Mean-Variance Utility Functions and the Investment Behaviour of Canadian Life Insurance Companies

Abstract

In recent years, considerable effort has been directed toward establishing the nature of the investment behaviour of life insurance companies. In this dissertation an extended portfolio analysis model was developed for the simultaneous determination of the efficient composition of insurance and investment activities of a life insurance company. This was done within a model that takes advantage of the existing finance foundations and the concepts and techniques of modern demand system analysis. Unlike current models which used quadratic programming techniques and are interested in the construction of efficient sets, we have used a utility maximization approach. A two parameter portfolio model was constructed utilizing elements of utility theory and of the theory of insurance. The model provided us with the proportion of assets held in the balance sheet as well as which liabilities are used to raise the necessary capital. The model developed has sufficient empirical content to yield hypotheses about life insurance portfolio behaviour and thus was tested using appropriate econometric techniques. A comparative static analysis yielded elasticities of substitution between financial assets and liabilities. The estimation of these elasticities in the context of a flexible functional form model, forms a central part of this dissertation. More specifically, by utilizing a mean-variance portfolio framework and a general Box-Cox utility function we were able to model the demand for assets and liabilities. by an insurance company. On empirical grounds we found that, in general, the square root quadratic utility function best fits the data. We also tried to evaluate the square root quadratic approximation by showing that, broadly speaking, it yields signs for elasticities of substitution which are consistant with the theory. A by-product of the model developed is the ability to compare stock and mutual life insurance companies. The common belief that mutual companies follow a riskier path in the way they conduct their business was supported by the results in this study. The results obtained from the study are-of significant importance since life insurance companies have substantial obligations to millions of households in the economy. Furthermore, despite the extraordinary decline in the importance of the life insurance industry in the bond and mortgage markets during the sixties and the seventies, the industry is still a major supplier of funds to those markets.