This paper analyzes the effect of uncertainty about the mean return on the risky asset on the portfolio decisions of an investor who has a long investment horizon. Building on the earlier work of Detemple (1986), Dothan and Feldman (1986), and Gennotte (1986), it is shown that the possibility of future learning about the mean return on the risky asset induces the investor to take a larger or smaller position in the risky asset than she would if there were no learning, the direction of the effect depending on whether the investor is more or less risk tolerant than the logarithmic investor whose portfolio decisions are unaffected by the possibility of future learning. Numerical calculations show that uncertainty about the mean return on the market portfolio has a significant effect on the portfolio decision of an investor with a 20 year horizon if her assessment of the market risk premium is based solely on the Ibbotson and Sinquefield (1995) data.

M. J. Brennan, The Optimal Number of Securities in a Risky Asset Portfolio When There are Fixed Costs of Transacting: Theory and Some Empirical Results, The Journal of Financial and Quantitative Analysis, Vol. 10, No. 3 (Sep., 1975), pp. 483-496

The Capital Asset Pricing Model of Sharpe [10, 1964], Lintner [8, 1965], and Mossin [9, 1966] showed how it was possible to derive under fairly stringent assumptions the conditions for equilibrium in a market for risky assets. Recent work has been directed at relaxing these assumptions, and this paper extends the progress made thus far by deriving some properties of capital market equilibrium when investors are faced with divergent borrowing and lending rates and when these rates may vary among investors.

The form of the Pareto optimal general insurance contract has been investigated by Borch [5], Arrow [3], and Raviv [16]. This paper extends their work to the consideration of the optimal investment portfolio insurance contract. This is a contract whose payoff depends upon the investment performance of some specified portfolio of common stocks. Portfolio insurance differs from general insurance in two important ways. First, investment portfolio insurance lacks the property of stochastic independence between losses on different contracts which is characteristic of general insurance, and this has led some actuaries to question whether portfolio insurance contracts should be sold in view of the risks they pose for the solvency of insurance companies. Recent developments in the theory of option pricing suggest, however, that under certain assumptions an insurance company will be able to eliminate the risks associated with portfolio insurance contracts by following an appropriately defined investment strategy. Secondly, there exists a market for the pricing of investment risks, the securities market; and, under appropriate assumptions, the equilibrium price of portfolio insurance contracts may be determined without specification of the preferences of insurance companies. This permits consideration of insurance company preference functions to be dispensed with, in marked contrast to the earlier literature concerned with general insurance, which treats insurance company preferences symmetrically with those of the insurance purchaser. In addition, since the characteristics of the insured portfolio are known to the insurer, and the performance of the portfolio is beyond the control of the insured, portfolio insurance is not prone to the problems of adverse selection and moral hazard which are liable to arise in general insurance.

An important aggregation problem is the derivation of equilibrium security prices which are independent of the allocation of initial wealth among investors. The problem is of interest because, if investors are conceived as being endowed with initial holdings of securities, it is clear that the initial wealth allocation which depends on security prices is endogenous to the model. Although he addresses a differently defined objective, Rubinstein [8] has shown that sufficient conditions for the solution of the problem described above are conditions that permit construction of “composite” (representative) investors whose resources, beliefs, and tastes depend on the exogenous specifications of the economy (viz., the beliefs and tastes of all investors and production conditions) but not on the initial allocation of securities.