South African Actuarial Journal Volume 10 (2010)


Generating interest-rate scenarios for fixed-income portfolio optimisation

Author(s): H Raubenheimer and MF Kruger
One of the main sources of uncertainty in the analysis of the risk and return properties of a portfolio of fixed-income securities is the stochastic evolution of the shape of the yield curve. The authors have estimated a model that fits the South African yield curve, using a Kalman filter. The model includes four latent factors and three observable macroeconomic variables (capacity utilisation, inflation and the repo rate). The goal is to capture the dynamic interactions between the macroeconomy and the yield curve in such a way that the resulting model can be used to generate interest-rate scenario trees that are suitable for fixed-income portfolio optimisation. An important input into the scenario generator is the investor’s view on the future evolution of the repo rate. In this paper, details of the model are provided and the results of the estimation and scenario generation are reported.
Keywords: Term structure; yield curve; Kalman filter; macroeconomic; scenario generation; Nelson–Siegel curve; Svensson curve

Generating interest-rate scenarios (pdf)


A stochastic-programming approach to integrated asset and liability management of insurance products with guarantees

Author(s): H Raubenheimer and MF Kruger
In recent years insurance products have become more complex by providing investors with various guarantees and bonus options. This increase in complexity has provided an impetus for the investigation into integrated asset- and liability-management frameworks that could realistically address dynamic portfolio allocation in a risk-controlled way. In this paper the authors propose a multi-stage dynamic stochastic-programming model for the integrated asset and liability management of insurance products with guarantees that minimises the down-side risk of these products. They investigate with-profit guarantee funds by including regular bonus payments while keeping the optimisation problem linear. The uncertainty is represented in terms of arbitragefree scenario trees using a four-factor yield-curve model that includes macroeconomic factors (inflation, capacity utilisation and the repo rate). They construct scenario trees with path-dependent intermediate discrete yield-curve outcomes suitable for the pricing of fixed-income securities. The main focus of the paper is the formulation and implementation of a multi-stage stochastic-programming model. The model is back-tested on real market data over a period of five years.
Keywords: Minimum guarantees; asset and liability management; stochastic programming; portfolio optimisation

A stochastic-programming approach (pdf)


A multiple Markov switching model for actuarial use in South Africa

Author(s): AJ Maitland
This paper introduces a new class of Markov switching models where switches in variables are not perfectly correlated. Maximum-likelihood estimates of the parameters are derived and shown to require only the smoothed inferences obtained from a univariate analysis of the variables. The framework is used to estimate a multiple Markov switching (MMS) model of South African financial and economic variables, which can be used for various actuarial applications, especially those involving long-term projections. Users may wish to set certain parameters in relation to future expectations rather than simply using estimates based on past data, but that process is not covered in this paper.
Keywords: Multivariate, multiple Markov switching, long-term, financial projections, actuarial, stochastic model, time-series models

A multiple Markov switching model (pdf)


Modelling the market in a risk-averse world: the case of South Africa

Author(s): RJ Thomson
In this paper, descriptive models of real returns on the South African market portfolio are developed and analysed. The ‘market portfolio’ is taken to comprise listed equity and government bonds, aggregated in proportion to their market capitalisation from time to time. The models have the attributes that, conditionally on information at the start of a year:
• the real return on the market portfolio during that year is normally distributed; and
• the market price of risk during that year is reasonably greater than zero.

For the purpose of predictive modelling, the best of the models considered was found to be a linear function of the risk-free rate. For that purpose it was decided to use ex-ante estimates of expected returns. This led to bias in the observed mean returns, which negates the rational expectations hypothesis. In the light of the literature on the subject, this is considered acceptable for these purposes.
Keywords: Market portfolio, risk aversion, South Africa, bias

Modelling the market (pdf)


Guest editorial: Some thoughts on retirement fund reform

SAAJ Volume 10 Guest editorial (pdf)

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