One size fits all: How many default funds does a pension scheme need?
David Blake, Mel Duffield, Ian Tonks, Alistair Haig, Dean Blower & Laura MacPhee.
Abstract
In this paper, we analyse the number of default investment funds appropriate for an occupational defined contribution pension scheme. Using a unique dataset of member risk attitudes and characteristics from a survey of a large UK pension scheme, we apply cluster analysis to identify two distinct groups of members in their 40s and 50s. Further analysis indicated that the risk attitudes of the two groups were not significantly different, allowing us to conclude that a single lifestyle default fund is appropriate.
Key words:
investment choices, cluster analysis, risk attitudes, risk capacity, defined contribution pension schemes.
JEL: G11, G41
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
Abstract
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
CBDX: A Workhorse Mortality Model from the Cairns-Blake-Dowd Family
Kevin Dowd, Andrew J.G. Cairns & David Blake
Abstract
The purpose of this paper is to identify a workhorse mortality model for the adult age range (i.e., excluding the accident hump and younger ages). It applies the “general procedure” (GP) of Hunt and Blake (2014) to identify an age-period model that fits the data well before adding in a cohort effect that captures the residual year-of-birth effects arising in the original age-period model. The resulting model is intended to be suitable for a variety of populations, but economises on the number of period effects in comparison with a full implementation of the GP. We estimate the model using two different iterative Maximum Likelihood (ML) approaches – one Partial ML and the other Full ML – that avoid the need to specify identifiability constraints.
Key Words:
mortality rates, Cairns-Blake-Dowd mortality model, CBDX mortality model
JEL codes:
G220, G230, J110
Insight into Stagnating Life Expectancy: Analysing Cause of Death Patterns across Socio-economic Groups
Malene Kallestrup-Lamb, Soren Kjaergaard, & Carsten P. T. Rosenskjold
Abstract
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;
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.
Abstract
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
Quantifying Loss Aversion: Evidence from a UK Population Survey
David Blake, Edmund Cannon and Douglas Wright
Abstract
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.
Keywords:
Behavioural finance, loss aversion, expected utility, survey data
JEL: C83, C90, G40
Abstract
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.
Keywords:
Actuarial Science, Black ’76 model, CBD mortality models, Equity Release, No Negative Equity Guarantee, Prudential Regulation
JEL Classification: G2, G3.
Abstract
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.
Abstract
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.
Keywords:
mortality rates, Cairns-Blake-Dowd mortality model, CBDX mortality model, Lee-Carter mortality model, projection, extreme old age.
Abstract
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
