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 tofund 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. Keywords: Portfolio diversification; index concentration; weight-based diversification; risk-based diversification; correlation; covariance; market regimes
{"title":"Defining and measuring portfolio diversification","authors":"Emlyn Flint, A. Seymour, F. Chikurunhe","doi":"10.4314/SAAJ.V20I1.2","DOIUrl":"https://doi.org/10.4314/SAAJ.V20I1.2","url":null,"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 tofund 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. \u0000Keywords: Portfolio diversification; index concentration; weight-based diversification; risk-based diversification; correlation; covariance; market regimes","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"20 1","pages":"17-48"},"PeriodicalIF":0.2,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43176542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
{"title":"A stochastic investment model for actuarial use in South Africa","authors":"Y. Şahin, S. Levitan","doi":"10.4314/SAAJ.V20I1.3","DOIUrl":"https://doi.org/10.4314/SAAJ.V20I1.3","url":null,"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","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"20 1","pages":"49-79"},"PeriodicalIF":0.2,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44107937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"An investigation of an overlap in penalty calculations: profit commission in reinsurance treaties versus profit commission in binder agreements for underwriting managers","authors":"C. Kilian","doi":"10.4314/SAAJ.V20I1.1","DOIUrl":"https://doi.org/10.4314/SAAJ.V20I1.1","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"20 1","pages":"1-16"},"PeriodicalIF":0.2,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47852751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Comparison of numerical methods to price zero coupon bonds in a two-factor CIR model","authors":"S. Emslie, S. Mataramvura","doi":"10.4314/SAAJ.V20I1.5","DOIUrl":"https://doi.org/10.4314/SAAJ.V20I1.5","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"20 1","pages":"109-147"},"PeriodicalIF":0.2,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48929700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"The contribution of South Africa’s insurers to systemic risk: thoughts for policymakers","authors":"R. Rusconi","doi":"10.4314/SAAJ.V20I1.6","DOIUrl":"https://doi.org/10.4314/SAAJ.V20I1.6","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"20 1","pages":"149-210"},"PeriodicalIF":0.2,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49055624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Abstracts of recent postgraduate theses and dissertations at South African universities","authors":"Conrad Beyers","doi":"10.4314/SAAJ.V20I1","DOIUrl":"https://doi.org/10.4314/SAAJ.V20I1","url":null,"abstract":"","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"20 1","pages":"211-217"},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.Keywords: Benchmark; risk; capitalisation weight; equal weight; efficiency; rebalancing; costs; returns
{"title":"Considering the use of an equal-weighted index as a benchmark for South African equity investors","authors":"BH Taljaard, E. Maré","doi":"10.4314/saaj.v19i1.3","DOIUrl":"https://doi.org/10.4314/saaj.v19i1.3","url":null,"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.Keywords: Benchmark; risk; capitalisation weight; equal weight; efficiency; rebalancing; costs; returns","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"19 1","pages":"53-70"},"PeriodicalIF":0.2,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47161782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mbj Carswell, D. Ng, Z. Eydatoula, Sheena Murray, M. Curtis
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 nvestigation.Keyword: Benefit statements; defined-contribution; persuasive communication; informative communication
{"title":"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, Sheena Murray, M. Curtis","doi":"10.4314/saaj.v19i1.1","DOIUrl":"https://doi.org/10.4314/saaj.v19i1.1","url":null,"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 nvestigation.Keyword: Benefit statements; defined-contribution; persuasive communication; informative communication","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"19 1","pages":"1-25"},"PeriodicalIF":0.2,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47765496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Book Title: Finance, Society and Sustainability: How to Make the Financial System Work for the Economy, People and PlanetBook Author: N. SilverPalgrave Macmillan, London (2017)
{"title":"Book Review: Finance, Society and Sustainability: How to Make the Financial System Work for the Economy, People and Planet","authors":"R. Thomson","doi":"10.4314/SAAJ.V18I1.D","DOIUrl":"https://doi.org/10.4314/SAAJ.V18I1.D","url":null,"abstract":"Book Title: Finance, Society and Sustainability: How to Make the Financial System Work for the Economy, People and PlanetBook Author: N. SilverPalgrave Macmillan, London (2017)","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46356925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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