Instructions to Authors for SA Actuarial Journals

Individuals or teams planning to submit papers to the SAAJ for publication are advised to read through the following documents to ensure that their drafts are consistent with SAAJ standards. For those papers accepted for publication, this would help to ensure a smoother transition to completion of the process.

Editor of SAAJ

Conrad Beyers is the editor of the SA Actuarial Journal.  Any queries may be directed to Conrad at: or by telephone at +27 822130585.

South African Actuarial Journals

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 South African Actuarial Journal 2020 – Content


 An investigation of an overlap in penalty calculations: profit commission in reinsurance treaties versus profit commission in binder agreements for underwriting managers

Author: Cornelius G Kilian

ABSTRACT: Reinsurance treaties and binder agreements regulate penalty calculations in the event the insurer
and underwriting manager is unprofitable and/or profitable. The formulae and different premium terminologies are investigated to calculate loss ratios and whether there is an overlap in sliding scale penalty calculations/formulae relevant to loss ratios of treaties and binder agreements. Treaties and binder agreements generally use sliding scale penalties to calculate reinsurance commission or sharing in the insurer’s profits by an underwriting manager and is in conflict with the Conventional Penalties Act 15 of 1962 of South Africa. The Conventional Penalties Act 15 of 1962 must guide reinsurers and insurers in their profit calculations formulae to prevent any form of sliding scale penalties relevant to loss ratios. It is therefore suggested that a standard template of profit calculations and terminologies should be used in binder agreements to prevent different calculations of loss ratios in the short term insurance landscape. This will guide the Financial Conduct Authority Services (previously the Financial Services Board) to understand loss ratios of affordable short term financial products when compared to loss ratios of other short term financial products in South Africa.

 Defining and measuring portfolio diversification

Authors: E Flint, A Seymour and F Chikurunhe

ABSTRACT: It is often said that diversification is the only ‘free lunch’ available to investors; meaning that a properly diversified portfolio reduces total risk without necessarily sacrificing expected return. However, achieving true diversification is easier said than done, especially when we do not fully know what we mean when we are talking about diversification. While the qualitative purpose of diversification is well known, a satisfactory quantitative definition of portfolio diversification remains elusive. In this research, we summarise a wide range of diversification measures, focusing our efforts on those most commonly used in practice. We categorise each measure based on which portfolio aspect it focuses on: cardinality, weights, returns, risk or higher moments. We then apply these measures to a range of South African equity indices, thus giving a diagnostic review of historical local equity diversification and, perhaps more importantly, providing a description of the investable opportunity set available to fund managers in this space. Finally, we introduce the idea of diversification profiles. These regimedependent profiles give a much richer description of portfolio diversification than their single-value counterparts and also allow one to manage diversification proactively based on one’s view of future market conditions.

 A stochastic investment model for actuarial use in South Africa

Authors: By Ş Şahin and S Levitan

ABSTRACT: In this paper, we propose a stochastic investment model for actuarial use in South Africa by modelling price inflation rates, share dividends, long-term and short-term interest rates for the period 1960–2018 and inflation-linked bonds for the period 2000–2018. Possible bi-directional relations between the economic series have been considered, the parameters and their confidence intervals have been estimated recursively to examine their stability, and the model validation has been tested. The model is designed to provide long-term forecasts that should find application in long-term modelling for institutions such as pension funds and life insurance companies in South Africa.


Sustaining the life insurance industry in the Fourth Industrial Revolution

Authors: By Lynne Molloy and Linda Ronnie

ABSTRACT: As the Fourth Industrial Revolution (4IR) continues to change the ways of doing business across industries, organisations around the world are grappling with the unprecedented challenges imposed by radical and widespread technological change. In the face of this dilemma, the South African life insurance industry has remained remarkably resilient, exhibiting very little adaptation in terms of structural, cultural, or business model innovation. However, the stable environmental conditions that once enabled this position for incumbent organisations are weakening. Transformational change, like that in the adjacent financial services industry, is imminent and adaptation on the part of incumbent insurers will be vital to sustaining relevance. This research examines the organisational beliefs and capabilities of South African insurance companies regarding the 4IR in order to gauge the current challenges within the broader industry. Semi-structured interviews were conducted with 12 senior leaders and decisionmakers from across the industry. A qualitative inductive analysis shows the inhibitors and enablers of digital innovation within the organisations. The pervasive lack of trust, agility, and urgency within the sector are cited as inhibitors of digital innovation. Enablers include a continuous learning mindset within the organisation, partnerships within the broader ecosystem, and the role of senior leaders for shaping cultural attitudes and structures. Overall, these findings show a disparity between what insurers know they must do to proactively lead change, enact digital innovation, and remain relevant, and what they are actually executing. Recommendations are provided for addressing this gap.


Comparison of numerical methods to price zero coupon bonds in a two-factor CIR model

Authors: By S Emslie & S Mataramvura

ABSTRACT: In this paper we price a zero coupon bond under a Cox–Ingersoll–Ross (CIR) two-factor model using various numerical schemes. To the best of our knowledge, a closed-form or explicit price functional is not trivial and has been less studied. The use and comparison of several numerical methods to determine the bond price is one contribution of this paper. Ordinary differential equations (ODEs),  finite difference schemes and simulation are the three classes of numerical methods considered. These are compared on the basis of computational efficiency and accuracy, with the second aim of this paper being to identify the most efficient numerical method. The numerical ODE methods used to solve the system of ODEs arising as a result of the affine structure of the CIR model are more accurate and efficient than the other classes of methods considered, with the Runge–Kutta ODE method being the most efficient. The Alternating Direction Implicit (ADI) method is the most efficient of the finite difference scheme methods considered, while the simulation methods are shown to be inefficient. Our choice of considering these methods instead of the other known and apparently new numerical methods (eg Fast Fourier Transform (FFT) method, Cosine (COS) method, etc.) is motivated by their popularity in handling interest rate instruments.


The contribution of South Africa’s insurers to systemic risk: thoughts for policymakers

Authors: By Rob Rusconi

ABSTRACT: The rationale for regulating financial markets is strong. First, these markets have a critical role to play in the well-being of economies of all sizes. Second, the consequences of failure of these markets is frequently felt well outside of the markets themselves. This regulation should be based on the foundation of a clearly-written publicly-stated set of objectives. One of these objectives ought to be the mitigation of systemic risk, that is the risk that the actions of a financial-sector entity could trigger widespread damage to large parts of the financial markets and to the real economy. Establishing and utilising an appropriate mix of regulatory methods, however, is rendered extraordinarily challenging by the intrinsic complexity, delicacy even, of these markets. This paper explores these issues, applies them to insurance markets, in general and then in South Africa, and asks whether more could be done by South Africa’s insurance regulators to mitigate the systemic risk attributable to the country’s insurers. At heart is the concern that increasingly sophisticated efforts to measure and manage entity-specific risk may have the consequence of adding materially to systemic risk.


 The effectiveness of South African defined-contribution occupational fund benefit
statements to inform and persuade: framework and initial applications

Authors: MBJ Carswell, D Ng, Z Eydatoula, SH Murray and M Curtis

ABSTRACT: Members of defined-contribution retirement funds may be able to make choices that affect their retirement outcomes. The benefit statement is considered a key resource in this process, and trustees and administrators may design these statements specifically to inform and persuade members to make appropriate choices to improve their retirement outcomes. For a statement to be theoretically effective at informing members it should be effective at communicating the inherent risks, be appropriate for the audience, have meaningful and realistic illustrations, use reasonable and consistent assumptions and show sensitivity to these assumptions, be balanced and complete, include a statement of principal assumptions and definitions of key terms and outline the options available. For a statement to be theoretically persuasive it should use emotion appropriately, identify behaviour to change, identify the member’s needs and create a link between these needs and the behaviour to change, be positively framed, personalised and appropriately timed. These characteristics can be used to develop a framework to assess the theoretical effectiveness of benefit statements. This framework was applied to a small sample of administrator benefit statements to assess their effectiveness. When member data from one fund were analysed, it was found that improving the theoretical effectiveness of the benefit statement for this fund was not sufficient to improve the contribution rate. This merits a larger scale investigation.

 Regime-based tactical allocation for equity factors and balanced portfolios

Author: E Flint and E Maré

ABSTRACT: It is now an accepted fact that the majority of financial markets worldwide are neither normal nor constant, and South Africa is no exception. One idea that can be used to understand such markets and has been gaining popularity recently is that of regimes and regime-switching models. In this research, we consider whether regimes can add value to the asset allocation process. Four methods for regime identification—economic cycle variables, fundamental valuation metrics, technical market indicators and statistical regime-switching models—are discussed and tested on two asset universes—longonly South African equity factor returns and representative balanced portfolio asset class returns. We find several promising regime indicators and use these to create two regime-based tactical allocation frameworks. Out-of-sample testing on both the equity factor and balanced asset class data shows very promising results, with both regime-based tactical strategies outperforming their respective static benchmarks on an absolute return and risk-adjusted return basis. We also turn our attention to a potentially major recent development in the local fund management space; namely, the introduction of Capped Shareholder-Weighted indices as new benchmarks. We provide comparative analysis between the capped and uncapped Shareholder-Weighted indices in terms of sector weights, stock concentration, currency exposure and factor risk contributions.


 Considering the use of an equal-weighted index as a benchmark for South African
equity investors

Authors: BH Taljaard and E Maré

ABSTRACT: We analyse and discuss the use of an equal-weighted index as an alternative to the market capitalisation weighted (cap-weighted) index as a benchmark for active equity portfolios in the South African equity market. Our findings indicate that equal-weighted portfolios are, in general, more efficient than capweighted portfolios and that random active portfolios tend to display significantly improved risk-return characteristics when using an equal-weighted index as a benchmark. We find our results are robust to transaction costs involved with rebalancing.

 Extending the normal retirement age in occupational defined contribution funds in South Africa

Authors: SE Abraham, KL Malherbe and MBJ Carswell

ABSTRACT: This paper addresses the problems of insufficient retirement savings and increasing longevity through the consideration of extending the retirement age. It is a pilot study of South African employers’ and employees’ perspectives on extending the normal retirement age in occupational retirement funds and the implications thereof. The data used for this paper were collected from two surveys conducted amongst South African employers and employees who are part of occupational retirement funds. The results indicate that most employers appear to have a positive attitude toward older employees, rating positive attributes such as reliability, experience, productivity and loyalty to the firm highly. The most significant factors in predicting whether an employee would be willing to work past the normal retirement age include employees’ expectations with respect to retirement and retirement lifestyle, current age, and
whether they believe they will accumulate sufficient savings by their company’s normal retirement age. This study provides a base on which further analysis should be performed to understand whether the occupational sector in South Africa is willing to extend the normal retirement age.

 Mortality risks, reinsurance and risk-based supervision

Author: T Mourik

ABSTRACT: Under risk-based supervision, mortality risks are generally considered proportional to the number of insured lives (N). This assumption is, however, incorrect for volatility mortality risks (this being the key justification for life insurance), as this risk is proportional to √N. The main benefits of reinsurance are consequently not properly reflected in the risk-based capital requirements under risk-based supervision Pillar 1. Similar findings apply to unexpired risks, also called ‘premium risks’, in non-life insurance. In this article, volatility risks shall therefore be thoroughly considered in the formulation and assessment of the insurer’s reinsurance policy, i.e., under risk-based supervision Pillar 2.

 A framework for simulating systemic risk and its application to the South African banking sector

Authors: NM Walters, FJC Beyers, AJ van Zyl & RJ van den Heever

ABSTRACT: We present a network-based framework for simulating systemic risk that considers shock propagation in banking systems. In particular, the framework allows the modeller to reflect a top-down framework where a shock to one bank in the system affects the solvency and liquidity position of other banks, through systemic market risks and consequential liquidity strains. We illustrate the framework with an application using South African bank balance sheet data. Spikes in simulated assessments of systemic risk agree closely with spikes in documented subjective assessments of this risk. This indicates that network models can be useful for monitoring systemic risk levels. The model results are sensitive to liquidity risk and market sentiment and therefore the related parameters are important considerations when using a network approach to systemic risk modelling.

 The Life Esidimeni arbitration and the actuarial quantification of constitutional damages

Author: GA Whittaker

ABSTRACT: In the instance of a claim for constitutional damages where an aggrieved party makes a claim against the State for damages resulting from its failure to uphold a constitutional imperative, how are such damages to be quantified? Under South African law there is no formula and extremely limited precedent outlining the calculation of constitutional damages. This paper will consider the Life Esidimeni Arbitration proceedings against the Gauteng Department of Health pursuant to the tragic mass death, torture and disappearance of mental health care users from the perspective of an actuary acting as an expert witness for the families of the deceased. There is no manual for calculating the monetary value of a life. Notwithstanding, this paper will set out the considerations made to reach monetary compensation as argued by the legal representatives of the families, as substantiated by the actuary and as eventually awarded by the Arbitrator.

 Linear predictor of the discounted renewal aggregate claims with dependent inter-occurrence times

Author: F Adékambi

ABSTRACT: In this paper we derive the first two moments and a linear predictor of the compound discounted renewal aggregate claims when taking into account dependence within the inter-occurrence times. Using specific mixtures of exponential distributions to define the dependence structure between the inter occurrence times, we compare the accuracy of the proposed linear predictor to the simulated value of that sum.

Other documents:

Editorial: Ringing the changes: Ecological economics and actuarial science
Cumulative index
Abstracts of recent postgraduate theses and dissertations at South African universities
Abstracts of articles in other South African journals
Book review

Throughput in the UCT Actuarial Science programme: a microcosm of the profession’s transformation challenge

Authors: Dave Strugnell and Shivani Ranchod

ABSTRACT: We employ survival analysis to investigate throughput rates, and certain demographic and educational factors that exert a significant influence on them, in the Actuarial Science programme at the University of Cape Town. The results contextualise the huge transformation challenge facing the profession, and also point to some of the features of the educational landscape which have the power to overcome them.


Life reinsurance, excess loss treaties, Lyapunov central limit theorem

Authors: Nick (Nikolaos) Georgiopoulos

ABSTRACT: Primary life insurers need to calculate life reinsurance recoverables for excess-of-loss life reinsurance treaties for solvency purposes as in Solvency II. However, assuming deterministic mortality, the recoverables of excess-of-loss treaties could be zero because the surviving lives are too few to trigger the excess-of-loss barrier. Resorting to simulation may be cumbersome as it may call for blending into a deterministic mortality model such as those of commercial vendors. In this paper we describe an alternative method to avoid simulation that is fast and accurate and can easily be blended into existing commercial software. The results can be used in many instances such as supervisory reporting, reinsurance pricing and risk management.


Estimating option-implied distributions in illiquid markets and implementing the Ross recovery theorem

Authors: Emlyn Flint and Eben Maré

ABSTRACT: In this research we describe how forward-looking information on the statistical properties of an asset can be extracted directly from options market data and demonstrate how this can be practically applied to portfolio management. Although the extraction of a forward-looking risk-neutral distribution is well-established in the literature, the issue of estimating distributions in an illiquid market is not. We use the deterministic SVI volatility model to estimate weekly risk-neutral distribution surfaces. The issue of calibration with sparse and noisy data is considered at length and a simple but robust fitting algorithm is proposed. We further attempt to extract real-world implied information by implementing the recovery theorem introduced by Ross (2015). Recovery is an ill-posed problem that requires careful consideration. We describe a regularisation methodology for extracting real-world implied distributions and implement this method on a history of SVI volatility surfaces. We analyse the first four moments
from the implied risk-neutral and real-world implied distributions and use them as signals within a simple tactical asset allocation framework, finding promising results.


Other documents:

Editorial: Research is a sound investment
Cumulative index
Abstracts of recent postgraduate theses and dissertations at South African universities
Abstracts of articles in other South African journals

The impact of behavioural economics and finance on retirement provision

Author: N van Zyl and DJJ van Zyl

ABSTRACT: The significant shift from defined benefit to defined contribution retirement funds in South Africa has led to many fund members bearing responsibility for a range of risks. Many of these risks, such as those related to investment, longevity and cognitive deterioration are unavoidable. Another category of risk is that related to the choices made by government, employers, trustees, advisors and/or individuals at either national, scheme or individual level. These choices may also pose a threat to a member’s financial wellbeing in retirement. Behavioural economics and finance helps to explain the choices made by these stakeholders in the retirement industry. The authors explain this concept in the context of industry stakeholders and the unique South African economic and demographic landscape, focusing on defined contribution retirement funds. Key behavioural insights applicable to the retirement industry are explored and, where practical, illustrated by stakeholder behaviour. Possible ways to harness these insights in order to improve retirement wellbeing are then discussed.


Changes in mortality of people living with HIV in South Africa and their potential implications for life assurers

Authors: ML Strydom, D Corubolo and C Nel

ABSTRACT: This research investigates the impact of improved (and improving) mortality experience in South Africa as a result of the increased (and increasing) access to antiretroviral treatment on South African life assurers, the entry-level insurance market and the wider South African economy. The research focuses on various potential impacts on the entry-level insurance market, including new business profitability, product development and pricing, market penetration and the potential for increased savings. This research has been done with the assistance of four of the main South African life offices and also draws on the new THEMBISA AIDS model on which a working paper has been produced. The research is based on the THEMBISA model in order to investigate the potential impact of alternative mortality scenarios on typical entry-level products within the industry where the scenarios have been based on actual current and proposed antiretroviral roll-out strategies by the Department of Health.  Potential improvements to profitability, premium reductions, benefit enhancements and cashback benefits are quantified using a profit test model for entry-level market  products.


A method of parameterising a feed forward multi-layered perceptron artificial neural network, with reference to South African financial markets

Authors: ML Smith, FJC Beyers and JP de Villiers

ABSTRACT: No analytic procedures currently exist for determining optimal artificial neural network structures and parameters for any given application. Traditionally, when artificial neural networks have been applied to financial modelling problems, structure and parameter choices are often made a priori without sufficient consideration of the effect of such choices. A key aim of this study is to develop a general method that could be used to construct artificial neural networks by exploring the model structure and parameter space so that informed decisions could be made relating to the model design. In this study, a formal approach is followed to determine suitable structures and parameters for a Feed Forward
Multi-layered Perceptron artificial neural network with a Resilient Propagation learning algorithm with a single hidden layer. This approach is demonstrated through the modelling of four South African economic variables, namely the average monthly returns on the money, bond and equity markets as well as monthly inflation. Artificial neural networks can be constructed on the aforementioned variables in isolation or, jointly, in an integrated model. The performance of a range of more traditional time series models is compared with that of the artificial neural network models. The results suggest that, on a statistical level, artificial neural networks perform as well as time series models at forecasting the returns for financial markets. Hybrid models, combining artificial neural networks with the time series models, are constructed, trained and tested for the money market and for the rate of inflation. They appear to add value to the time series models when forecasting inflation, but not for the money market.


International benchmarking of hospital utilisation: how does the South African private sector compare?

Authors: S Ranchod, B Childs, M Abraham and R Taylor

ABSTRACT: We benchmark the hospital-inpatient admission rates and average length of stay of the South African medical scheme population against a set of international comparators. Such a comparison is useful in developing reasonable expectations of the utilisation achievable in the private-hospital sector in South Africa, and as a means of identifying unusual characteristics of the South African environment. Such comparisons should be done on a like-for-like basis, and explicitly adjusted for differences in data definitions, patient demographics and clinical case mix. Structural differences between countries must be considered in interpreting results. We use an economic basis for determining the comparator set rather than a health-systems basis. Detailed case-mix data by country is not available so demographic and broad disease-grouping categories are used as proxies. A further limitation is that day cases are excluded. Considering two separate data sources, South Africa appears to have relatively high admission rates with low average lengths of stay. On a combined basis, the bed days used per 1 000 medical scheme beneficiaries for South Africa appears near the lower end of the spectrum, which suggests that the South African private sector is making relatively efficient use of its hospital resources.


The significance of claims fraud in microinsurance and a statistical method to channel limited fraud identification resources

Authors: PJF Agostinho and CJ Cherry

ABSTRACT: In the past decade, the topic of microinsurance has received much attention from researchers around the world as the drive to alleviate persistent global poverty intensifies. Although microinsurance is a powerful tool that can be used to assist in the fight against poverty by acting as a safety net for policyholders, the problem of claims fraud is a serious threat to its long-term sustainability. Analysis of the existing literature reveals a severe shortage of research into the problem of microinsurance claims fraud, even though we have found that it poses a greater threat in microinsurance than regular insurance. In this paper we highlight the problem of claims fraud in low-income markets and we explain how fraud has the potential to make microinsurance initiatives unsustainable. After establishing that action is needed to combat fraud in microinsurance, we briefly present a number of fraud mitigation techniques that have been successful in conventional insurance. However, certain characteristics that differentiate microinsurance from regular insurance reveal that most of these fraud combating approaches are not appropriate to microinsurance; the proportionately higher costs of identifying claims fraud relative to policy size, the lack of data and the lack of resources experienced by microinsurers render these methods impractical and unaffordable in the context of microinsurance. We proceed to demonstrate the workings of a statistical method known as Principle Component Analysis of Ridit Scores (the Pridit method), initially developed by Brockett et al. (2002) which has been shown to effectively identify fraudulent claims without the need for a training sample. The method can thus easily be applied by microinsurers to assist in the detection of claims fraud. While this method of fraud detection is not without limitations, it may provide a pragmatic and cost-effective way for microinsurers to begin tackling claims fraud. In this paper, the method is clearly explained by means of a worked example to help microinsurers implement the method at low cost.

Other documents:

Editorial: Ringing the changes: Ecological economics and actuarial science
Cumulative index
Abstracts of recent postgraduate theses and dissertations at South African universities
Abstracts of articles in other South African journals