back to 27.0%. However, this is still more than three times the maximum level of auto-enrolment contributions that will be required – these peak at 8% of earnings in 2019. It is also nearly seven times the current average level of contributions, which in 2015 stood at 4.0% of earnings. If contribution rates to defined contribution arrangements do not rise, a large proportion of the population will reach retirement with inadequate retirement savings. This paper revisits and extends analysis I first published in 2008, which looked at the change in the cost and value of defined benefit pensions from 1995 to 2005 (Sweeting, 2008)

A Piecewise Linear Cohort Extension to the Cairns-Blake-Dowd Model

Age-Period-Cohort (“APC”) models have been criticised on a number of grounds. One area of concern is in relation to projecting future cohorts. However, we would argue that such projection is unnecessary in some key cases, such as for closed defined benefit pension schemes. More fundamental issues relate to the fit itself. APC models typically use at least one parameter for each cohort, in addition to those used for parameters age and period. This leads to a large number of parameters which are not necessarily independent. However, the model we propose here uses a potentially far smaller number of parameters that essentially describe times where a new type of cohort emerges. This is similar to the trend-change models of mortality improvement discussed by as described by Sweeting (2011), Coelho and Nunes (2011), and van Berkum et al (2014). Because this cohort approach identifies a small number of changes in cohort rather than imposing a new cohort parameter for each year of birth, this reduces the risk of interdependence

Surfing the Tsunami: A Plan for State Pension Reform

For some years the affordability of the UK State Pension has been an issue. And for some years, the most visible answer to this issue has been to raise the State Pension Age. However, increasing the State Pension Age has a much greater impact on the least well-off — and they are the ones who are most dependent on this benefit. Just as importantly, increasing the State Pension Age is unlikely to control the cost of State Pensions in the long run. Perhaps instead of using the State Pension Age alone, it is worth visiting the concept of means-testing. This would not be unprecedented. In fact, when the Old Age Pension was introduced in 1909, it was brought in as a means-tested benefit. Using means-testing, whether alone or in conjunction with increases to the State Pension Age, could help to control the cost of the UK State Pension. What’s more, it could do so equitably, ensuring that those who most need it are more likely to receive it

The cost and value of UK pensions

Over the last twenty years, the extent of defined benefit provision has declined substantially in the United Kingdom. Whilst most of the focus has been on deficits relating to past benefit accrual, the increasing cost of future benefit accrual is also important. There are two reasons for this. First, the change in the cost of defined benefit accrual represents the difference in the earnings for employees with membership of a defined benefit scheme and those with membership of a defined contribution scheme. Second, the current cost of defined benefit accrual gives an indication of the cost of an adequate pension. As such, it can be compared with levels of contribution to defined contribution schemes to determine whether these are adequate. I therefore look at how the cost of pensions has changed relative to the cost of non-pensions earnings. I also look at the main components of the change in pensions cost - those relating to benefits payable, discount rates and longevi ty - to analyse their relative importance. I find that the cost of employing a member of defined benefit pension scheme has consistently outpaced the cost of employing someone in a defined contribution arrangement. I also find that the current cost of accrual is significantly higher than the average level of payments to defined contribution schemes

Natriuretic peptides and integrated risk assessment for cardiovascular disease. an individual-participant-data meta-analysis

BACKGROUND: Guidelines for primary prevention of cardiovascular diseases focus on prediction of coronary heart disease and stroke. We assessed whether or not measurement of N-terminal-pro-B-type natriuretic peptide (NT-proBNP) concentration could enable a more integrated approach than at present by predicting heart failure and enhancing coronary heart disease and stroke risk assessment. METHODS: In this individual-participant-data meta-analysis, we generated and harmonised individual-participant data from relevant prospective studies via both de-novo NT-proBNP concentration measurement of stored samples and collection of data from studies identified through a systematic search of the literature (PubMed, Scientific Citation Index Expanded, and Embase) for articles published up to Sept 4, 2014, using search terms related to natriuretic peptide family members and the primary outcomes, with no language restrictions. We calculated risk ratios and measures of risk discrimination and reclassification across predicted 10 year risk categories (ie, <5%, 5% to <7·5%, and ≥7·5%), adding assessment of NT-proBNP concentration to that of conventional risk factors (ie, age, sex, smoking status, systolic blood pressure, history of diabetes, and total and HDL cholesterol concentrations). Primary outcomes were the combination of coronary heart disease and stroke, and the combination of coronary heart disease, stroke, and heart failure. FINDINGS: We recorded 5500 coronary heart disease, 4002 stroke, and 2212 heart failure outcomes among 95 617 participants without a history of cardiovascular disease in 40 prospective studies. Risk ratios (for a comparison of the top third vs bottom third of NT-proBNP concentrations, adjusted for conventional risk factors) were 1·76 (95% CI 1·56-1·98) for the combination of coronary heart disease and stroke and 2·00 (1·77-2·26) for the combination of coronary heart disease, stroke, and heart failure. Addition of information about NT-proBNP concentration to a model containing conventional risk factors was associated with a C-index increase of 0·012 (0·010-0·014) and a net reclassification improvement of 0·027 (0·019-0·036) for the combination of coronary heart disease and stroke and a C-index increase of 0·019 (0·016-0·022) and a net reclassification improvement of 0·028 (0·019-0·038) for the combination of coronary heart disease, stroke, and heart failure. INTERPRETATION: In people without baseline cardiovascular disease, NT-proBNP concentration assessment strongly predicted first-onset heart failure and augmented coronary heart disease and stroke prediction, suggesting that NT-proBNP concentration assessment could be used to integrate heart failure into cardiovascular disease primary prevention