Discussion Paper WP2001

Insight into Stagnating Life Expectancy:  Analysing Cause of Death Patterns across Socio-economic Groups
Malene Kallestrup-Lamb, Soren Kjaergaard, & Carsten P. T. Rosenskjold
This article analyzes the complexity of female longevity improvements. As socio-economic status is found to influence health and mortality, we partition all individuals, at each age in every year, into five socio-economic groups based on an affluence measure that combine an individual’s income and wealth. We identify the particular socio-economic groups that have been driving the standstill for Danish females. Within each socio-economic group, we further analyze the cause of death patterns. The decline in life expectancy for Danish females is present for four out of five subgroups, however with particular large decreases for the low-middle and middle affluence groups. Cancers, smoking related causes, and other diseases particularly contribute to the stagnation. Moreover, cardiovascular and cerebrovascular diseases are found to be important for capturing the following catch-up in longevity. JEL Classification: J11; C53; G22 Keywords: Mortality; Affluence Groups; Health Inequality; Cause of Death;

Discussion Paper WP-1913

Grouping Individual Investment Preferences in Retirement Savings: A Cluster Analysis of a USS Members Risk Attitude Survey.
David Blake, Mel Duffield, Ian Tonks, Alistair Haig, Dean Blower & Laura MacPhee.
Cluster analysis is used to identify homogeneous groups of members of USS in terms of risk attitudes. There are two distinct clusters of members in their 40s and 50s. One had previously ‘engaged’ with USS by making additional voluntary contributions. It typically had higher pay, longer tenure, less interest in ethical investing, lower risk capacity, a higher percentage of males, and a higher percentage of academics than members of the ‘disengaged’ cluster. Conditioning only on the attitude to risk responses, there are 18 clusters, with similar but not identical membership, depending on which clustering method is used. The differences in risk aversion across the 18 clusters could be explained largely by differences in the percentage of females and the percentage of couples. Risk aversion increases as the percentage of females in the cluster increases, while it reduces as the percentage of couples increases because of greater risk sharing within the household. Characteristics that other studies have found important determinants of risk attitudes, such as age, income and (pension) wealth, do not turn out to be as significant for USS members. Further, despite being on average more highly educated than the general population, USS members are marginally more risk averse than the general population, controlling for salary, although the difference is not significant.
Key words:
investment choices, cluster analysis, risk attitudes, risk capacity, defined contribution pension schemes JEL:    G11, G41

Discussion Paper WP1912

Quantifying Loss Aversion:  Evidence from a UK Population Survey
David Blake, Edmund Cannon and Douglas Wright
We estimate loss aversion using on an online survey of a representative sample of over 4,000 UK residents. The average aversion to a loss of £500 relative to a gain of the same amount is 2.41, but loss aversion varies significantly with characteristics such as gender, age, education, financial knowledge, social class, employment status, management responsibility, income, savings and home ownership. Other influencing factors include marital status, number of children, ease of savings, rainy day fund, personality type, emotional state, newspaper and political party. However, once we condition on all the profiling characteristics of the respondents, some factors, in particular gender, cease to be significant, suggesting that gender differences in risk and loss attitudes might be due to other factors, such as income differences.
Behavioural finance, loss aversion, expected utility, survey data JEL: C83, C90, G40

Discussion Paper WP1911

We outline the valuation process for a No-Negative Equity Guarantee in an Equity Release Mortgage loan and for an Equity Release Mortgage that has such a guarantee. Illustrative valuations are provided based on the Black ’76 put pricing formula and mortality projections based on the M5, M6 and M7 mortality versions of the Cairns-Blake-Dowd (CBD) family of mortality models. Results indicate that the valuations of No-Negative Equity Guarantees are high relative to loan amounts and subject to considerable model risk but that the valuations of Equity Release Mortgage loans are robust to the choice of mortality model. Results have significant ramifications for industry practice and prudential regulation.
Actuarial Science, Black ’76 model, CBD mortality models, Equity Release, No Negative Equity Guarantee, Prudential Regulation
JEL Classification: G2, G3.

Discussion Paper WP1910

In 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.

Discussion Paper WP1909

This 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.
mortality rates, Cairns-Blake-Dowd mortality model, CBDX mortality model, Lee-Carter mortality model, projection, extreme old age.

Discussion Paper WP1907

This 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 Words
Age-Period-Cohort mortality model, age effect, projection, extreme old age, term annuity

Discussion Paper WP1906

An 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.

Discussion Paper WP1905

Since 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 Words
On/off switching; deaths; actuarial models; period and cohort effects; life insurance costs  

Discussion Paper WP1904

This 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.