Risk in the Macro Financial Investment Equations of Pension Funds and Life Insurance Companies

Abstract

This paper has two purposes. The first is to introduce risk into the macro investment equation of pension funds and life insurance companies and the second is to investigate whether the two moment model is sufficient to explain their investment behavior. Part I is concerned with developing a framework within which the two variables of the model are included in the investment equations of two types of securities; corporate bonds and corporate stocks. Part II deals with the hypothesis and the prior specification of the model. In Part III the regression results for life insurance companies, for noninsiired pension funds, and for state and local pension funds are introduced and analyzed. The findings show that risk is highly significant in the equations regressed. In addition, the model provides a good description of the investment behavior of the institutions investigated, and the results indicate that the two moment model is sufficient to explain their behavior. While risk has played a prime role in current portfolio selection literature, its role has been surprisingly insignificant in aggregate econometric models describing the investments of financial institutions. In most of these models, the investment macro equation is explained primarily by different rates of interest,1 with the specification that the sign of the coefficient of its own rate is positive and the signs of other rates depend on whether the type of security regressed is a substitute or a I. B. Ibrahim, Ph.D., is Assistant Professor of Business Economics and Quantitative Methods in the College of Business Administration of the University of Hawaii. This paper was submitted in March, 1973. The author is grateful to Professor Toshiyuki Otsuki for his helpful comments and suggestions. 'De Leeuw, Frank, A Model of Financial Behavior, The Brookings Quarterly Econometric Model of the United States, J. S. Duesenberry, C. Fromm, L. R. Klein, and E. Kuh (Eds.), Chicago, Rand McNally & Co., 1965, -p. 465-529. complement. It is negative if it is a substitute, and positive if it is a complement.2 This treatment, even though based on the degree of risk similarity and dis-similarity among different assets, certainly is no substitute for its explicit introduction into the investment equation. This paper has two purposes. The first is to introduce risk into the macro investment equations of pension funds and life insurance companies, and the second is to investigate whether the two moment model is sufficient to explain their investment behavior. The two moment model has recently been criticized on various grounds mainly due to the restrictive assumptions under which it is considered valid.3 2 Silber, William L., Portfolio Behavior of Financial Institutions, New York, Holt, Rinehart, & Winston, Inc., 1970, pp. 7-17. 3For a critical evaluation of the mean variance model see Samuelson. Paul A.. General Proof