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South African Actuarial Journal Volume 11 (2011)

 

The arbitrage-free equilibrium pricing of liabilities in an incomplete market: Application to a South African retirement fund

Author(s): RJ Thomson
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 In an unpublished application of the pricing method it was found that, except for quite short-term liabilities, the computational demands of the pricing algorithm became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.
Keywords: Market value of liabilities; dynamic mean–variance hedging; equilibrium market models; incomplete markets

The arbitrage-free equilibrium pricing (pdf)

 

The capital-asset pricing model: the case of South Africa

Author(s): TL Reddy and RJ Thomson
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.
Keywords: Capital-asset pricing model; beta; JSE Securities Exchange; excess return

The capital-asset pricing model (pdf)

 

Promoting quality in the actuarial assessment of quantum of
damages in South Africa

Author(s): MW Lowther
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.
Keywords: Professionalism; professionalisation; professional practice; actuarial quality framework; assessment of quantum of damages; loss of support; loss of earnings

Promoting quality in the actuarial assessment (pdf)

 

Damages for personal injury and death: legal aspects relevant to actuarial assessments

Author(s): RJ Koch
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.
Keywords: Quantum; damages; loss; support; breadwinner; dependant; earnings; claimant; defendant; differencing; capitalisation; contingencies; accelerated benefits; inheritance; apportionment; two-parts-one-part; MVA; RAF; COID

Damages for personal injury and death.pdf

 

Editorial: Long run se voet: debunking the mantra of the equity cult

SAAJ Volume 11 Editorial (pdf)

The views and opinions expressed in this journal are, unless otherwise stated, those of the authors. Editorial opinion or comment is, unless otherwise stated, that of the Editor and publication thereof does not indicate the agreement of the Actuarial Society of South Africa.

Actuarial Society of South Africa
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ISSN-8: 1680-2179
ISSN-13: 977-1680-2170-02