Abstract: This paper investigates catastrophe risk for South African life insurers by considering the additional deaths that could arise from a 1-in-200 year mortality shock. Existing South African academic research on catastrophic risk has mostly focused on property losses and the resulting impact on property insurance companies. Life catastrophe risks have not been extensively modelled in a South African context. Local research would be beneficial in terms of quantifying these catastrophic risks for South African life insurers, and would assist firms when assessing their own catastrophe mortality solvency requirements under the new Solvency Assessment and Management (SAM) regime by providing a summary of data relating to various past catastrophes. In this paper we model a wide range of catastrophes to assess such mortality risk faced by life insurance companies in South Africa. An extensive exercise was undertaken to obtain data for a wide range of catastrophes and these data were used to derive severity and frequency distributions for each type of catastrophe. Data relating to global events were used to supplement South African data
where local data were sparse. Data sources included official government statistics, industry reports and historical news reports. Since, by nature, catastrophic events are rare, little data are available for certain types of catastrophe. This means there is a large degree of uncertainty underlying some of the estimates. Simulation techniques were used to derive estimated distributions for the potential number of deaths for particular catastrophic events. The calculated overall shock for the national population was 2.6 deaths per thousand, which was lower than the SAM Pillar 1 shock of 3.2 deaths per thousand for the same population

Abstract:The aim of this paper is to investigate the expenditure incurred by health insurers arising from the provision of benefits during the 12 months preceding a beneficiary’s death. Concern is expressed in parts of the international literature about the extent of resources directed towards those at the end of life, particularly given increased longevity and technological advancement. Two types of investigation are discussed: first, a comparison of costs in the last year of life with costs in earlier years prior to death and, second, a comparison of decedent and survivor costs within a calendar year. Within each investigation, further detailed analyses were performed with particular emphasis on the distribution of last-year-oflife costs by age and category of expenditure. A South African dataset is used to illustrate the suggested methodology. The average cost in the last year of life is found to be 3.3 times higher than the average cost in the second last year of life. Average decedent costs are found to be 17.85 times higher than average survivor costs in 2012, on a risk-adjusted basis. The majority of these costs (83.35% in 2012) form part of the Prescribed Minimum Benefit package.

Abstract:As the principal decision-makers in retirement funds, trustees have a number of duties placed upon them including a duty of care, a duty of impartiality, a duty to avoid and manage conflicts of interest, a duty to act in accordance with the purpose of the fund and a duty of accountability. Decision-making by trustees and the actuaries that assist them can be informed by considering various ethical theories. This paper reviews the theory of right action, virtue theory and the ethics of care, together with the theory of justice, and interprets the duties of trustees and actuaries in terms of these theories. After consideration of other frameworks for ethical decision-making, a six-step decision-making framework based on the actuarial control cycle is developed to provide an initial attempt to formalise the process
of ethical decision-making in South African retirement funds. This framework is applied to case studies involving the review of surplus apportionment, an investment policy statement, the distribution of death benefits, and annuitisation options. The case studies illustrate that, although the framework itself does not provide ethical solutions, it assists trustees, and the actuaries who advise them, with the process of making an ethical decision.

Abstract:In this paper, we consider the Markovian model for the actuarial modelling of health insurance policies modified by the inclusion of durational effects (the time elapsed since entering a given state) on the aggregate payment streams, where the force of interest is a diffusion process. We derive differential equations for the first moment of the present value of the aggregate amount of benefits. We also give two examples to illustrate our results.

Abstract:This paper aims to introduce jump tests to the actuarial community. In actuarial science, semimartingales are extensively used in the models for interest rates, options, variable annuities and equity-linked annuities. Those models usually assume without justification that the underlying asset process follows a continuous stochastic process such as a geometric Brownian motion, for the market data sometimes tell a different story. Choosing between a continuous model and a model with jumps is not only important for pricing of insurance products but also crucial for implementing other post-sales risk management measures such as dynamic liability hedging. A test for jumps allows actuaries to rigorously test whether the underlying asset process has jumps, which is the first critical step in model selection. The ability to
conduct the test should thus belong to the repertoire of every expert and practitioner working in this field. In this paper, we review several major tests for jumps, describe their advantages and disadvantages, and offer suggestions for their implementation. We also implement several tests using real data, enabling practitioners to apply these tests in their work.

Abstract:A methodology for the assessment of the probable maximum loss associated with an earthquake is described and applied to the Cape Town central business district. The calculations are based on the effect of the two largest earthquakes that occurred in Milnerton in 1809 and Ceres–Tulbagh in 1969. The investigation concludes that if buildings and infrastructure in an area follow the SANS Standard 10160 for seismic loading of 0.1g, they are exposed to significant seismic risk. The main purpose of
this research is not the accurate quantification of expected losses to Cape Town’s infrastructure, but to raise awareness between civil engineers, the insurance industry and disaster management agencies that seismic hazard is an issue in South Africa and must be considered as a potential threat to its residents and infrastructure.

Abstract: The purpose of this study is to investigate the pricing of variable annuity embedded derivatives using a suitably refined model for the underlying assets, in this case the Johannesburg Securities Exchange FTSE/JSE All Share Index (ALSI). This is a practical issue that life insurers face worldwide in the management of embedded derivatives. We consider the Variance-Gamma (VG) framework to model the underlying data series. The VG process is useful in option pricing given its ability to model higher moments, skewness and kurtosis and to capture observed market dynamics. The framework is able to address the inadequacies of some deterministic pricing approaches used by life insurers, given the increasing complexity of the option-like products sold

Abstract: The Sunday Times Discovery Healthiest Company Index Survey collected a dataset of 13578 responses from corporate employees in 101 companies. This dataset has been used to assess the prevalence of self-reported modifiable health-risk factors and the association with chronic conditions. The analysis indicates that there is a greater likelihood of an individual reporting a chronic condition where their lifestyle risk factors are outside of the healthy range. This suggests that there are opportunities to manage the costs of health insurance, medical expenses and productivity losses by applying risk management tools aimed at addressing modifiable risk factors.

Abstract: This paper investigates the performance of South African general equity unit trusts relative to the FTSE/JSE All Share Index during the period January 1994 to December 2012. The period under investigation was split into six further sub-periods each having a specific economic cycle: a downturn, average growth or robust growth. Unit trusts are shown to have underperformed in economic downturns and outperformed in periods of robust growth, while no conclusions can be made about unit trust performance during periods of average growth. Overall, unit trusts showed slight outperformance, but this was not found to be persistent.

Abstract: Contemporary actuarial and accounting practices (APN 110 in the South African context) require the use of market-consistent models for the valuation of embedded investment derivatives. These models have to be calibrated with accurate and up-to-date market data. Arguably, the most important variable in the valuation of embedded equity derivatives is implied volatility. However, accurate long-term volatility estimation is difficult because of a general lack of tradable, liquid medium- and long-term derivative instruments, be they exchange-traded or over the counter. In South Africa, given the relatively short-term nature of the local derivatives market, this is of particular concern. This paper attempts to address this concern by: —providing a comprehensive, critical evaluation of the long-term volatility models most commonly used in practice, encompassing simple historical volatility estimation and econometric, deterministic and stochastic volatility models; and
—introducing several fairly recent nonparametric alternative methods for estimating long-term volatility, namely break-even volatility and canonical option valuation.
The authors apply these various models and methodologies to South African market data, thus providing practical, long-term volatility estimates under each modelling framework whilst accounting for real-world difficulties and constraints. In so doing, they identify those models and methodologies they consider to be most suited to long-term volatility estimation and propose best estimation practices within each identified area. Thus, while application is restricted to the South African market, the general discussion, as well as the suggestion of best practice, in each of the evaluated modelling areas remains relevant for all long-term volatility estimation.

Abstract:In this paper, the methodology underlying the graduation of the mortality of members of group schemes in South Africa underwritten by life insurance companies under group life-insurance arrangements is described and the results are presented. A multivariate parametric curve was fitted to the data for the working ages 25 to 65 and comparisons are made with the mortality rates from the SA85–90 ultimate rates for insured lives and the ASSA2008 AIDS and demographic model. The results show that the mortality of members of group schemes is lower than that of the general population, mortality decreasing with increasing salary, as would be expected. For males it was found that there were differences in mortality rates by industry for a given salary band, whereas for females these differences only occurred in the lower salary bands. Furthermore, there is evidence of the healthy-worker effect at ages 60 and above, where the mortality rates appear to level off or even decrease as age increases. This contrasts with the mortality rates from the SA85–90 ultimate rates for insured lives and the ASSA2008 AIDS and demographic model, which increase exponentially.

Abstract: An accurate measure of the change in the price of medical-scheme cover over time is necessary to inform health and social-security policy, and would provide consumers, employers and the regulator with a useful benchmark. A medical-scheme contribution index based on gross contributions to open medical schemes is constructed using the Paasche formula and a sample of schemes for the period 2006 to 2010. The results of the index indicate a 17,48% increase in real contributions over the period.

Abstract: In this paper, the mortality of members of group schemes underwritten by South African life insurance companies is investigated. The research provides some indication of the level or mortality of this population as a whole, which apart from being useful for costing group schemes in future could be used, to the extent that these data represent the mortality of those in formal employment, in the costing of a national retirement scheme. Rates of mortality are investigated by several demographic factors such as age, sex, salary and industry of employment.

Abstract: Individuals in defined-contribution retirement funds currently have a number of options as to how to finance their post-retirement spending. The paper considers the ranking of selected annuitisation strategies by the probability of ruin and by expected discounted utility under different scenarios. ‘Ruin’ is defined as occurring when income falls below a given threshold, but does not relate to the extent of that deficit. If there is insufficient money to buy an inflation-linked annuity at retirement, then the minimisation of the probability of ruin tends to result in living annuities with a high equity content. This is because the objective function does not reflect the extent of shortfall of income or the investor’s level of risk aversion. The authors argue that this is a limitation to using the minimisation of the probability of ruin. Expected discounted utility may be more difficult to apply in practice, because of the complexity of explaining the approach to investors and the need to estimate a greater number of parameters explicitly. The authors argue that the use of expected discounted utility is, however, likely to be more representative of most investors’ perception of risk, and illustrate its use by applying an extended discounted utility model that caters for the bequest motive and different reference income levels.

Abstract:Access to healthcare is considered to be a basic human right. This paper explores the concept of access to public healthcare, with a particular focus on affordability, accessibility and accommodation. Furthermore, it highlights certain issues around the concept of access in the South African setting, by analysing the results from the General Household Surveys (2002–2009). Affordability of healthcare services and the positioning of the facilities were not identified as being key barriers to access. Instead, other aspects, such as accommodation to the patients’ needs and acceptability of services received had greater significance and should be prioritised in terms of any proposed healthcare reforms.

Abstract:This paper presents the results of an investigation into whether age or work status are statistically significant determinants of the change in the consumption rate at and in retirement. This research used data from the Income and Expenditure Survey 2005–2006 for households comprising one or two adults. It was found that gifting and non-healthcare consumption, which includes gifting, are not influenced by age or work status. Certain households were found to have higher healthcare
consumption after retirement than before retirement. This result challenges the belief that retired households have lower consumption than working households, all other things equal, and may therefore necessitate an upward adjustment to retirement adequacy goals.

Abstract: The globalisation of the financial services industry and the increasing complexity of insurance products, among other factors, have led to the development of new regulatory systems for insurers globally (and, in particular, in South Africa). The primary intention of these systems is to protect the interests of policyholders by ensuring that insurance companies remain solvent in most foreseeable circumstances. In South Africa, new regulation, known as Solvency Assessment and Management (SAM), is expected in 2015, but this regulation is to apply only to insurance companies and not to medical schemes. This paper considers the implications of the application of capital requirements under Quantitative Impact Study 1 to the measurement of capital adequacy in South African medical schemes. Data from 2006, 2007 and 2008 were used to parameterise the non-SLT health-underwriting risk module (i.e. the risk module relating to health-underwriting risk that is not similar to life techniques), which was then used to determine the level of economic capital that schemes would have been required to hold in 2009. The results showed an overall
reduction in the capital requirements of medical schemes, as compared with the current statutory minimum requirements, and therefore an increase in the proportion of medical schemes that are found to be solvent.

Abstract:This paper presents the results of an investigation into whether age or work status are statistically significant determinants of the change in the consumption rate at and in retirement. This research used data from the Income and Expenditure Survey 2005–2006 for households comprising one or two adults. It was found that gifting and non-healthcare consumption, which includes gifting, are not influenced by age or work status. Certain households were found to have higher healthcare
consumption after retirement than before retirement. This result challenges the belief that retired households have lower consumption than working households, all other things equal, and may therefore necessitate an upward adjustment to retirement adequacy goals.

Abstract: Despite the importance of retirement adequacy goals to public policy, retirement fund design and personal financial planning, there has been little formal research on the estimation of retirement adequacy goals for South African households. This research derived estimated retirement adequacy goals for employed one- and two-adult households. A consumption-smoothing model with a minimum-income underpin was developed to estimate wealth–earnings ratio goals using data from the Income and Expenditure Survey 2005–2006. Household wealth–earnings ratio goals were estimated to be between 10,5 and 18,2 times annual salary depending on retirement age,
household composition, income, location, age, education, household income distribution, home ownership and salary support. Considering current retirement savings rates, retirement before age 67 is unlikely to be affordable for most households.

Abstract:The Pension Funds Second Amendment Act, 2001 required funds to provide statutory minimum benefits for exiting members and pensioners. Any surplus arising at the statutory valuation following the promulgation of this Act was to be distributed—initially to former members and pensioners to top up their benefits to the statutory minimum, and then equitably to all stakeholders. Surplus available in retirement funds was originally estimated at R80bn, but the surplus distributed by May 2012 was only about R47,6bn. This paper considers some reasons for this discrepancy and, in particular, gives an analysis of 447 surplus valuation reports. It shows that, by strengthening their valuation assumptions and motivating contingency reserves, actuaries reduced the surplus by R10bn for these 447 funds. The paper questions whether the strengthening of valuation bases was justified and examines critically the new actuarial methods introduced following the promulgation
of the Act.

Abstract: In this paper the actuarial assessment of damages for personal injury and death is discussed in the context of South African law. The legal framework imposes a variety of calculation rules that need to be born in mind if an actuary is to produce a quality product. This framework changes with the passage of time. The purpose of the paper is to summarise the current state of affairs and highlight issues deserving of further actuarial discussion.

Abstract: In prior work by the author the method of pricing the liabilities of a financial institution by means of dynamic mean–variance hedging is applied to an incomplete market that is nevertheless in equilibrium with homogeneous expectations. In subsequent work a long-term equilibrium model is developed and parameterised for the South African market. The aim of this paper is to apply the latter model to the pricing method with a view to quantifying the effects of non-additivity due
to incompleteness, guarantees implicit in reasonable expectations of pension increases and the sensitivity of the price of illustrative liabilities to the parameters of the model. The application is to retirement-fund benefits in the South African market. In an unpublished application of the pricing method it was found that, except for quite short-term liabilities, the computational demands of the pricing algorithm became excessive. The main reason for this was that the algorithm calls for simulations within simulations: for each year of the term of liabilities, a large number of simulations is required, and for each such simulation another large number of simulations is required. In this article consideration is given to the reduction of the computational demands of the algorithm.

Abstract: This paper tests the empirical validity of the capital-asset pricing model (CAPM) for the South African share market. For the investigation, quarterly total returns from ten sectoral indices listed on the JSE Securities Exchange from 30 June 1995 to 30 June 2009, were used. As expressed in the securities market line, the CAPM suggests that higher risk, as measured by beta, is associated with higher expected returns. In addition, the theoretical underpinnings of the CAPM are that it explains expected excess return, and that the relationship between expected return and beta is linear. In this investigation the above-mentioned predictions of the CAPM were tested. Direct tests of the securities market line were made, using both prior betas and in-period betas. A nonparametric test was also made. Regression analysis was used to test hypotheses based on both individual sectoral indices and portfolios constructed from those indices according to their betas. These tests were
made for individual years as well as for all periods combined. It was found that while, on the assumption that the residuals of the return-generating function are normally distributed, the CAPM could be rejected for certain periods, the use of the CAPM for long-term actuarial modelling in the South African market can be reasonably justified.

Abstract: In this paper the actuarial assessment of damages for personal injury and death is discussed in the context of South African law. The legal framework imposes a variety of calculation rules that need to be born in mind if an actuary is to produce a quality product. This framework changes with the passage of time. The purpose of the paper is to summarise the current state of affairs and highlight issues deserving of further actuarial discussion.

Abstract: This paper applies a quality framework theory to a field of actuarial practice. The paper is relevant to the professionalism of actuaries in general, and to those who assess the quantum of damages in particular. Quality framework theories propose that practitioners need to apply a range of technical and normative capabilities to provide a quality professional service. This paper suggests the various capabilities that are needed by actuaries in the field of assessment of the quantum of damages, and orders them by applying a quality framework. A methodology for practitioners to benchmark the quality of their practice is outlined. In South Africa, there is no formal curriculum, canon, or specific guidance for actuaries practising in this field. The paper therefore also contributes to the professionalisation of the field by reviewing and recording relevant literature, and provisionally filling gaps in it from personal experience of the author as practitioner in this field. The paper concludes by suggesting that this approach could also help professionalise other fields of actuarial practice.