The optimal growth portfolio as pricing portfolio for dynamically traded assets

This thesis addresses the problem of valuing assets which can be traded dynamically over time. The problem is addressed in both an "arbitrage" framework and in a standard dynamic equilibrium framework. The principal result of the thesis is the identification of a compact and intuitively rich representation of equilibrium asset prices for the dynamic setting. Specifically, it is shown that the optimal growth portfolio acts a "pricing portfolio" for dynamically traded assets, with this term justified by the results: (1) the expected return of any asset is equal to the risk free rate plus the asset's covariance with the optimal growth portfolio and (2) the price of any derivative asset is equal to the expected net present value of its cashflows when the return of the optimal growth portfolio is used as discount rate.; A second important result of the thesis is the identification of the sources of uncertainty which impact the cashflows of the traded securities or which affect the form of individuals' possibly state dependent preferences as the basic determinants of security price changes over time. It is shown that there must be, at a minimum, as many of these "fundamental risks" as there are non-redundant securities, and that in general individuals will choose their investment portfolios to track each such risk. Together these results imply that (1) the distribution of security returns must be a non-stationary function of the numerous "fundamental risks" and (2) separation based portfolio choice and asset pricing results cannot have content in the dynamic setting. When combined with the optimal growth portfolio pricing result, the fundamental risk basis of individuals' portfolio demands makes possible a direct comparison of the portfolio choice and asset pricing results of the single period and dynamic settings. This comparison shows that although the investors' demands for securities as hedges against changes in the fundamental risks cause the market portfolio to differ from the optimal growth portfolio in the dynamic setting, the "dynamic efficiency" of the optimal growth portfolio demonstrates an important parallel between the results presented here and the CAPM's result for the single period setting.